Tootfinder

Long strings of composite values of polynomials and a basis of order 2
Artyom Radomskii
https://arxiv.org/abs/2506.15641 https://arxi…

Long strings of composite values of polynomials and a basis of order 2
We show that for any polynomial $f: \mathbb{Z}\to \mathbb{Z}$ with positive leading coefficient and irreducible over $\mathbb{Q}$, if $N$ is large enough then there are two strings of consecutive positive integers $I_{1}=\{n_1-m,\ldots, n_1+m\}$ and $I_{2}=\{n_2-m, \ldots, n_2+m\}$, where $m = [(\log N) (\log \log N)^{1/325525}]$, such that $I_{1}\cup I_{2} \subset [1, N]$, $N = n_1 + n_2$, and $f(n)$ is composite for any $n\in I_{1}\cup I_{2}$. This extends the result in [5] which showed the s…

${\sf QMA}={\sf QMA}_1$ with an infinite counter
Stacey Jeffery, Freek Witteveen
https://arxiv.org/abs/2506.15551 https://arxiv.org/p…

${\sf QMA}={\sf QMA}_1$ with an infinite counter
A long-standing open problem in quantum complexity theory is whether ${\sf QMA}$, the quantum analogue of ${\sf NP}$, is equal to ${\sf QMA}_1$, its one-sided error variant. We show that ${\sf QMA}={\sf QMA}^{\infty}= {\sf QMA}_1^{\infty}$, where ${\sf QMA}_1^\infty$ is like ${\sf QMA}_1$, but the verifier has an infinite register, as part of their witness system, in which they can efficiently perform a shift (increment) operation. We call this register an ``infinite counter'', and compare it t…

A general solution for the 1-2 conjecture using real numbers
Kecai Deng, Hongyuan Qiu
https://arxiv.org/abs/2506.14253 https://arxiv.…

A general solution for the 1-2 conjecture using real numbers
The 1-2 conjecture posits that for every graph, weights from $\{1,2\}$ can be assigned to its vertices and edges so that adjacent vertices have distinct weighted degrees. This paper demonstrates that any set of two distinct real numbers $\{a,b\}$ can achieve the same goal, thereby confirming the 1-2 conjecture in a broader context.

$\Sigma^1_3$ sets in the Sacks model
Jonathan Schilhan
https://arxiv.org/abs/2506.15308 https://arxiv.org/pdf/2506.15308

$Σ^1_3$ sets in the Sacks model
We show that in the iterated Sacks model over the constructible universe the Mansfield-Solovay Theorem holds for $Σ^1_3$ sets. In particular, every $\mathbfΣ^1_3$ set is Marczewski measurable and the optimal complexity for a Bernstein set is $Δ^1_4$. Based on a result by Kanovei, we also briefly show how to separate the Mansfield-Solovay Theorem at non-trivial levels of the projective hierarchy.

Is 1:1 Always Most Powerful? Why Unequal Allocation Merits Broader Consideration
Lukas Pin, Stef Baas, David S. Robertson, Sof\'ia S. Villar
https://arxiv.org/abs/2507.13036

Is 1:1 Always Most Powerful? Why Unequal Allocation Merits Broader Consideration
The principle of allocating an equal number of patients to each arm in a randomized controlled trial is widely accepted as the standard strategy for maximising the trial's statistical power. However, this long-held belief only holds true if the treatment groups have equal outcome variances, a condition that is often not met in practice. This paper questions the prevalent practice of exclusively defaulting to equal randomisation (ER) and posits that a departure from a 1:1 ratio can be both valid…

The HOMFLYPT skein module of $S^1 \times S^2$ via braids
Ioannis Diamantis
https://arxiv.org/abs/2507.12826 https://arxiv.org/pdf/250…

The HOMFLYPT skein module of $S^1 \times S^2$ via braids
In this paper we compute the HOMFLYPT skein module of $S^1 \times S^2\, \cong \, L(0, 1)$, denoted $\mathcal{S}(S^1 \times S^2)$, using braid-theoretic techniques. We extend the Lambropoulou invariant, $X$, for links in the solid torus ST to links in $S^1 \times S^2$, by solving an infinite system of equations of the form $X_{\widehat{a}} = X_{\widehat{bbm(a)}}$, where $bbm(a)$ denotes all possible band moves applied to $a$, for all $a$ in a basis of $\mathcal{S}(ST)$. We show that the free par…

Fractional instantons in 2d $\mathbb{C}P^{N-1}$ model and 4d Yang-Mills theory with 't Hooft twists
Yui Hayashi, Tatsuhiro Misumi, Muneto Nitta, Keisuke Ohashi, Yuya Tanizaki
https://arxiv.org/abs/2507.12802

Fractional instantons in 2d $\mathbb{C}P^{N-1}$ model and 4d Yang-Mills theory with 't Hooft twists
We derive the explicit formula for fractional BPS lumps (or fractional instantons) in the $\mathbb{C}P^{N-1}$ nonlinear sigma model on a two-dimensional torus under various shift-clock twisted boundary conditions. After regularizing the $\mathbb{C}P^{N-1}$ model by an $N$-component Abelian-Higgs model, those twisted boundary conditions introduce nontrivial 't~Hooft fluxes $p/N$ for the $U(1)$ gauge field, and the topological charge becomes fractionalized as $k+p/N\in \mathbb{Z}+p/N$. The moduli…

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes
Spencer Becker-Kahn, Paul Minter, Neshan Wickramasekera
https://arxiv.org/abs/2507.13148

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes
We study stationary integral $n$-varifolds $V$ in the unit ball $B_1(0)\subset\mathbb{R}^{n+k}$. Allard's regularity theorem establishes the existence of $ε= ε(n,k)\in (0,1)$ for which if $V$ is $ε$-close (as varifolds) to the plane $P_0 = \{0\}^k\times\mathbb{R}^n$ with multiplicity 1 then, in $B_{1/2}(0)$, $V$ is represented by a single $C^{1,α}$ minimal graph. However, when instead $P_0$ occurs with multiplicity $Q\in \{2,3,\dotsc\}$, simple examples show that this conclusion, now as a m…

Emergence of charm-strange dibaryons with negative parity via baryon-baryon interactions
Yu-Yue Cui, Xiao-Mei Tang, Qi Huang, Rui Chen
https://arxiv.org/abs/2507.12958

