Tootfinder

Reconstructing Laurent expansion of rational functions using p-adic numbers
Tianya Xia, Li Lin Yang
https://arxiv.org/abs/2506.08452 https://

Reconstructing Laurent expansion of rational functions using p-adic numbers
We propose a novel method for reconstructing Laurent expansion of rational functions using $p$-adic numbers. By evaluating the rational functions in $p$-adic fields rather than finite fields, it is possible to probe the expansion coefficients simultaneously, enabling their reconstruction from a single set of evaluations. Compared with the reconstruction of the full expression, constructing the Laurent expansion to the first few orders significantly reduces the required computational resources. …

Induced rational exponents and bipartite subgraphs in $K_{s, s}$-free graphs
Zichao Dong, Jun Gao, Ruonan Li, Hong Liu
https://arxiv.org/abs/2506.09020 htt…

Induced rational exponents and bipartite subgraphs in $K_{s, s}$-free graphs
In this paper, we study a general phenomenon that many extremal results for bipartite graphs can be transferred to the induced setting when the host graph is $K_{s, s}$-free. As manifestations of this phenomenon, we prove that every rational $\frac{a}{b} \in (1, 2), \, a, b \in \mathbb{N}_+$, can be achieved as Turán exponent of a family of at most $2^a$ induced forbidden bipartite graphs, extending a result of Bukh and Conlon [JEMS 2018]. Our forbidden family is a subfamily of theirs which is…

Maximal minors of $1$-generic matrices have rational singularities
Trung Chau, Manoj Kummini
https://arxiv.org/abs/2506.08385 https://

Maximal minors of $1$-generic matrices have rational singularities
We show that the quotient ring by the ideal of maximal minors of a $1$-generic matrix has rational singularities. This answers a conjecture of Eisenbud (1988) that such rings are normal, and generalizes a result of Conca, Mostafazadehfard, Singh and Varbaro (2018) that generic Hankel determinantal rings have rational singularities in characteristic zero.

Periodic curves for general endomorphisms of $\mathbb C\mathbb P^1\times \mathbb C\mathbb P^1$
Fedor Pakovich
https://arxiv.org/abs/2506.09948 https://

Periodic curves for general endomorphisms of $\mathbb C\mathbb P^1\times \mathbb C\mathbb P^1$
We show that for a general rational function $A$ of degree $m \geq 2$, any decomposition of its iterate $A^{\circ n}$, $n \geq 1$, into a composition of indecomposable rational functions is equivalent to the decomposition $A^{\circ n}$ itself. As an application, we prove that if $(A_1, A_2)$ is a general pair of rational functions, then the endomorphism of $\mathbb C\mathbb P^1 \times \mathbb C\mathbb P^1$ given by $(z_1, z_2) \mapsto (A_1(z_1), A_2(z_2))$ admits a periodic curve that is neithe…

For some reason, this does not strike as a rational act by ICE. Who do they think are responsible for getting food from the farm to the markets? (Critiquing on woke values is pointless, so I'm appealing to the self interest of those who think food comes from the supermarket)

ICE agents chase after farmworkers as they flee fields during latest raid in Ventura County | abc7.com
Immigration%20and%20Customs%20Enforcement%20(ICE)%20targeted%20workers%20on%20produce%20farms%20in%20Ventura%20County%20Tuesday%20morning%20in%20one%20of%20the%20latest%20raids.

For some reason, this does not strike as a rational act by ICE. Who do they think are responsible for getting food from the farm to the markets? (Critiquing on woke values is pointless, so I'm appealing to the self interest of those who think food comes from the supermarket)

ICE agents chase after farmworkers as they flee fields during latest raid in Ventura County | abc7.com
Immigration%20and%20Customs%20Enforcement%20(ICE)%20targeted%20workers%20on%20produce%20farms%20in%20Ventura%20County%20Tuesday%20morning%20in%20one%20of%20the%20latest%20raids.

Maximal curves with respect to quadratic extensions over finite fields
Yves Aubry (IMATH, I2M, UTLN), Fabien Herbaut (UCA INSPE, UniCA, IMATH), Julien Monaldi (IMATH)
https://arxiv.org/abs/2506.08603

Maximal curves with respect to quadratic extensions over finite fields
We propose a detailed study of a canonical bound which relates the numbers of rational points of a curve over a finite field with that over its quadratic extension. Alternative proofs which relate to the variance enable to complete the inequality in a symmetrical way and to obtain optimal refinements. We focus on the curves reaching the bound, which we call Diophantinemaximal curves. We provide different characterizations and stress natural links with the curves which attain the Ihara bound. As…

Fast Ramanujan-type Series for Logarithms. Part I
Jorge Zuniga
https://arxiv.org/abs/2506.08245 https://arxiv.org/pdf/2506.08245

Fast Ramanujan-type Series for Logarithms. Part I
This report introduces new series and variations of some hypergeometric type identities for fast computing of logarithms $\log\,p$ for small positive integers $p$. These series were found using Wilf Zeilberger (WZ) method and/or integer detection algorithms (LLL) providing highly efficient linearly convergent rational approximants for these constants. Some of the new identities are of $_4F_3$ type, but higher ones are found as well and hypergeometric series for log p, with variable p, have been…

This https://arxiv.org/abs/2405.02430 has been replaced.
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How to generate all possible rational Wilf-Zeilberger forms?
Wilf-Zeilberger pairs are fundamental in the algorithmic theory of Wilf and Zeilberger for computer-generated proofs of combinatorial identities. Wilf-Zeilberger forms are their high-dimensional generalizations, which can be used for proving and discovering convergence acceleration formulas. This paper presents a structural description of all possible rational such forms, which can be viewed as an additive analog of the classical Ore-Sato theorem. Based on this analog, we show a structural deco…

Rational Superautotrophic Diplomacy (SupraAD); A Conceptual Framework for Alignment Based on Interdisciplinary Findings on the Fundamentals of Cognition
Andrea Morris
https://arxiv.org/abs/2506.05389

Rational Superautotrophic Diplomacy (SupraAD); A Conceptual Framework for Alignment Based on Interdisciplinary Findings on the Fundamentals of Cognition
Populating our world with hyperintelligent machines obliges us to examine cognitive behaviors observed across domains that suggest autonomy may be a fundamental property of cognitive systems, and while not inherently adversarial, it inherently resists containment and control. If this principle holds, AI safety and alignment efforts must transition to mutualistic negotiation and reciprocal incentive structures, abandoning methods that assume we can contain and control an advanced artificial gene…

