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A Unified Framework for Integer Programming Formulation of Graph Matching Problems
Bahram Alidaee, Haibo Wang, Hugh Sloan
https://arxiv.org/abs/2406.07666 …

A Unified Framework for Integer Programming Formulation of Graph Matching Problems
Graph theory has been a powerful tool in solving difficult and complex problems arising in all disciplines. In particular, graph matching is a classical problem in pattern analysis with enormous applications. Many graph problems have been formulated as a mathematical program and then solved using exact, heuristic, and/or approximated-guaranteed procedures. On the other hand, graph theory has been a powerful tool in visualizing and understanding complex mathematical programming problems, especia…

Extending class group action attacks via sesquilinear pairings
Joseph Macula, Katherine E. Stange
https://arxiv.org/abs/2406.10440 https://

Extending class group action attacks via sesquilinear pairings
We introduce a new tool for the study of isogeny-based cryptography, namely pairings which are sesquilinear (conjugate linear) with respect to the $\mathcal{O}$-module structure of an elliptic curve with CM by an imaginary quadratic order $\mathcal{O}$. We use these pairings to study the security of problems based on the class group action on collections of oriented ordinary or supersingular elliptic curves. This extends work of both (Castryck, Houben, Merz, Mula, Buuren, Vercauteren, 2023) and…

Group theory of cyclic cubic number fields
Daniel C. Mayer, Siham Aouissi, Bill Allombert, Abderazak Soullami
https://arxiv.org/abs/2406.06030 https://

Group theory of cyclic cubic number fields
Astonishing new discoveries with quartets and octets of cyclic cubic fields sharing a common conductor are presented. Four kinds of graphs describing cubic residue conditions among the prime divisors of the conductor enforce elementary bi- or tricyclic 3-class groups and either a metabelian 3-class field tower group of coclass at least two or a closed Andozhskii-Tsvetkov group of order 6561. In the latter situation, abelian type invariants of first and second order are required for the identifi…

On the block size spectrum of the multiplicative Beta coalescent
Frederic Alberti, Florin Boenkost, Fernando Cordero
https://arxiv.org/abs/2406.08972 https…

On the block size spectrum of the multiplicative Beta coalescent
In this work we introduce the (exchangeable, but non-consistent) multiplicative $Λ$-coalescent, which accounts for the connected components (blocks) of the dynamic $Λ$-random graph. This is the random graph analogue of the classical $Λ$-coalescent studied in mathematical population genetics; it is an exchangeable and consistent random graph process. This work considers the case where $Λ$ is the beta measure. We prove a dynamic law of large numbers for the numbers of blocks containing $1,...…

The Genesis of a Theorem
John Labute
https://arxiv.org/abs/2406.08233 https://arxiv.org/pdf/2406.08233…

The Genesis of a Theorem
In this article we trace the genesis of a theorem that gives for the first time examples of Galois group $G_S$ of the maximal $p$-extension of $\mathbb{Q}$, unramified outside a finite set of primes not containing $p$, that are of cohomological dimension $2$. The pro-$p$-group $G_S$ is a fab pro-$p$-group which means that all its derived factors are finite.

This https://arxiv.org/abs/2405.14084 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Algebraic Independence of Special Points on Shimura Varieties
Given a correspondence $V$ between a connected Shimura variety $S$, a commutative connected algebraic group $G$, and $n \in \mathbb{N}$, we prove that the $V$-images of any $n$ special points on $S$ outside a proper Zariski closed subset are algebraically independent. Our result unifies previous unlikely intersection results on multiplicative independence and linear independence. We prove multiplicative independence of differences of singular moduli, generalizing previous results by Pila-Tsimer…

On the block size spectrum of the multiplicative Beta coalescent
Frederic Alberti, Florin Boenkost, Fernando Cordero
https://arxiv.org/abs/2406.08972 https…

On the block size spectrum of the multiplicative Beta coalescent
In this work we introduce the (exchangeable, but non-consistent) multiplicative $Λ$-coalescent, which accounts for the connected components (blocks) of the dynamic $Λ$-random graph. This is the random graph analogue of the classical $Λ$-coalescent studied in mathematical population genetics; it is an exchangeable and consistent random graph process. This work considers the case where $Λ$ is the beta measure. We prove a dynamic law of large numbers for the numbers of blocks containing $1,...…

This https://arxiv.org/abs/2304.05035 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Ideal class groups of division fields of elliptic curves and everywhere unramified rational points
Let $E$ be an elliptic curve over $\mathbb{Q}$, $p$ an odd prime number and $n$ a positive integer. In this article, we investigate the ideal class group $\mathrm{Cl}(\mathbb{Q}(E[p^n]))$ of the $p^n$-division field $\mathbb{Q}(E[p^n])$ of $E$. We introduce a certain subgroup $E(\mathbb{Q})_{\mathrm{ur},p^n}$ of $E(\mathbb{Q})$ and study the $p$-adic valuation of the class number $\#\mathrm{Cl}(\mathbb{Q}(E[p^n]))$. In addition, when $n = 1$, we further study $\mathrm{Cl}(\mathbb{Q}(E[p]))$ as …

This https://arxiv.org/abs/2403.16603 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Zp-extensions of a totally p-adic imaginary quadratic field -- With an appendix by Jean-François Jaulent
Let k be an imaginary quadratic field, and let p be an odd prime number split in k. We analyze some properties of arbitrary Zp-extensions K/k. These properties are governed by the Hase norm residue symbol of the fundamental p-unit of k, in terms of the valuation $δ$p(k) of a Fermat quotient, which determines the order of the logarithmic class group Clogk (Theorem 2.2, Appendix 1) and leads, under some conditions, to generalizations of Gold's criterion characterizing $λ$p(K/k) = 1 (Theorems 5.…

Fourier transform in cyclic groups
Yves Benoist (CNRS)
https://arxiv.org/abs/2406.11529 https://arxiv.org/pdf/2406.11529

Fourier transform in cyclic groups
On a cyclic group of prime order, the non-trivial Dirichlet characters together with their Fourier transforms are functions that vanish at 0 and whose modulus is constant outside 0. Answering a question of H. Cohn, we construct new functions with these properties for non-safe primes. The proof relies on Floer homology. In the appendix we also apply this method to the biunimodular functions problem.