Emergence of charm-strange dibaryons with negative parity via baryon-baryon interactions
Within the framework of the one-boson-exchange model, we systematically perform a coupled channel analysis of the $P-$wave interactions between a charm baryon and light baryon, the involved channels include $Ξ_cN$, $Λ_cΣ$, $Ξ_c^{\prime}N$, $Σ_cΛ$, $Ξ_c^*N$, $Σ_c^*Λ$, $Σ_cΣ$, and $Σ_c^*Σ$. Our results can predict several possible molecular candidates, such as a $Ξ_c^{\prime}N$ molecule with $I(J^P)=0(1^-)$, $Ξ_c^{*}N$ molecules with $0(0^-, 1^-, 2^-)$, $Σ_cΣ$ molecules with $0(1…

Optimal regularity results in Sobolev-Lorentz spaces for lilnear elliptic equations with $L^1$- or measure data
Hyunseok Kim, Young-Ran Lee, Jihoon Ok
https://arxiv.org/abs/2506.15005

Optimal regularity results in Sobolev-Lorentz spaces for lilnear elliptic equations with $L^1$- or measure data
It has been well known that if $Ω$ is a bounded $C^1$-domain in $\R^n,\ n \ge 2$, then for every Radon measure $f$ on $Ω$ with finite total variation, there exists a unique weak solution $u\in W_0^{1,1}(Ω)$ of the Poisson equation $-Δu=f$ in $Ω$ satisfying $\nabla u \in L^{n/(n-1),\infty}(Ω;\R^n )$. In this paper, optimal regularity properties of the solution $u$ are established in Sobolev-Lorentz spaces $L_α^{p,q}(Ω)$ of order $ α$ less than but arbitrarily close to $2$. More precisel…

Replaced article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- Boolformer: Symbolic Regression of Logic Functions with Transformers
d'Ascoli, Renard, Papadopoulos, Bengio, Susskind, Abb\'e

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Rewriting techniques for relative coherence
Samuel Mimram

Replaced article(s) found for cs.PL. https://arxiv.org/list/cs.PL/new
[1/1]:
- An Algebraic Approach to Asymmetric Delegation and Polymorphic Label Inference (Technical Report)
Silei Ren, Co\c{s}ku Acay, Andrew C. Myers

Replaced article(s) found for cs.RO. https://arxiv.org/list/cs.RO/new
[1/1]:
Design and Evaluation of an Uncertainty-Aware Shared-Autonomy System with Hierarchical Conservati...

Replaced article(s) found for cs.CR. https://arxiv.org/list/cs.CR/new
[1/1]:
- TBDetector:Transformer-Based Detector for Advanced Persistent Threats with Provenance Graph
Wang, Wen, Zhang, Zhao, Ma, Luo, Xu, Nie, Wu, Liu

Replaced article(s) found for cs.SE. https://arxiv.org/list/cs.SE/new
[1/1]:
- Machine Learning Systems: A Survey from a Data-Oriented Perspective
Christian Cabrera, Andrei Paleyes, Pierre Thodoroff, Neil D. Lawrence

Optimal Convergence Rates of Deep Neural Network Classifiers
Zihan Zhang, Lei Shi, Ding-Xuan Zhou
https://arxiv.org/abs/2506.14899 https://

Optimal Convergence Rates of Deep Neural Network Classifiers
In this paper, we study the binary classification problem on $[0,1]^d$ under the Tsybakov noise condition (with exponent $s \in [0,\infty]$) and the compositional assumption. This assumption requires the conditional class probability function of the data distribution to be the composition of $q+1$ vector-valued multivariate functions, where each component function is either a maximum value function or a Hölder-$β$ smooth function that depends only on $d_*$ of its input variables. Notably, $d_…

Chow cohomology and Lefschetz (1,1)-theorem
Ananyo Dan, Inder Kaur
https://arxiv.org/abs/2506.13220 https://arxiv.org/pdf/2506.13220

Chow cohomology and Lefschetz (1,1)-theorem
Any smooth, projective variety satisfies the Hodge conjecture in codimension one, known as the Lefschetz (1,1) theorem. Totaro formulated a version for singular varieties. He asked whether the natural Bloch-Gillet-Soulé cycle class map from the operational Chow group to the (1,1)-classes in the weight graded piece of the cohomology group is surjective? In this short article, we give a sufficient criterion for this to hold. In particular, we show that several singular varieties with at worst is…

A 1/2-Approximation for Budgeted $k$-Submodular Maximization
Chenhao Wang
https://arxiv.org/abs/2507.12875 https://arxiv.org/pdf/2507…

A 1/2-Approximation for Budgeted $k$-Submodular Maximization
A $k$-submodular function naturally generalizes submodular functions by taking as input $k$ disjoint subsets, rather than a single subset. Unlike standard submodular maximization, which only requires selecting elements for the solution, $k$-submodular maximization adds the challenge of determining the subset to which each selected element belongs. Prior research has shown that the greedy algorithm is a 1/2-approximation for the monotone $k$-submodular maximization problem under cardinality or m…

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[1/5]:
- Boolformer: Symbolic Regression of Logic Functions with Transformers
d'Ascoli, Renard, Papadopoulos, Bengio, Susskind, Abb\'e

Replaced article(s) found for cs.HC. https://arxiv.org/list/cs.HC/new
[1/1]:
- Implementation Considerations for Automated AI Grading of Student Work
Zewei (Victor), Tian, Alex Liu, Lief Esbenshade, Shawon Sarkar, Zachary Zhang, Kevin He, Min Sun

Replaced article(s) found for cs.CV. https://arxiv.org/list/cs.CV/new
[1/3]:
- An Event-based Algorithm for Simultaneous 6-DOF Camera Pose Tracking and Mapping
Masoud Dayani Najafabadi, Mohammad Reza Ahmadzadeh

Replaced article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[1/4]:
- LLM-Enhanced User-Item Interactions: Leveraging Edge Information for Optimized Recommendations
Xinyuan Wang, Liang Wu, Liangjie Hong, Hao Liu, Yanjie Fu

Machine learning many-body potentials for charged colloids in primitive 1:1 electrolytes
Thijs ter Rele, Gerardo Campos-Villalobos, Ren\'e van Roij, Marjolein Dijkstra
https://arxiv.org/abs/2507.12934