This https://arxiv.org/abs/2112.12859 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Countable, Dense, Dedekind-Complete Subset of $\mathbb{R}$ Constructed by Extending $\mathbb{Q}$ via Simultaneous Marking of Closed Intervals with Rational Endpoints
This article explores the model-dependent nature of set cardinality, emphasizing that cardinality is not absolute but varies across different axiomatic frameworks. Although Cantor's diagonal argument shows the real numbers are non-denumerable within ZF (Zermelo-Fraenkel set theory), the precise cardinality of the continuum remains unsettled and depends critically on model assumptions. For instance, under Gödel's inner-model axiom V=Ultimate L, the Continuum Hypothesis (CH) holds, whereas Marti…

Generic orbits, normal bases, and generation degree for fields of rational invariants
Ben Blum-Smith, Harm Derksen
https://arxiv.org/abs/2506.05650 https:/…

Generic orbits, normal bases, and generation degree for fields of rational invariants
For a linear representation of a finite group in coprime characteristic, we bound the degrees of the invariant polynomials needed to generate the field of rational invariants as a field, in terms of the degrees of the polynomials needed to span the field of rational functions as a vector space over the invariant field. This provides a far-reaching generalization of a recent result of Edidin and Katz.

This https://arxiv.org/abs/2504.08472 has been replaced.
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Simultaneous Rational Number Codes: Decoding Beyond Half the Minimum Distance with Multiplicities and Bad Primes
In this paper, we extend the work of (Abbondati et al., 2024) on decoding simultaneous rational number codes by addressing two important scenarios: multiplicities and the presence of bad primes (divisors of denominators). First, we generalize previous results to multiplicity rational codes by considering modular reductions with respect to prime power moduli. Then, using hybrid analysis techniques, we extend our approach to vectors of fractions that may present bad primes. Our contributions incl…

Rational and non-rational two-dimensional conformal field theories arising from lattices
Maria Stella Adamo, Luca Giorgetti, Yoh Tanimoto
https://arxiv.org/abs/2506.01008

Rational and non-rational two-dimensional conformal field theories arising from lattices
For a (finite-dimensional) real Hilbert space $\mathfrak h$ and an orthogonal projection $p$, we consider the associated Heisenberg Lie algebra and the two-dimensional Heisenberg conformal net. Given an even lattice $Q$ in $\mathfrak h$ with respect to the indefinite bilinear form on $\mathfrak h$ defined by $p$, we construct a two-dimensional conformal net ${\mathcal A}_Q$ extending the Heisenberg conformal net. Moreover, with a certain discreteness assumption on the spectrum of the extension,…

Low degree subvarieties of universal hypersurfaces
Yifeng Huang, Borys Kadets, Olivier Martin
https://arxiv.org/abs/2506.08848 https://

Low degree subvarieties of universal hypersurfaces
We study irreducible subvarieties $Z$ of the universal hypersurface $\mathcal{X}/B$ of degree $d$ and dimension $n$. We prove that when $d$ is sufficiently large, degree $kd$ subvarieties $Z$ which dominate $B$ come from intersection with a family of degree $k$ projective varieties parametrized by $B$. This answers a question raised independently by Farb and Ma. Our main tools consist of a Grassmannian technique due to Riedl and Yang, a theorem of Mumford-Roitman on rational equivalence of zero…

Groups admitting Wirtinger presentations and Gromov hyperbolic groups
Toshiyuki Akita
https://arxiv.org/abs/2506.07143 https://arxiv.…

Groups admitting Wirtinger presentations and Gromov hyperbolic groups
Twisted Wirtinger presentations are generalizations of the classical Wirtinger presentations of knot and link groups. In this paper, we prove that if a finitely generated group admitting a twisted Wirtinger presentation is Gromov hyperbolic, then its second rational homology group vanishes. Moreover, if the group is torsion-free, then its second integral homology group also vanishes.

Robust predicate and function computation in continuous chemical reaction networks
Kim Calabrese, David Doty, Mina Latifi
https://arxiv.org/abs/2506.06590 …

Robust predicate and function computation in continuous chemical reaction networks
We initiate the study of rate-constant-independent computation of Boolean predicates and numerical functions in the continuous model of chemical reaction networks (CRNs), which model the amount of a chemical species as a nonnegative, real-valued *concentration*. Real-valued numerical functions have previously been studied, finding that exactly the continuous, piecewise rational linear functions $f: \mathbb{R}_{> 0}^k \to \mathbb{R}_{> 0}$ can be computed *stably*, a.k.a., *rate-independently*, …

This https://arxiv.org/abs/2409.01198 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF Rational Linkages
This study presents a set of algorithms that deal with trajectory planning of rational single-loop mechanisms with one degree of freedom (DoF). Benefiting from a dual quaternion representation of a rational motion, a formula for direct (forward) kinematics, a numerical inverse kinematics algorithm, and the generation of a driving-joint trajectory are provided. A novel approach using the Gauss-Newton search for the one-parameter inverse kinematics problem is presented. Additionally, a method for…

Also solange Aktienindizes sowas wie „psychologisch wichtige“ Marken kennen, kann mir keiner was vom rational handelnden homo oeconomicus erzählen.

Multiple rational normal forms in Lie theory
Dmitriy Voloshyn
https://arxiv.org/abs/2506.01530 https://arxiv.org/pdf/2506.01530

Multiple rational normal forms in Lie theory
We study the decomposition of a generic element $g \in G$ of a connected reductive complex algebraic group $G$ in the form $g = N(g) B(g) \bar{u} N(g)^{-1}$ where $N: G \dashrightarrow \mathcal{N}_-$ and $B : G \dashrightarrow \mathcal{B}_+$ are rational maps onto a unipotent subgroup $\mathcal{N}_-$ and a Borel subgroup $\mathcal{B}_+$ opposite to $\mathcal{N}_-$, and $\bar{u}$ is a representative of a Weyl group element $u$. We introduce a class of rational Weyl group elements that give rise …

Irregular traces of multiple SLE(0) systems with multiple marked points
Jiaxin Zhang
https://arxiv.org/abs/2506.07513 https://arxiv.o…

Irregular traces of multiple SLE(0) systems with multiple marked points
In this supplementary note, we study the traces of multiple SLE(0) systems with two or more additional marked points. For general chordal configurations, the traces correspond to the real locus of real rational functions; in the radial case, they correspond to the horizontal trajectories of residue-free quadratic differentials. In both settings, we establish the regularity of the trajectories near singularities: no spiraling occurs, and no two trajectories asymptotically converge to the same …

A modern perspective on rational homotopy theory
Eleftherios Chatzitheodoridis
https://arxiv.org/abs/2505.23322 https://arxiv.org/pdf…

A modern perspective on rational homotopy theory
In Quillen's paper on rational homotopy theory, the category of 1-reduced simplicial sets is endowed with a family of model structures, the most prominent of which is the one whose weak equivalences are the rational homotopy equivalences. In this paper, we give a modern approach to this family of model structures.