Machine learning many-body potentials for charged colloids in primitive 1:1 electrolytes
Effective interactions between charged particles dispersed in an electrolyte are most commonly modeled using the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential, where the ions in the suspension are coarse-grained out at mean-field level. However, several experiments point to shortcomings of this theory, as the distribution of ions surrounding colloids is governed by nontrivial correlations in regimes of strong Coulomb coupling (e.g. low temperature, low dielectric constant, high ion valency,…

Rota-Baxter operators on compact simple Lie groups and algebras
Saveliy V. Skresanov
https://arxiv.org/abs/2506.14324 https://arxiv.o…

Rota-Baxter operators on compact simple Lie groups and algebras
A Rota-Baxter operator on a Lie group $ G $ is a smooth map $ B : G \to G $ such that $ B(g)B(h) = B(gB(g)hB(g)^{-1}) $ for all $ g, h \in G $. This concept was introduced in 2021 by Guo, Lang and Sheng as a Lie group analogue of Rota-Baxter operators of weight 1 on Lie algebras. We show that the only Rota-Baxter operators on compact simple Lie groups are the trivial map and the inverse map. A similar description for Rota-Baxter operators of weight 1 on compact simple Lie algebras is provided.

Asteroseismology of four eccentric double-lined spectroscopic eclipsing binaries
Alexios Liakos
https://arxiv.org/abs/2506.14395 https://

Asteroseismology of four eccentric double-lined spectroscopic eclipsing binaries
Photometric data from the Transiting Exoplanet Survey Satellite (TESS) mission and radial velocities from the Gaia mission and ground-based observations were used to model the light curves and calculate the physical parameters of the eccentric eclipsing systems CH Ind, V577 Oph, CX Phe, and TIC 35481236. The components of these systems have temperatures between 6450 and 7500 K, masses between 1.4 and 1.85 solar masses, and radii between 1.49 and 3.05 solar radii. The residuals of these models w…

Replaced article(s) found for cs.CY. https://arxiv.org/list/cs.CY/new
[1/1]:
- Dataset resulting from the user study on comprehensibility of explainable AI algorithms
Bobek, Koryci\'nska, Krakowska, Mozolewski, Rak, Zych, W\'ojcik, Nalepa

Predicting the resolved CO emission of $z=1-3$ star-forming galaxies
R. Anirudh, Melanie Kaasinen, Gerg\"o Popping, Desika Narayanan, Karolina Garcia, Dariannette Valentin-Martinez
https://arxiv.org/abs/2506.13899

Predicting the resolved CO emission of $z=1-3$ star-forming galaxies
(Abridged) Resolved observations of the CO emission from $z=1-3$ star-forming galaxies are becoming increasingly common, with new high-resolution surveys on the horizon. We aim to inform the interpretation of this resolved CO emission by creating synthetic observations and testing to what extent routinely observed CO transitions can be used to trace H$_2$ across galaxy disks. To this end, we extract $z=1-3$ massive star-forming galaxies (on and above the main sequence) from the SIMBA cosmologic…

Replaced article(s) found for cs.CL. https://arxiv.org/list/cs.CL/new
[1/3]:
- A Logically Consistent Chain-of-Thought Approach for Stance Detection
Bowen Zhang, Daijun Ding, Liwen Jing, Hu Huang

Replaced article(s) found for cs.DC. https://arxiv.org/list/cs.DC/new
[1/1]:
- AAPA: An Archetype-Aware Predictive Autoscaler with Uncertainty Quantification for Serverless Wor...
Zhang, Vippagunta, Nandagopal, Raman, Xu, Pfeiffer, Chatterjee, Tan, Guo, Jiang

On $p$-th cyclotomic field and cyclotomic matrices involving Jacobi sums
Hai-Liang Wu, Li-Yuan Wang, Hao Pan
https://arxiv.org/abs/2506.14316 https://

On $p$-th cyclotomic field and cyclotomic matrices involving Jacobi sums
As a complement to our previous article, in this paper we determine the explicit values of $\det\left[J_p(χ^{ki},χ^{kj})\right]_{1\le i,j\le n-1}$ and $\det \left[J_p(χ^{ki},χ^{kj})\right]_{0\le i,j\le n-1}$, where $p$ is a prime, $1\le k

Efficient Qudit Circuit for Quench Dynamics of $2 1$D Quantum Link Electrodynamics
Rohan Joshi, Michael Meth, Jan C. Louw, Jesse J. Osborne, Kevin Mato, Martin Ringbauer, Jad C. Halimeh
https://arxiv.org/abs/2507.12589

Efficient Qudit Circuit for Quench Dynamics of $2+1$D Quantum Link Electrodynamics
A major challenge in the burgeoning field of quantum simulation for high-energy physics is the realization of scalable $2+1$D lattice gauge theories on state-of-the-art quantum hardware, which is an essential step towards the overarching goal of probing $3+1$D quantum chromodynamics on a quantum computer. Despite great progress, current experimental implementations of $2+1$D lattice gauge theories are mostly restricted to relatively small system sizes and two-level representations of the gauge …

The homology torsion growth of determinantal hypertrees
Andr\'as M\'esz\'aros
https://arxiv.org/abs/2506.14694 https://ar…

The homology torsion growth of determinantal hypertrees
Fix a dimension $d\ge 2$, and let $T_n$ be a random $d$-dimensional determinantal hypertree on $n$ vertices. We prove that \[\frac{\log|H_{d-1}(T_n,\mathbb{Z})|}{n\choose {d}}\] converges in probability to a constant $c_d$, which satisfies \[\frac{1}2 \log\left(\frac{d+1}e\right)\le c_d\le \frac{1}2 \log\left(d+1\right) .\]

The Non-Orientable Four-Ball Genus of a New Infinite Family of Torus Knots
Shreya Sinha
https://arxiv.org/abs/2507.12606 https://arxi…

The Non-Orientable Four-Ball Genus of a New Infinite Family of Torus Knots
We extend previous work by using a combination of band surgeries and known bounds to compute $γ_4(T_{4n, (2n\pm1)^2 + 4n-2}) = 2n-1$ for all $n \geq 1$. We further generalize this result by showing that $γ_4(T_{4n + 2k, n(4n + 2k) - 1}) = γ_4(T_{4n + 2k, (n+2)(4n + 2k) - 1}) = 2n-1 + k$ for all $n \geq 1$ and $k \geq 0$. All knots in this family are counterexamples to Batson's conjecture.