This https://arxiv.org/abs/2505.23436 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csAI_…

Emergent Risk Awareness in Rational Agents under Resource Constraints
Advanced reasoning models with agentic capabilities (AI agents) are deployed to interact with humans and to solve sequential decision-making problems under (approximate) utility functions and internal models. When such problems have resource or failure constraints where action sequences may be forcibly terminated once resources are exhausted, agents face implicit trade-offs that reshape their utility-driven (rational) behaviour. Additionally, since these agents are typically commissioned by a h…

This https://arxiv.org/abs/2504.11666 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A note on the second supplementary law of rational power residue symbols
As a natural generalization of the Legendre symbol, the $q$-th power residue symbol $(a/p)_q$ is defined for primes $p$ and $q$ with $p\equiv 1 \bmod q$. In this paper, we generalize the second supplementary law by providing an explicit condition for $(q/p)_q = 1$, when $p$ has a special form $p = \sum_{i=0}^{q-1} m^i n^{q-1-i}$. This condition is expressed in terms of the polylogarithm $\mathrm{Li}_{1-q}(x)$ of negative index. Our proof relies on an argument similar to Lemmermeyer's proof of E…

Large Berry curvature effects induced by extended nodal structures: Rational design strategy and high-throughput materials predictions
Wencheng Wang, Minxue Yang, Wei Chen, Xiangang Wan, Feng Tang
https://arxiv.org/abs/2506.03871

Large Berry curvature effects induced by extended nodal structures: Rational design strategy and high-throughput materials predictions
Berry curvature can drastically modify the electron dynamics, thereby offering an effective pathway for electron manipulation and novel device applications. Compared to zero-dimensional nodal points in Weyl/Dirac semimetals, higher-dimensional extended nodal structures, such as nodal lines and nodal surfaces, are more likely to intersect the Fermi surface, leading to large Berry curvature effects without fine-tuning the chemical potential. In this work, we propose a strategy that utilizes strai…

CORA: Coalitional Rational Advantage Decomposition for Multi-Agent Policy Gradients
Mengda Ji, Genjiu Xu, Liying Wang
https://arxiv.org/abs/2506.04265 http…

CORA: Coalitional Rational Advantage Decomposition for Multi-Agent Policy Gradients
This work focuses on the credit assignment problem in cooperative multi-agent reinforcement learning (MARL). Sharing the global advantage among agents often leads to suboptimal policy updates as it fails to account for the distinct contributions of agents. Although numerous methods consider global or individual contributions for credit assignment, a detailed analysis at the coalition level remains lacking in many approaches. This work analyzes the over-updating problem during multi-agent policy…

This https://arxiv.org/abs/2412.03290 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Holographic reconstruction for AdS Wilson line networks and scalar Witten diagrams
We find a holographic reconstruction formula for gravitational Wilson line network operators in AdS$_2$ evaluated between Ishibashi states of the algebra $sl(2,\mathbb{R})$. It is given in integral form where the integrand is the global conformal block multiplied by a smearing function which is the product of the scalar bulk-to-boundary propagators. The integral can be explicitly calculated as multidimensional series of which arguments are rational functions of endpoint coordinates. In the case…

My colleague had a question about rational functions that needed a little algebra to answer, leading me to update my supplemental course notes on abstract algebra (where I've used the Beachy/Blair textbook). A main goal of the notes is to stake out my position on the notation for rngs vs. rings.
https://use…

This https://arxiv.org/abs/1908.03249 has been replaced.
link: https://scholar.google.com/scholar?q=a

Pairwise Rational Points on a Parabola
This paper presents a solution to the following open problem in Number Theory and Geometry: How many points can you find on the (half) parabola $y=x^2$, $x>0$, so that the distance between any pair of them is rational? This problem sounds like a geometry problem, but it is likely to require techniques in number theory. That's because, to determine if the distance between (a,b) and (s,t) is rational, you need to test whether $(a-s)^2$ + $(b-t)^2$ is the square of a rational number...and such que…

Morita equivalence classes for crossed product of rational rotation algebras
Sayan Chakraborty, Pratik Kumar Kundu
https://arxiv.org/abs/2505.19869 https:/…

Morita equivalence classes for crossed product of rational rotation algebras
We study the Morita equivalence classes of crossed products of rotation algebras $A_θ$, where $θ$ is a rational number, by finite and infinite cyclic subgroups of $\mathrm{SL}(2, \mathbb{Z})$. We show that for any such subgroup $F$, the crossed products $A_θ\rtimes F$ and $A_{θ'} \rtimes F$ are strongly Morita equivalent, where both $θ$ and $θ'$ are rational. Combined with previous results for irrational values of $θ$, our result provides a complete classification of the crossed products…

This https://arxiv.org/abs/2502.03415 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Cycles on abelian 2n-folds of Weil type from secant sheaves on abelian n-folds
A. Weil identified a 2-dimensional space of rational classes of Hodge type (n,n) in the middle cohomology of every 2n-dimensional abelian variety with a suitable complex multiplication by an imaginary quadratic number field. These abelian varieties are said to be of Weil type and these Hodge classes are known as Weil classes. We prove that the Weil classes are algebraic for all abelian sixfold of Weil type of discriminant -1, for all imaginary quadratic number fields. The algebraicity of the We…

This https://arxiv.org/abs/2401.13577 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Three-Torsion Subgroups and Wild Conductor Exponents of Plane Quartics
In this paper we give an algorithm to find the 3-torsion subgroup of the Jacobian of a smooth plane quartic curve with a marked rational point. We describe $3-$torsion points in terms of cubics which triply intersect the curve, and use this to define a system of equations whose solution set corresponds to the coefficients of these cubics. We compute the points of this zero-dimensional, degree $728$ scheme first by approximation, using homotopy continuation and Newton-Raphson, and then using con…

Permutations with a fixed number of 321 patterns
Michael Waite
https://arxiv.org/abs/2506.05712 https://arxiv.org/pdf/2506.05712

Permutations with a fixed number of 321 patterns
We bound the number of permutations with a fixed number $r$ of $321$ patterns by a constant times the number of permutations which avoid $321$. We use this to show that the ordinary generating function for permutations with $r$ copies of $321$ patterns is not rational.