Replaced article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
Distributed controller synthesis for deadlock avoidance
https://

Replaced article(s) found for cs.PL. https://arxiv.org/list/cs.PL/new
[1/1]:
- A refined operational semantics for FreeCHR
Sascha Rechenberger, Thom Fr\"uhwirth

Cosmic Strings in Multi-Step Symmetry Breaking
Akifumi Chitose, Masahiro Ibe, Satoshi Shirai, Yaxuan Wen
https://arxiv.org/abs/2506.15194 https://

Cosmic Strings in Multi-Step Symmetry Breaking
We investigate cosmic strings arising from a hierarchical gauge symmetry breaking sequence, $\mathrm{SU}(2) \times \mathrm{U}(1) \rightarrow \mathrm{U}(1) \times \mathrm{U}(1) \rightarrow \mathrm{U}(1)' \rightarrow \text{Nothing}$. This pattern gives rise to two distinct classes of cosmic strings: light, stable strings formed at a later stage, and heavy, metastable strings originating from an earlier stage. Our focus is on the heavy strings, which may decay either before or after the final $\ma…

Special vector fields on Riemannian manifolds of constant negative sectional curvature and conservation laws
Keti Tenenblat, Alice Barbora Tumpach
https://arxiv.org/abs/2506.14960

Special vector fields on Riemannian manifolds of constant negative sectional curvature and conservation laws
We show that any $n$-dimensional Riemannian manifold with constant negative sectional curvature admits local orthonormal vector fields such that one of them $v_1$ is tangent to geodesics and the other $n-1$ vector fields are tangent to horocycles. We prove that the $1$-form dual to $v_1$ is a closed form. We show how the closed form can be used to obtain conservation laws for PDEs whose generic solutions define metrics on open subsets with constant negative sectional curvature. These results ex…

Bubbling saddles of the gravitational index
Davide Cassani, Alejandro Ruip\'erez, Enrico Turetta
https://arxiv.org/abs/2507.12650 https://

Bubbling saddles of the gravitational index
We consider the five-dimensional supergravity path integral that computes a supersymmetric index, and uncover a wealth of semiclassical saddles with bubbling topology. These are complex finite-temperature configurations asymptotic to $S^1\times\mathbb{R}^4$, solving the supersymmetry equations. We assume a ${\rm U}(1)^3$ symmetry given by the thermal isometry and two rotations, and present a general construction based on a rod structure specifying the fixed loci of the ${\rm U}(1)$ isometries a…

Replaced article(s) found for cs.CR. https://arxiv.org/list/cs.CR/new
[1/1]:
DSAC: Low-Cost RowHammer Mitigation Using In-DRAM Stochastic and Approximate Counting Algorithm
…

Replaced article(s) found for stat.ML. https://arxiv.org/list/stat.ML/new
[1/1]:
- Conformal inference for regression on Riemannian Manifolds
Alejandro Cholaquidis, Fabrice Gamboa, Leonardo Moreno

Replaced article(s) found for cs.SE. https://arxiv.org/list/cs.SE/new
[1/1]:
Vul-RAG: Enhancing LLM-based Vulnerability Detection via Knowledge-level RAG

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[1/7]:
- A Semi-Supervised Approach for Abnormal Event Prediction on Large Operational Network Time-Series...
Yijun Lin, Yao-Yi Chiang

Replaced article(s) found for cs.HC. https://arxiv.org/list/cs.HC/new
[1/1]:
Gaze-informed Signatures of Trust and Collaboration in Human-Autonomy Teams

Four squares from three numbers
Andrej Dujella, L\'aszl\'o Szalay
https://arxiv.org/abs/2506.14013 https://arxiv.org/pdf/2506…

Four squares from three numbers
We show that there are infinitely many triples of positive integers a, b, c (greater than 1) such that ab + 1, ac + 1, bc + 1 and abc + 1 are all perfect squares.

Scaling-Up the Pretraining of the Earth Observation Foundation Model PhilEO to the MajorTOM Dataset
Nikolaos Dionelis, Jente Bosmans, Riccardo Musto, Giancarlo Paoletti, Simone Sarti, Giacomo Cascarano, Casper Fibaek, Luke Camilleri, Bertrand Le Saux, Nicolas Long\'ep\'e
https://arxiv.org/abs/2506.14765

Scaling-Up the Pretraining of the Earth Observation Foundation Model PhilEO to the MajorTOM Dataset
Today, Earth Observation (EO) satellites generate massive volumes of data, with the Copernicus Sentinel-2 constellation alone producing approximately 1.6TB per day. To fully exploit this information, it is essential to pretrain EO Foundation Models (FMs) on large unlabeled datasets, enabling efficient fine-tuning for several different downstream tasks with minimal labeled data. In this work, we present the scaling-up of our recently proposed EO Foundation Model, PhilEO Geo-Aware U-Net, on the u…

Nonvanishing Higher Derived Limits without $w\diamondsuit_{\omega_1}$
Nathaniel Bannister
https://arxiv.org/abs/2506.14183 https://ar…

Nonvanishing Higher Derived Limits without $w\diamondsuit_{ω_1}$
We prove a common refinement of theorems of Bergfalk and of Casarosa and Lambie-Hanson, showing that under certain hypotheses, the higher derived limits of a certain inverse system of abelian groups $\mathbf{A}$ do not vanish. The refined theorem has a number of interesting corollaries, including the nonvanishing of the second derived limit of $\mathbf{A}$ in many of the common models of set theory of the reals and in the Mitchell model. In particular, we disprove a conjecture of Bergfalk, HruÅ…

Replaced article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[1/5]:
- "Generate" the Future of Work through AI: Empirical Evidence from Online Labor Markets
Jin Liu, Xingchen Xu, Xi Nan, Yongjun Li, Yong Tan

AbGen: Evaluating Large Language Models in Ablation Study Design and Evaluation for Scientific Research
Yilun Zhao, Weiyuan Chen, Zhijian Xu, Manasi Patwardhan, Yixin Liu, Chengye Wang, Lovekesh Vig, Arman Cohan
https://arxiv.org/abs/2507.13300

AbGen: Evaluating Large Language Models in Ablation Study Design and Evaluation for Scientific Research
We introduce AbGen, the first benchmark designed to evaluate the capabilities of LLMs in designing ablation studies for scientific research. AbGen consists of 1,500 expert-annotated examples derived from 807 NLP papers. In this benchmark, LLMs are tasked with generating detailed ablation study designs for a specified module or process based on the given research context. Our evaluation of leading LLMs, such as DeepSeek-R1-0528 and o4-mini, highlights a significant performance gap between these …

Replaced article(s) found for cs.CY. https://arxiv.org/list/cs.CY/new
[1/1]:
Formalising Anti-Discrimination Law in Automated Decision Systems
https:…

Cold gas in a post-starburst pair at z ~ 1.4: major mergers as a pathway to quenching in the HeavyMetal survey
Katherine A. Suess, Aliza G. Beverage, Mariska Kriek, Justin S. Spilker, Rachel Bezanson, Vincenzo R. D'Onofrio, Jenny E. Greene, Jamie Lin, Yuanze Luo, Desika Narayanan, Imad Pasha, Sedona H. Price, David J. Setton, Margaret E. Verrico, Yunchong Zhang

Cold gas in a post-starburst pair at z ~ 1.4: major mergers as a pathway to quenching in the HeavyMetal survey
Recent observations at low redshift have revealed that some post-starburst galaxies retain significant molecular gas reservoirs despite low ongoing star formation rates, challenging theoretical predictions for galaxy quenching. To test whether this finding holds during the peak epoch of quenching, here we present ALMA CO(2-1) observations of five spectroscopically confirmed post-starburst galaxies at z ~ 1.4 from the HeavyMetal survey. While four galaxies are undetected in CO emission, we detec…

Improved Decomposition Bounds for Partition Polytopes and Odd-Covers
Steffen Borgwardt, Zden\v{e}k Dvo\v{r}\'ak, Bryce Frederickson, Abigail Nix, Youngho Yoo
https://arxiv.org/abs/2507.12748

Improved Decomposition Bounds for Partition Polytopes and Odd-Covers
The assignments of a set of $m$ items into $n$ clusters of prescribed sizes $κ_1,\dots,κ_n$ can be encoded as the vertices of the \emph{partition polytope} $\mathrm{PP}(κ_1,\dots,κ_n)$. We prove that, if $K = \max\{κ_1,\dots,κ_n\}$, then the combinatorial diameter of $\mathrm{PP}(κ_1,\dots,κ_n)$ is at most $\lceil 3K/2\rceil$. This improves the previously known upper bound of $2K$. A \emph{cycle} (resp.~\emph{path}) \emph{odd-cover} of a graph $G$ is a set $\mathcal{H}$ of cycles (res…

Replaced article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- A Logic of Knowledge and Justifications, with an Application to Computational Trust
Francesco A. Genco

Replaced article(s) found for cs.SE. https://arxiv.org/list/cs.SE/new
[1/1]:
- Predicting the Understandability of Computational Notebooks through Code Metrics Analysis
Ghahfarokhi, Asadi, Asgari, Mohammadi, Heydarnoori, Rizi

Replaced article(s) found for stat.ML. https://arxiv.org/list/stat.ML/new
[1/1]:
Generalized Random Forests using Fixed-Point Trees
https://…

Replaced article(s) found for cs.HC. https://arxiv.org/list/cs.HC/new
[1/1]:
- A Design Space for Multiscale Visualization
Mara Solen, Matt Oddo, Tamara Munzner

Replaced article(s) found for cs.CV. https://arxiv.org/list/cs.CV/new
[1/3]:
Maximizing Information in Domain-Invariant Representation Improves Transfer Learning

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$
Kenji Terao
https://arxiv.org/abs/2507.13199 https://arxiv…

Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$
We give a classification of the degrees of the points with rational $j$-invariant on the modular curves $X_{0}(n)$ and $X_{1}(n)$. The degrees which occur infinitely often are computed unconditionally, while those which occur finitely often are determined assuming a conjecture of Zywina. To achieve this, we define the notion of $\mathcal{H}$-closures of subgroups of $\operatorname{GL}_{2}(\widehat{\mathbb{Z}})$, and compute the $\mathcal{B}_{0}(n)$- and $\mathcal{B}_{1}(n)$-closures of images o…

An exponential improvement for Ramsey lower bounds
Jie Ma, Wujie Shen, Shengjie Xie
https://arxiv.org/abs/2507.12926 https://arxiv.or…

An exponential improvement for Ramsey lower bounds
We prove a new lower bound on the Ramsey number $r(\ell, C\ell)$ for any constant $C > 1$ and sufficiently large $\ell$, showing that there exists $\varepsilon=\varepsilon(C)> 0$ such that \[ r(\ell, C\ell) \geq \left(p_C^{-1/2} + \varepsilon\right)^\ell, \] where $p_C \in (0, 1/2)$ is the unique solution to $C = \frac{\log p_C}{\log(1 - p_C)}$. This provides the first exponential improvement over the classical lower bound obtained by Erdős in 1947.

Replaced article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[1/4]:
OpsEval: A Comprehensive IT Operations Benchmark Suite for Large Language Models

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- A two-sorted theory of nilpotent Lie algebras
Christian d'Elb\'ee, Isabel M\"uller, Nicholas Ramsey, Daoud Siniora

Replaced article(s) found for cs.CY. https://arxiv.org/list/cs.CY/new
[1/1]:
- Inverted Classroom in der Einf\"uhrungsveranstaltung Programmierung
Ulrich von Zadow, Natalie Kiesler

Replaced article(s) found for cs.CL. https://arxiv.org/list/cs.CL/new
[1/4]:
- HiURE: Hierarchical Exemplar Contrastive Learning for Unsupervised Relation Extraction
Shuliang Liu, Xuming Hu, Chenwei Zhang, Shu`ang Li, Lijie Wen, Philip S. Yu

[2025-06-18 Wed (UTC), 1 new article found for cs.PL Programming Languages]
toXiv_bot_toot

Short monochromatic odd cycles
Oliver Janzer, Fredy Yip
https://arxiv.org/abs/2506.14910 https://arxiv.org/pdf/2506.14910

Short monochromatic odd cycles
It is easy to see that every $k$-edge-colouring of the complete graph on $2^k+1$ vertices contains a monochromatic odd cycle. In 1973, Erdős and Graham asked to estimate the smallest $L(k)$ such that every $k$-edge-colouring of $K_{2^k+1}$ contains a monochromatic odd cycle of length at most $L(k)$. Recently, Girão and Hunter obtained the first nontrivial upper bound by showing that $L(k)=O(\frac{2^k}{k^{1-o(1)}})$, which improves the trivial bound by a polynomial factor. We obtain an exponen…