This https://arxiv.org/abs/2504.08648 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Rational constitutive law for the viscous stress tensor in incompressible two-phase flows: Derivation and tests against a 3D benchmark experiment
We analyze the representation of viscous stresses in the one-fluid formulation of the two-phase Navier-Stokes equations, the model on which all computational approaches making use of a fixed mesh to discretize the flow field are grounded. Recognizing that the Navier-Stokes-like equations that are actually solved in these approaches imply a spatial filtering, we show by considering a specific two-dimensional flow configuration that the proper representation of the viscous stress tensor requires …

The Free Functional Calculus in General
Julian Bushelli
https://arxiv.org/abs/2506.00170 https://arxiv.org/pdf/2506.00170

The Free Functional Calculus in General
The classical theory of free analysis generalizes the noncommutative (nc) polynomials and rational functions, easily providing such results as an nc analogue of the Jacobian conjecture. However, the classical theory misses out on important functions, such as the Schur complement. This paper presents a generalization of free functions, viewing them as a natural categorial structure: functors between functor categories that commute with natural transformation. We study this construction on genera…

Differential Spectrum and Boomerang Spectrum of Some Power Mapping
Yuehui Cui, Jinquan Luo
https://arxiv.org/abs/2506.05738 https://a…

Differential Spectrum and Boomerang Spectrum of Some Power Mapping
Let $f(x)=x^{s(p^m-1)}$ be a power mapping over $\mathbb{F}_{p^n}$, where $n=2m$ and $\gcd(s,p^m+1)=t$. In \cite{kpm-1}, Hu et al. determined the differential spectrum and boomerang spectrum of the power function $f$, where $t=1$. So what happens if $t\geq1$? In this paper, we extend the result of \cite{kpm-1} from $t=1$ to general case. We use a different method than in \cite{kpm-1} to determine the differential spectrum and boomerang spectrum of $f$ by studying the number of rational points o…

This https://arxiv.org/abs/2310.02204 has been replaced.
link: https://scholar.google.com/scholar?q=a

Determinisation and Unambiguisation of Polynomially-Ambiguous Rational Weighted Automata
We study the determinisation and unambiguisation problems of weighted automata over the rational field: Given a weighted automaton, can we determine whether there exists an equivalent deterministic, respectively unambiguous, weighted automaton? Recent results by Bell and Smertnig show that the problem is decidable, however they do not provide any complexity bounds. We show that both problems are in PSPACE for polynomially-ambiguous weighted automata.

This https://arxiv.org/abs/2504.21726 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Notes sur l'application d'Albanese pour les zéro-cycles
For a smooth projective variety X over an arbitrary field k, we discuss the surjectivity of the Albanese map from the Chow group of zero-cycles of degree zero on X to the group of rational points of the Albanese variety of X. Over arithmetic fields, we use Severi-Brauer fibrations to produce examples where the map is not surjective. For varieties X over the complex field, we discuss the question after extension of the complex field to function fields of varieties. This is related to C. Voisin's…

Tensor-based multivariate function approximation: methods benchmarking and comparison
Athanasios C. Antoulas, Ion Victor Gosea, Charles Poussot-Vassal, Pierre Vuillemin
https://arxiv.org/abs/2506.04791

Tensor-based multivariate function approximation: methods benchmarking and comparison
In this note, we evaluate the performances, the features and the user-experience of some methods (and their implementations) designed for tensor- (or data-) based multivariate function construction and approximation. To this aim, a collection of multivariate functions extracted from contributive works coming from different communities, is suggested. First, these functions with varying complexity (e.g. number and degree of the variables) and nature (e.g. rational, irrational, differentiable or n…

The Multivariate Herglotz-Nevanlinna Class: Superresolution
Mainak Bhowmik, Mihai Putinar
https://arxiv.org/abs/2505.24425 https://ar…

The Multivariate Herglotz-Nevanlinna Class: Superresolution
Unique solutions of bounded, or equivalently, non-negative real part, holomorphic interpolation in several complex variables with finite prescribed data are very rare, with rational inner functions in a polydisk as the best understood examples. We analyze the continuity of global solutions as functions of the finite interpolation data in neighborhoods of elements distinguished by this uniqueness property. Our study covers rational inner functions in the polydisk and automorphisms of the Euclide…

Cosmetic surgeries on knots in homology spheres and the Casson--Walker invariant
Kazuhiro Ichihara, In Dae Jong
https://arxiv.org/abs/2506.02682 https://…

Cosmetic surgeries on knots in homology spheres and the Casson--Walker invariant
We study cosmetic surgeries on a knot in a homology sphere. Several constraints on knots and surgery slopes to admit such surgeries are given. Our main ingredient is the rational surgery formula of the Casson--Walker invariant for 2-component links in the 3-sphere.

💯💯💯
"If a billionaire bought one of your local haunts, renamed it, humiliated the employees, brought back many of the people who’d been banned for harassing other regulars, eliminated basic rules of decency, started having town halls with Republicans and a leader of the #AfD, taking your business elsewhere would be perfectly rational."
#

This https://arxiv.org/abs/2505.21477 has been replaced.
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Variétés réelles connexes non stablement rationnelles
Let $R$ be the field of real Puiseux series. It is a real closed field. We construct the first examples of smooth intersections of two quadrics in $\mathbb{P}_R^5$ and smooth cubic hypersurfaces in $\mathbb{P}_R^4$ which are not stably rational but for which the space $X(R)$ of $R$-points is semi-algebraically connected. The question of constructing such examples over the field of real numbers $\mathbb{R}$ remains open.