Replaced article(s) found for stat.ML. https://arxiv.org/list/stat.ML/new
[1/1]:
- Local minima of the empirical risk in high dimension: General theorems and convex examples
Kiana Asgari, Andrea Montanari, Basil Saeed

Replaced article(s) found for cs.CV. https://arxiv.org/list/cs.CV/new
[1/4]:
- Bi-VLDoc: Bidirectional Vision-Language Modeling for Visually-Rich Document Understanding
Chuwei Luo, Guozhi Tang, Qi Zheng, Cong Yao, Lianwen Jin, Chenliang Li, Yang Xue, Luo Si

Evaluating Explainability: A Framework for Systematic Assessment and Reporting of Explainable AI Features
Miguel A. Lago, Ghada Zamzmi, Brandon Eich, Jana G. Delfino
https://arxiv.org/abs/2506.13917

Evaluating Explainability: A Framework for Systematic Assessment and Reporting of Explainable AI Features
Explainability features are intended to provide insight into the internal mechanisms of an AI device, but there is a lack of evaluation techniques for assessing the quality of provided explanations. We propose a framework to assess and report explainable AI features. Our evaluation framework for AI explainability is based on four criteria: 1) Consistency quantifies the variability of explanations to similar inputs, 2) Plausibility estimates how close the explanation is to the ground truth, 3) F…

Cyclic proof theory of positive inductive definitions
Gianluca Curzi, Lukas Melgaard
https://arxiv.org/abs/2507.13057 https://arxiv.o…

Cyclic proof theory of positive inductive definitions
We study cyclic proof systems for $μ\mathsf{PA}$, an extension of Peano arithmetic by positive inductive definitions that is arithmetically equivalent to the (impredicative) subsystem of second-order arithmetic $Π^1_2$-$\mathsf{CA}_0$ by Möllefeld. The main result of this paper is that cyclic and inductive $μ\mathsf{PA}$ have the same proof-theoretic strength. First, we translate cyclic proofs into an annotated variant based on Sprenger and Dam's systems for first-order $μ$-calculus, whose…

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
Higher arity stability and the functional order property
https://

Replaced article(s) found for cs.CL. https://arxiv.org/list/cs.CL/new
[1/3]:
Compression of enumerations and gain
https://arxiv…

Curve equations from expansions of 1-forms at a nonrational point
Raymond van Bommel, Edgar Costa, Bjorn Poonen, Padmavathi Srinivasan
https://arxiv.org/abs/2506.14026

Curve equations from expansions of 1-forms at a nonrational point
We exhibit an algorithm to compute equations of an algebraic curve over a computable characteristic 0 field from the power series expansions of its regular 1-forms at a nonrational point of the curve, extending a 2005 algorithm of Baker, González-Jiménez, González, and Poonen for expansions at a rational point. If the curve is hyperelliptic, the equations present it as an explicit double cover of a smooth plane conic, or as a double cover of the projective line when possible. If the curve is…

Approximate polymorphisms of predicates
Yaroslav Alekseev, Yuval Filmus
https://arxiv.org/abs/2506.12155 https://arxiv.org/pdf/2506.1…

Approximate polymorphisms of predicates
A generalized polymorphism of a predicate $P \subseteq \{0,1\}^m$ is a tuple of functions $f_1,\dots,f_m\colon \{0,1\}^n \to \{0,1\}$ satisfying the following property: If $x^{(1)},\dots,x^{(m)} \in \{0,1\}^n$ are such that $(x^{(1)}_i,\dots,x^{(m)}_i) \in P$ for all $i$, then also $(f_1(x^{(1)}),\dots,f_m(x^{(m)})) \in P$. We show that if $f_1,\dots,f_m$ satisfy this property for most $x^{(1)},\dots,x^{(m)}$ (as measured with respect to an arbitrary full support distribution $μ$ on $P$), th…

Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights
Krishnakumar Balasubramanian, Nathan Ross
https://arxiv.org/abs/2507.12686

Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights
We study the Finite-Dimensional Distributions (FDDs) of deep neural networks with randomly initialized weights that have finite-order moments. Specifically, we establish Gaussian approximation bounds in the Wasserstein-$1$ norm between the FDDs and their Gaussian limit assuming a Lipschitz activation function and allowing the layer widths to grow to infinity at arbitrary relative rates. In the special case where all widths are proportional to a common scale parameter $n$ and there are $L-1$ hid…

VisionThink: Smart and Efficient Vision Language Model via Reinforcement Learning
Senqiao Yang, Junyi Li, Xin Lai, Bei Yu, Hengshuang Zhao, Jiaya Jia
https://arxiv.org/abs/2507.13348

VisionThink: Smart and Efficient Vision Language Model via Reinforcement Learning
Recent advancements in vision-language models (VLMs) have improved performance by increasing the number of visual tokens, which are often significantly longer than text tokens. However, we observe that most real-world scenarios do not require such an extensive number of visual tokens. While the performance drops significantly in a small subset of OCR-related tasks, models still perform accurately in most other general VQA tasks with only 1/4 resolution. Therefore, we propose to dynamically proc…

SANGAM: SystemVerilog Assertion Generation via Monte Carlo Tree Self-Refine
Adarsh Gupta, Bhabesh Mali, Chandan Karfa
https://arxiv.org/abs/2506.13983 http…

SANGAM: SystemVerilog Assertion Generation via Monte Carlo Tree Self-Refine
Recent advancements in the field of reasoning using Large Language Models (LLMs) have created new possibilities for more complex and automatic Hardware Assertion Generation techniques. This paper introduces SANGAM, a SystemVerilog Assertion Generation framework using LLM-guided Monte Carlo Tree Search for the automatic generation of SVAs from industry-level specifications. The proposed framework utilizes a three-stage approach: Stage 1 consists of multi-modal Specification Processing using Sign…

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- On homomorphic images of ultraproducts
Samuel M. Corson

Discretized Rotation with fixed initial points
Shigeki Akiyama, Bill Mance
https://arxiv.org/abs/2507.12654 https://arxiv.org/pdf/250…

Discretized Rotation with fixed initial points
We prove that if $\max\{|a_0|,|a_1|\}\le 10$ and $λ\in\ ]-2,2[$, then the sequence defined by $$ 0 \le a_{n+2} +λa_{n+1}+a_n<1 $$ is periodic.