GPU Implementation of Zippel Method for Feynman Integral Reconstruction
Alexander V. Smirnov, Boris I. Rozhnov, Vadim V. Voevodin
https://arxiv.org/abs/2505.24256

GPU Implementation of Zippel Method for Feynman Integral Reconstruction
The Zippel algorithm performs a rational reconstruction of multivariate polynomials and aims specifically at the sparse case. It is applied in different fields of science, lately becoming an important step in Feynman integral reduction in elementary particle physics. In some cases with multiple variables it might become a bottleneck for the whole evaluation so that different optimizations are required. In this paper we describe how we ported the classical Zippel algorithm together with its bala…

No Trade Under Verifiable Information
Spyros Galanis
https://arxiv.org/abs/2506.04944 https://arxiv.org/pdf/2506.04944

No Trade Under Verifiable Information
No trade theorems examine conditions under which agents cannot agree to disagree on the value of a security which pays according to some state of nature, thus preventing any mutual agreement to trade. A large literature has examined conditions which imply no trade, such as relaxing the common prior and common knowledge assumptions, as well as allowing for agents who are boundedly rational or ambiguity averse. We contribute to this literature by examining conditions on the private information of…

This https://arxiv.org/abs/2407.03078 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Counting Rational Points In Non-Isotropic Neighborhoods of Manifolds
In this manuscript, we initiate the study of the number of rational points with bounded denominators, contained in a non-isotropic $δ_1\times\ldots\times δ_R$ neighborhood of a compact submanifold $\mathcal{M}$ of codimension $R$ in $\mathbb{R}^{M}$. We establish an upper bound for this counting function which holds when $\mathcal{M}$ satisfies a strong curvature condition, first introduced by Schindler-Yamagishi in \cite{schindler2022density}. Further, even in the isotropic case when $δ_1=\…

This https://arxiv.org/abs/2405.00295 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

Proof of Sampling: A Nash Equilibrium-Based Verification Protocol for Decentralized Systems
This paper introduces the Proof of Sampling (PoSP) protocol, a Nash Equilibrium-based verification mechanism, and its application to decentralized machine learning inference through spML. Our protocol has a pure strategy Nash Equilibrium, compelling rational participants to act honestly. It economically disincentivizes dishonest behavior, making it costly for participants to compromise the network's integrity. In our spML protocol, we apply PoSP to decentralized inference for AI applications vi…

This https://arxiv.org/abs/2408.06616 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Gromov-Witten invariants in family and quantum cohomology
A moduli space of stable maps to the fibers of a fiber bundle is constructed. The new moduli space is a family version of the classical moduli space of stable maps to a non-singular complex projective variety. The virtual cycle for this moduli space is also constructed, and an analogue of Gromov-Witten invariants is defined. As an application, we recover the formula for the number of rational degree d curves in P3, whose image lies in a plane in P3 (known as planar curves in P3), intersecting r…

This https://arxiv.org/abs/2212.05260 has been replaced.
link: https://scholar.google.com/scholar?q=a

Examining marginal properness in the external validation of survival models with squared and logarithmic losses
Scoring rules promote rational and honest decision-making, which is important for model evaluation and becoming increasingly important for automated procedures such as `AutoML'. In this paper we survey common squared and logarithmic scoring rules for survival analysis, with a focus on their theoretical and empirical properness. We introduce a marginal definition of properness and show that both the Integrated Survival Brier Score (ISBS) and the Right-Censored Log-Likelihood (RCLL) are theoretic…

This https://arxiv.org/abs/2504.21003 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Efficient application of the Voigt functions in the Fourier transform
In this work, we develop a method of rational approximation of the Fourier transform (FT) based on the real and imaginary parts of the complex error function \[ w(z) = e^{-z^2}(1 - {\rm{erf}}(-iz)) = K(x,y) + iL(x,y), \quad z = x + iy, \] where $K(x,y)$ and $L(x,y)$ are known as the Voigt and imaginary Voigt functions, respectively. In contrast to our previous rational approximation of the FT, the expansion coefficients in this method are not dependent on values of a sampled function. As the va…

This https://arxiv.org/abs/2504.21059 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A remark on the number of automorphisms of some algebraic structures
In these notes we look at the following question. Given a category $\mathcal C$ of algebraic structure (e.g. the category of groups, monoids, partial groups, ...) and a rational $r\in \mathbb Q$, does there exists an element $x\in \mathcal C$ such that the size of its automorphism group $\text{Aut}_{\mathcal C} (x)$ divided by the size of $x$ (whatever that would means) is equal to $r$\,? To our knowledge, this question was introduced by Tărnăuceanu in the category of groups. Here, we answer …

Free Circle Actions on the Product of Three Spheres
Dimpi, Hemant Kumar Singh
https://arxiv.org/abs/2505.21993 https://arxiv.org/pdf/…

Free Circle Actions on the Product of Three Spheres
The orbit spaces of free S^0-actions on the mod 2 cohomology product of three spheres, S^n x S^m x S^l, 1 <= n <= m <= l have been determined in [6]. In this paper, we extend these findings to free S^1-actions on the rational cohomology product of three spheres. This extension also builds upon the work of Dotzel et al. [7], who studied free circle actions on the rational cohomology product of two spheres. Additionally, we establish Borsuk-Ulam type theorems.

This https://arxiv.org/abs/2409.18421 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Moment varieties of the inverse Gaussian and gamma distributions are nondefective
We show that the parameters of a $k$-mixture of inverse Gaussian or gamma distributions are algebraically identifiable from the first $3k-1$ moments, and rationally identifiable from the first $3k+2$ moments. Our proofs are based on Terracini's classification of defective surfaces, careful analysis of the intersection theory of moment varieties, and a recent result on sufficient conditions for rational identifiability of secant varieties by Massarenti--Mella.