SciVer: Evaluating Foundation Models for Multimodal Scientific Claim Verification
Chengye Wang, Yifei Shen, Zexi Kuang, Arman Cohan, Yilun Zhao
https://arxiv.org/abs/2506.15569

SciVer: Evaluating Foundation Models for Multimodal Scientific Claim Verification
We introduce SciVer, the first benchmark specifically designed to evaluate the ability of foundation models to verify claims within a multimodal scientific context. SciVer consists of 3,000 expert-annotated examples over 1,113 scientific papers, covering four subsets, each representing a common reasoning type in multimodal scientific claim verification. To enable fine-grained evaluation, each example includes expert-annotated supporting evidence. We assess the performance of 21 state-of-the-art…

Neighbor Connectivity of Undirected Toroidal Meshes
Hui-Ming Huang, Ruichao Niu, Min Xu, Jou-Ming Chang
https://arxiv.org/abs/2506.14240 https://

Neighbor Connectivity of Undirected Toroidal Meshes
In this paper, we examine the neighbor connectivity, denoted as $κ_{NB}$, of the undirected toroidal mesh $C(d_1,d_2,\ldots,d_n)$. We demonstrate that $κ_{NB}(C(d_1,d_2,\ldots,d_n)) = n$ for all $n \ge 2$ and $d_i \ge 3$ (for $1 \le i \le n$). Additionally, we perform a computer simulation experiment on neighbor connectivity in undirected toroidal meshes. This experiment not only supports our theoretical findings with empirical results but also provides a deeper understanding of neighbor stru…

VisText-Mosquito: A Multimodal Dataset and Benchmark for AI-Based Mosquito Breeding Site Detection and Reasoning
Md. Adnanul Islam, Md. Faiyaz Abdullah Sayeedi, Md. Asaduzzaman Shuvo, Muhammad Ziaur Rahman, Shahanur Rahman Bappy, Raiyan Rahman, Swakkhar Shatabda
https://arxiv.org/abs/2506.14629

VisText-Mosquito: A Multimodal Dataset and Benchmark for AI-Based Mosquito Breeding Site Detection and Reasoning
Mosquito-borne diseases pose a major global health risk, requiring early detection and proactive control of breeding sites to prevent outbreaks. In this paper, we present VisText-Mosquito, a multimodal dataset that integrates visual and textual data to support automated detection, segmentation, and reasoning for mosquito breeding site analysis. The dataset includes 1,828 annotated images for object detection, 142 images for water surface segmentation, and natural language reasoning texts linked…

HapticCap: A Multimodal Dataset and Task for Understanding User Experience of Vibration Haptic Signals
Guimin Hu, Daniel Hershcovich, Hasti Seifi
https://arxiv.org/abs/2507.13318 …

HapticCap: A Multimodal Dataset and Task for Understanding User Experience of Vibration Haptic Signals
Haptic signals, from smartphone vibrations to virtual reality touch feedback, can effectively convey information and enhance realism, but designing signals that resonate meaningfully with users is challenging. To facilitate this, we introduce a multimodal dataset and task, of matching user descriptions to vibration haptic signals, and highlight two primary challenges: (1) lack of large haptic vibration datasets annotated with textual descriptions as collecting haptic descriptions is time-consum…

Replaced article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
- An introduction to the categorical p-adic Langlands program
Matthew Emerton, Toby Gee, Eugen Hellmann

Automating Steering for Safe Multimodal Large Language Models
Lyucheng Wu, Mengru Wang, Ziwen Xu, Tri Cao, Nay Oo, Bryan Hooi, Shumin Deng
https://arxiv.org/abs/2507.13255

Automating Steering for Safe Multimodal Large Language Models
Recent progress in Multimodal Large Language Models (MLLMs) has unlocked powerful cross-modal reasoning abilities, but also raised new safety concerns, particularly when faced with adversarial multimodal inputs. To improve the safety of MLLMs during inference, we introduce a modular and adaptive inference-time intervention technology, AutoSteer, without requiring any fine-tuning of the underlying model. AutoSteer incorporates three core components: (1) a novel Safety Awareness Score (SAS) that …

Meeting a Challenge raised by Ekhad and Zeilberger related to Stern's Triangle
Jinlong Tang, Guoce Xin
https://arxiv.org/abs/2506.13375 https://…

Meeting a Challenge raised by Ekhad and Zeilberger related to Stern's Triangle
This paper resolves an open problem raised by Ekhad and Zeilberger for computing $ω(10000)$, which is related to Stern's triangle. While $ν(n)$, defined as the sum of squared coefficients in $\prod_{i=0}^{n-1} (1 + x^{2^i} + x^{2^{i+1}})$, admits a rational generating function, the analogous function $ω(n)$ for $\prod_{i=0}^{n-1} (1 + x^{2^i+1} + x^{2^{i+1}+1})$ presents substantial computational difficulties due to its complex structure. We develop a method integrating constant term techn…

Replaced article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
P-adic L-functions for GL(3)
https://arxiv.o…

Multi-Agent Synergy-Driven Iterative Visual Narrative Synthesis
Wang Xi, Quan Shi, Tian Yu, Yujie Peng, Jiayi Sun, Mengxing Ren, Zenghui Ding, Ningguang Yao
https://arxiv.org/abs/2507.13285

Multi-Agent Synergy-Driven Iterative Visual Narrative Synthesis
Automated generation of high-quality media presentations is challenging, requiring robust content extraction, narrative planning, visual design, and overall quality optimization. Existing methods often produce presentations with logical inconsistencies and suboptimal layouts, thereby struggling to meet professional standards. To address these challenges, we introduce RCPS (Reflective Coherent Presentation Synthesis), a novel framework integrating three key components: (1) Deep Structured Narrat…

Transversal packings in families of percolated hypergraphs
Jie Han, Jie Hu, Shunan Wei, Donglei Yang
https://arxiv.org/abs/2507.12740 https://

Transversal packings in families of percolated hypergraphs
Let $F$ be a strictly $1$-balanced $k$-graph on $s$ vertices with $t$ edges and $δ_{F,d}^T$ be the infimum of $δ>0$ such that for every $α>0$ and sufficiently large $n\in \mathbb{N}$, every $k$-graph system $\mathbf H=\{H_{1}, H_{2}, \dots ,H_{tn}\}$ on the same $sn$ vertices with $δ_d(H_i)\ge (δ+α)\binom{sn-d}{k-d}$, $i\in [tn]$ contains a transversal $F$-factor, that is, an $F$-factor consisting of exactly one edge from each $H_i$. In this paper we prove the following result. Let $\math…