Propylenidene: A New Carbon Two-dimensional Material Featuring Tilted Dirac Cones
Jose A. S. Laranjeira, K. A. L. Lima, Nicolas F. Martins, Luis A. Cabral, L. A. Ribeiro Junior, Julio R. Sambrano
https://arxiv.org/abs/2506.03494

Propylenidene: A New Carbon Two-dimensional Material Featuring Tilted Dirac Cones
Two-dimensional (2D) carbon allotropes have drawn significant interest owing to their impressive physical and chemical characteristics. Following graphene's isolation, a wide range of 2D carbon materials has been suggested, each with distinct electronic, mechanical, and optical traits. Rational design and synthesis of new 2D carbon structures hinge on experimentally reported precursors. Here, we present a 2D carbon allotrope, propylenidene (PPD), originating from the highly strained bicycloprop…

This https://arxiv.org/abs/2409.02656 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Classification of exceptional Jacobi polynomials
We provide a full classification scheme for exceptional Jacobi operators and polynomials. The classification contains six degeneracy classes according to whether $α,β$ or $α\pmβ$ assume integer values. Exceptional Jacobi operators are in one-to-one correspondence with spectral diagrams, a combinatorial object that describes the number and asymptotic behaviour at the endpoints of $(-1,1)$ of all quasi-rational eigenfunctions of the operator. With a convenient indexing scheme for spectral dia…

How fake news can turn against its spreader
Dorje C. Brody, Tomooki Yuasa
https://arxiv.org/abs/2504.17820 https://arxiv.org/pdf/2504…

This https://arxiv.org/abs/2503.15398 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Separation of variables for higher rank integrable models: review of recent progress
Separation of variables (SoV) is a powerful method expected to be applicable for a wide range of quantum integrable systems, from models in condensed matter physics to gauge and string theories. Yet its full implementation for many higher rank examples, such as SU(N) spin chains with N>2, has remained elusive for a long time. In this pedagogical review we discuss the major progress achieved recently in understanding SoV for models of this type. In particular, for rational SU(N) spin chains we d…

This https://arxiv.org/abs/2504.16756 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Exact root-exponential convergence rates of lightning plus polynomial approximations for corner singularities
This paper builds rigorous analysis on the root-exponential convergence for the lightning schemes via rational functions in approximating corner singularity problems with uniform exponentially clustered poles proposed by Gopal and Trefethen. The start point is to set up the representations of $z^α$ and $z^α\log z$ in the slit disk and develop results akin to Paley-Wiener theorem, from which, together with the Poisson summation formula, the root-exponential convergence of the lightning plus po…

This https://arxiv.org/abs/2209.14273 has been replaced.
link: https://scholar.google.com/scholar?q=a

Derived equivalences for trigonometric double affine Hecke algebras
The trigonometric double affine Hecke algebra $\mathbf{H}_c$ for an irreducible root system depends on a family of complex parameters $c$ Given two families of parameters $c$ and $c'$ which differ by integers, we construct the translation functor from $\mathbf{H}_{c}\operatorname{-Mod}$ to $\mathbf{H}_{c'}\operatorname{-Mod}$ and prove that it induces equivalence of derived categories. This is a trigonometric counterpart of a theorem of Losev on the derived equivalences for rational Cherednik a…

Arithmetic properties and zeros of the Bergman kernel on a class of quotient domains
Luke D. Edholm, Vikram T. Mathew
https://arxiv.org/abs/2505.20489 http…

Arithmetic properties and zeros of the Bergman kernel on a class of quotient domains
An effective formula for the Bergman kernel on $\mathbb{H}_γ = \{|z_1|^γ< |z_2| < 1 \}$ is obtained for rational $γ= \frac{m}{n} >1$. The formula depends on arithmetic properties of $γ$, which uncovers new symmetries and clarifies previous results. The formulas are then used to study the Lu Qi-Keng problem. We produce sequences of rationals $γ_j \searrow 1$, where each $\mathbb{H}_{γ_j}$ has a Bergman kernel with zeros (while $\mathbb{H}_1$ is known to have a zero-free…

This https://arxiv.org/abs/2112.09041 has been replaced.
link: https://scholar.google.com/scholar?q=a

Ahlfors-regular conformal dimension and energies of graph maps
For a hyperbolic rational map $f$ with connected Julia set, we give upper and lower bounds on the Ahlfors-regular conformal dimension of its Julia set $J_f$ from a family of energies of associated graph maps. Concretely, the dynamics of $f$ is faithfully encoded by a pair of maps $π, ϕ: G_1 \to G_0$ between finite graphs that satisfies a natural expanding condition. Associated to this combinatorial data, for each $q \geq 1$, is a numerical invariant $\overline{E}^q[π,ϕ]$, its asymptotic $q$…

Balancing incentives in committee-based blockchains
Arian Baloochestani, Leander Jehl
https://arxiv.org/abs/2505.24482 https://arxiv.…

Balancing incentives in committee-based blockchains
Blockchain protocols incentivize participation through monetary rewards, assuming rational actors behave honestly to maximize their gains. However, attackers may attempt to harm others even at personal cost. These denial of profit attacks aim to reduce the rewards of honest participants, potentially forcing them out of the system. While existing work has largely focused on the profitability of attacks, they often neglect the potential harm inflicted on the victim, which can be significant even …

This https://arxiv.org/abs/2402.07141 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSC_…

Reading Rational Univariate Representations on lexicographic Groebner bases
In this contribution, we consider a zero-dimensional polynomial system in $n$ variables defined over a field $\mathbb{K}$. In the context of computing a Rational Univariate Representation (RUR) of its solutions, we address the problem of certifying a separating linear form and, once certified, calculating the RUR that comes from it, without any condition on the ideal else than being zero-dimensional. Our key result is that the RUR can be read (closed formula) from lexicographic Groebner bases o…

This https://arxiv.org/abs/2412.04265 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

On Extrapolation of Treatment Effects in Multiple-Cutoff Regression Discontinuity Designs
Regression discontinuity (RD) designs typically identify the treatment effect at a single cutoff point, which may not always be the primary interest. When and how, then, can we learn about treatment effects away from the cutoff? This paper addresses this question within a multiple-cutoff RD framework. We begin by examining the plausibility of the constant bias assumption proposed by Cattaneo, Keele, Titiunik, and Vazquez-Bare (2021) through the lens of rational decision-making behavior. We argu…

On Hodge--Witt cohomology of Drinfeld's upper half space over a finite field
Mattia Tiso
https://arxiv.org/abs/2506.06246 https://

On Hodge--Witt cohomology of Drinfeld's upper half space over a finite field
In this dissertation we study the Hodge-Witt cohomology of the $d$-dimensional Drinfeld's upper half space $\mathcal{X} \subset \mathbb{P}_k^d$ over a finite field $k$. We consider the natural action of the $k$-rational points $G$ of the linear group $\mathrm{GL}_{d+1}$ on $H^0(\mathcal{X},\mathrm{W}_nΩ_{\mathbb{P}_k^d}^i)$, making them natural $\mathrm{W}_n(k)[G]$-modules. To study these representations, we introduce a theory of differential operators over the Witt vectors for smooth $k$-sche…

Dicritical divisors and hypercurvettes
Enrique Artal Bartolo, Willem Veys
https://arxiv.org/abs/2505.24648 https://arxiv.org/pdf/2505…

Dicritical divisors and hypercurvettes
Germs of rational functions~$h$ on points $p$ of smooth varieties~$S$ define germs of rational maps to the projective line. Assume that $p$ is in the indeterminacy locus of $h$. If $π:\hat{S}\to S$ is a birational map which is an isomorphism outside $p$, then $h$ lifts to a germ of a rational map on $(\hat{S}, π^{-1}(p))$. The exceptional components $E_i$ of $π^{-1}(p)$ are classified according to the restriction of (the lift of) $h$ to $E_i$; the dicritical components are those where this r…

This https://arxiv.org/abs/2408.16394 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the asymptotics of elementary-abelian extensions of local and global function fields
We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic $p$. For local and rational function fields, we also give precise formulae for the number of elementary-abelian extensions with a fixed discriminant divisor, which describe a local-global principle.

This https://arxiv.org/abs/2505.04316 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

On local fields invariant under the action of topological defects
In the context of rational conformal field theories (RCFT) we look into the problem of constructing and classifying pairs consisting of a local operator and a topological defect which commutes or anticommutes with it. We discuss the bulk and boundary versions of the problem. In the latter one considers a conformal boundary condition, a boundary operator on it and a junction with a topological defect. In the case of the charge conjugation modular invariant commuting configurations in each proble…

How One Quiet Man Became Everyone's Sage: The Spiritual Recasting of Einstein
Galina Weinstein
https://arxiv.org/abs/2505.19695 https://

How One Quiet Man Became Everyone's Sage: The Spiritual Recasting of Einstein
This paper critically examines the central thesis of Kieran Fox's "I Am a Part of Infinity: The Spiritual Journey of Albert Einstein"-namely, that Einstein's intellectual development constitutes a coherent spiritual path culminating in a form of pantheistic mysticism shaped by both Western and Eastern traditions. Fox presents Einstein as the modern heir to a long-suppressed lineage of rational spirituality, extending from Pythagoras and Spinoza to Vedanta and Buddhism, unified by wonder, revere…

This https://arxiv.org/abs/2403.04088 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The classification of endotrivial complexes
Let $G$ be a finite group and $k$ a field of prime characteristic $p$. We give a complete classification of endotrivial complexes, i.e. determine the Picard group $\mathcal{E}_k(G)$ of the tensor-triangulated category $K^b({}_{kG}\mathbf{triv})$, the bounded homotopy category of $p$-permutation modules, which Balmer and Gallauer recently considered. For $p$-groups, we identify $\mathcal{E}_k(-)$ with the rational $p$-biset functor $CF_b(-)$ of Borel-Smith functions and recover a short exact seq…

Note on the size of a stable matching
Gregory Z. Gutin, Philip R. Neary, Anders Yeo
https://arxiv.org/abs/2505.24637 https://arxiv.or…

Note on the size of a stable matching
Consider a one-to-one two-sided matching market with workers on one side and single-position firms on the other, and suppose that the largest individually rational matching contains $n$ pairs. We show that the number of workers employed and positions filled in every stable matching is bounded from below by $\lceil\frac{n}{2}\rceil$ and we characterise the class of preferences that attain the bound.

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Liat Kessler, Nikolas Wardenski
https://arxiv.org/abs/2505.14000 https://

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Following Gonzales, we answer the question of whether the isomorphism type of a semi-free Hamiltonian $S^1$-manifold of dimension six is determined by certain data on the critical levels. We first give counter examples showing that Gonzales' assumptions are not sufficient for a positive answer. Then we prove that it is enough to further assume that the reduced spaces of dimension four are symplectic rational surfaces and the interior fixed surfaces are restricted to at most one level. The addit…

This https://arxiv.org/abs/2502.18128 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Intertwining operators for representations of covering groups of reductive $p$-adic groups
Let $G$ be a covering group of a reductive $p$-adic group. We study intertwining operators between parabolically induced representations of $G$ and prove that they satisfy certain adjointness relations. The Harish-Chandra $μ$-function is defined as a composition of such intertwining operators for opposite parabolic subgroups of $G$. It can be seen as a complex rational function and we give an explicit formula for it in terms of poles and zeros. The adjointness of the intertwining operators is …

This https://arxiv.org/abs/2402.07141 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSC_…

Reading Rational Univariate Representations on lexicographic Groebner bases
In this contribution, we consider a zero-dimensional polynomial system in $n$ variables defined over a field $\mathbb{K}$. In the context of computing a Rational Univariate Representation (RUR) of its solutions, we address the problem of certifying a separating linear form and, once certified, calculating the RUR that comes from it, without any condition on the ideal else than being zero-dimensional. Our key result is that the RUR can be read (closed formula) from lexicographic Groebner bases o…

This https://arxiv.org/abs/2311.01835 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Surjective rational maps and del Pezzo surfaces
We study surjective (not necessarily regular) rational endomorphisms $f$ of smooth del Pezzo surfaces $X$. We prove that under certain natural non\,-\,degeneracy condition $f$ can have degree bigger than $1$ only when $(-K_X^2) > 5$. Some structural properties of $f$ in the case $X = \p^2$ are also established.

This https://arxiv.org/abs/2505.07501 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

The Complexity of Pure Strategy Relevant Equilibria in Concurrent Games
We study rational synthesis problems for concurrent games with $ω$-regular objectives. Our model of rationality considers only pure strategy Nash equilibria that satisfy either a social welfare or Pareto optimality condition with respect to an $ω$-regular objective for each agent. This extends earlier work on equilibria in concurrent games, without consideration about their quality. Our results show that the existence of Nash equilibria satisfying social welfare conditions can be computed as …

This https://arxiv.org/abs/2403.06006 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Real-time observables in de Sitter thermodynamics
We study real-time finite-temperature correlators for free scalars of any mass in a $dS_{d+1}$ static patch in any dimension. We show that whenever the inverse temperature is a rational multiple of the inverse de Sitter temperature, certain Matsubara poles of the symmetric Wightman function disappear. At the de Sitter temperature, we explicitly show how the Lorentzian thermal correlators can all be obtained by analytic continuations from the round $S^{d+1}$. We establish the precise relation be…

Overgroups of the arboreal representation of PCF polynomial
Wayne Peng
https://arxiv.org/abs/2506.00456 https://arxiv.org/pdf/2506.00…