The cohomological Kudla conjecture for unitary Shimura varieties
Fran\c{c}ois Greer, Salim Tayou
https://arxiv.org/abs/2507.13299 https://

The cohomological Kudla conjecture for unitary Shimura varieties
We construct natural extensions of the Kudla--Millson generating series of cohomology classes of special cycles in compactified unitary Shimura varieties of signature $(n+1,1)$ and prove that they are holomorphic Hermitian modular forms. This proves the cohomological version of a conjecture of Kudla and Bruinier--Rosu--Zemel, in all codimensions up to the middle. We also develop the theory of Hermitian quasi-modular forms, with a particular focus on polynomial weighted theta functions, and prov…

Massive Supervised Fine-tuning Experiments Reveal How Data, Layer, and Training Factors Shape LLM Alignment Quality
Yuto Harada, Yusuke Yamauchi, Yusuke Oda, Yohei Oseki, Yusuke Miyao, Yu Takagi
https://arxiv.org/abs/2506.14681

Massive Supervised Fine-tuning Experiments Reveal How Data, Layer, and Training Factors Shape LLM Alignment Quality
Supervised fine-tuning (SFT) is a critical step in aligning large language models (LLMs) with human instructions and values, yet many aspects of SFT remain poorly understood. We trained a wide range of base models on a variety of datasets including code generation, mathematical reasoning, and general-domain tasks, resulting in 1,000+ SFT models under controlled conditions. We then identified the dataset properties that matter most and examined the layer-wise modifications introduced by SFT. Our…

Hamiltonian connectivity of some base-cobase graphs
Leonardo Mart\'inez-Sandoval, Kolja Knauer
https://arxiv.org/abs/2506.15049 https://

Hamiltonian connectivity of some base-cobase graphs
There has been wide interest in understanding which properties of base graphs of matroids extend to base-cobase graphs of matroids. A significant result of Naddef and Pulleyblank (1984) shows that the $1$-skeleton of any $(0,1)$-polytope is either a hypercube, or Hamiltonian-connected, i.e. there is a Hamiltonian path connecting any two vertices. In particular, this is true for base graphs of matroids. A natural question raised by Farber, Richter, and Shank (1985) is whether this extends to bas…

Replaced article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
- Semi-stable and splitting models for unitary Shimura varieties over ramified places. I
Ioannis Zachos, Zhihao Zhao

WikiMixQA: A Multimodal Benchmark for Question Answering over Tables and Charts
Negar Foroutan, Angelika Romanou, Matin Ansaripour, Julian Martin Eisenschlos, Karl Aberer, R\'emi Lebret
https://arxiv.org/abs/2506.15594

WikiMixQA: A Multimodal Benchmark for Question Answering over Tables and Charts
Documents are fundamental to preserving and disseminating information, often incorporating complex layouts, tables, and charts that pose significant challenges for automatic document understanding (DU). While vision-language large models (VLLMs) have demonstrated improvements across various tasks, their effectiveness in processing long-context vision inputs remains unclear. This paper introduces WikiMixQA, a benchmark comprising 1,000 multiple-choice questions (MCQs) designed to evaluate cross-…

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
Pattern-avoiding modified ascent sequences
https://

Is it easy to regularize a hypergraph with easy links?
Lior Gishboliner, Asaf Shapira, Yuval Wigderson
https://arxiv.org/abs/2506.15582 https://

Is it easy to regularize a hypergraph with easy links?
A partition of a (hyper)graph is $\varepsilon$-homogenous if the edge densities between almost all clusters are either at most $\varepsilon$ or at least $1-\varepsilon$. Suppose a $3$-graph has the property that the link of every vertex has an $\varepsilon$-homogenous partition of size $\text{poly}(1/\varepsilon)$. Does this guarantee that the $3$-graph also has a small homogenous partition? Terry and Wolf proved that such a $3$-graph has an $\varepsilon$-homogenous partition of size given by a…

Proof of a conjecture on eigenvalues of transposition graph
Cheng Yeaw Ku, Leyou Xu
https://arxiv.org/abs/2506.14419 https://arxiv.or…

Proof of a conjecture on eigenvalues of transposition graph
The transposition graph $Cay(S_n,T_n)$ is the Cayley graph on the symmetric group $S_n$ generated by the set $T_n$ of all transpositions. In this paper, we show that each integer in the interval $\left[-{\lfloor(2n+1)/3 \rfloor\choose 2}, {\lfloor(2n+1)/3 \rfloor\choose 2}\right]$ is an eigenvalue of $Cay(S_n,T_n)$. This proves a recent conjecture by Kravchuk \cite{Kravchuk}.

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
- Size of the largest sum-free subset of $[n]^3$, $[n]^4$, and $[n]^5$
Saba Lepsveridze, Yihang Sun

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
- Long mutation cycles
Sergey Fomin, Scott Neville
https:…

What is and is not inside a Cayley graph?
Kolja Knauer, Alvaro Soto Gomez
https://arxiv.org/abs/2506.14088 https://arxiv.org/pdf/2506…

What is and is not inside a Cayley graph?
In this note we show that there is a cubic graph of girth $5$ that is not a subgraph of any minimal Cayley graph. On the other hand, we show that any Generalized Petersen Graph $G(n,k)$ with $\gcd(n,k)=1$ is an induced subgraph of a minimal Cayley graph. These results give insights into two comments of László Babai in [L. Babai, \emph{Automorphism groups, isomorphism, reconstruction}. Graham, R. L. (ed.) et al., Handbook of combinatorics. Vol. 1-2, 1994].

Beyond the MaxCut problem in $H$-free graphs
Zhihan Jin, Aleksa Milojevi\'c, Istv\'an Tomon
https://arxiv.org/abs/2507.13298 https://

Beyond the MaxCut problem in $H$-free graphs
In a recent breakthrough, Zhang proves that if $G$ is an $H$-free graph with $m$ edges, then $G$ has a cut of size at least $m/2+c_Hm^{0.5001}$, making a significant step towards a well known conjecture of Alon, Bollobás, Krivelevich and Sudakov. We show that the methods of Zhang can be further boosted, and prove the following strengthening. If $G$ is a graph with $m$ edges and no clique of size $m^{1/2-δ}$, then $G$ has a cut of size at least $m/2+m^{1/2+\varepsilon}$ for some $\varepsilon=\…