Overgroups of the arboreal representation of PCF polynomial
Consider a number field $K$ and a rational function $f$ of degree greater than 1 over $K$. By taking preimages of $α\in K$ under successive iterates of $f$, an infinite $d$-ary tree $T_\infty$ rooted at $α$ can be constructed. An edge is assigned between two preimages $x$ and $y$ if $f(x)=y$. The absolute Galois group of $K$, acting on $T_\infty$ through tree automorphisms, generates a subgroup $\text{Gal}_f^\infty(α)$ in the group of all automorphisms of $T_\infty$, $\text{Aut}(T_\infty)$. …

This https://arxiv.org/abs/2505.12357 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The geometric K-theory of quotient stacks
Given a quotient of a regular noetherian separated algebraic space $X$ over a field by an affine algebraic group $G$ having finite stabilizers (with some mild technical conditions), G. Vezzosi and A. Vistoli defined the \emph{geometric part} of the rational equivariant K-theory $K(X,G)$ and conjectured that it is isomorphic to the rational K-theory of the quotient $X/G$. In this paper we refine the construction of geometric K-theory to the rational K-theory of a quotient stack $[X/G]$ over an a…

Symmetries of coefficients of three-term relations for basic hypergeometric series
Yuka Yamaguchi
https://arxiv.org/abs/2505.20798 https://

Symmetries of coefficients of three-term relations for basic hypergeometric series
Any three basic hypergeometric series ${}_{2}ϕ_{1}$ whose respective parameters $a, b, c$ and a variable $x$ are shifted by integer powers of $q$ are linearly related with coefficients that are rational functions of $a, b, c, q$, and $x$. This relation is called a three-term relation for ${}_{2}ϕ_{1}$. In this paper, we prove that the coefficients of the three-term relation for ${}_{2}ϕ_{1}$ considered in the author's earlier paper (2022) have ninety-six symmetries, and present explicit form…

Torsion of $\mathbb Q$-curves over number fields of small odd prime degree
Ivan Novak
https://arxiv.org/abs/2506.00753 https://arxiv.…

Torsion of $\mathbb Q$-curves over number fields of small odd prime degree
We determine all groups which occur as torsion subgroups of $\mathbb Q$-curves defined over number fields of degrees $3$, $5$ and $7$. In particular, we prove that every torsion subgroup of a $\mathbb Q$-curve defined over a number field of degree $3,5$ or $7$ already occurs as a torsion subgroup of an elliptic curve with rational $j$-invariant. As the quadratic case has been solved by Le Fourn and Najman, and the case of extensions of prime degree greater than $7$ has been solved by Cremona an…

This https://arxiv.org/abs/2504.05678 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

On The Merit Principle in Strategic Exchange
New fairness notions in align with the merit principle are proposed for designing exchange rules. We show that, for an obviously strategy-proof, efficient and individually rational rule, an upper bound of fairness attainable is that, if two agents possess objects considered the best by all others divided into two equal groups, then at least one receives her favorite object. Notably, it is not possible to guarantee them both receiving favorites. Our results thus indicate an unambiguous trade-off…

This https://arxiv.org/abs/2407.19999 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Auslander-Reiten annihilators
The Auslander-Reiten Conjecture for commutative Noetherian rings predicts that a finitely generated module is projective when certain Ext-modules vanish. But what if those Ext-modules do not vanish? We study the annihilators of these Ext-modules and formulate a generalisation of the Auslander-Reiten Conjecture. We prove this general version for high syzygies of modules over several classes of rings including analytically unramified Arf rings, 2-dimensional local normal domains with rational sin…

This https://arxiv.org/abs/2410.11968 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Codes on Weighted Projective Planes
We comprehensively study weighted projective Reed-Muller (WPRM) codes on weighted projective planes $\mathbb{P}(1,a,b)$. We provide the universal Gröbner basis for the vanishing ideal of the set $Y$ of $\mathbb{F}_q$--rational points of $\mathbb{P}(1,a,b)$ to get the dimension of the code. We determine the regularity set of $Y$ using a novel combinatorial approach. We employ footprint techniques to compute the minimum distance.

This https://arxiv.org/abs/2407.19999 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Auslander-Reiten annihilators
The Auslander-Reiten Conjecture for commutative Noetherian rings predicts that a finitely generated module is projective when certain Ext-modules vanish. But what if those Ext-modules do not vanish? We study the annihilators of these Ext-modules and formulate a generalisation of the Auslander-Reiten Conjecture. We prove this general version for high syzygies of modules over several classes of rings including analytically unramified Arf rings, 2-dimensional local normal domains with rational sin…

This https://arxiv.org/abs/2310.19597 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Automorphism groups of $\mathbb{P}^1$-bundles over ruled surfaces
We classify the pairs $(X,π)$, where $π\colon X\to S$ is a $\mathbb{P}^1$-bundle over a non-rational ruled surface $S$ and $\mathrm{Aut}^\circ(X)$ is relatively maximal, i.e., maximal with respect to the inclusion in the group $\mathrm{Bir}(X/S)$. The results hold over any algebraically closed field of characteristic zero.

This https://arxiv.org/abs/2207.01061 has been replaced.
link: https://scholar.google.com/scholar?q=a

Computing Vanishing Ideals for Toric Codes
Motivated by applications to the theory of error-correcting codes, we give methods for computing a generating set for the ideal generated by $β$-graded polynomials vanishing on certain subsets of a simplicial complete toric variety $X$ over a finite field $\mathbb{F}_q$, where $β$ is a $d\times r$ matrix whose columns generate a subsemigroup $\mathbb{N}β$ of $\mathbb{N}^d$. We also give a method for computing the vanishing ideal of the set of $\mathbb{F}_q$-rational points of $X$. When $β=[…

This https://arxiv.org/abs/2505.12364 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On a Riemann-Roch formula for stacks with finite cyclotomic inertia
B. Toen defined a Riemann-Roch map from the rational algebraic K-theory of a tame Deligne-Mumford quotient stack to the étale K-theory of its inertia. He proved that this map is an isomorphism and that it is covariant with respect to proper maps. Moreover G. Vezzosi and A. Vistoli proved a decomposition theorem for the equivariant K-theory of a noetherian scheme. In this paper we give a geometric definition of the Vezzosi-Vistoli decomposition, interpreting the pieces as corresponding to the c…