Algebraic Combinatorics最新文献_第5页

Resolutions of local face modules, functoriality, and vanishing of local h-vectors 局部面模的分辨率、函数性和局部h向量的消失

Algebraic Combinatorics Pub Date : 2022-09-08 DOI: 10.5802/alco.293

Matt Larson, S. Payne, A. Stapledon

引用次数: 0

Independent Spaces of q-Polymatroids q-多拟阵的独立空间

Algebraic Combinatorics Pub Date : 2022-09-08 DOI: 10.5802/alco.241

H. Gluesing-Luerssen, B. Jany

引用次数: 1

A generalisation of bar-core partitions 条形核心分区的推广

Algebraic Combinatorics Pub Date : 2022-09-08 DOI: 10.5802/alco.231

Dean Yates

引用次数: 2

Maximality of subfields as cliques in Cayley graphs over finite fields 有限域上Cayley图中作为群的子域的极大性

Algebraic Combinatorics Pub Date : 2022-09-02 DOI: 10.5802/alco.291

Chi Hoi Yip

引用次数: 3

Geometric vertex decomposition and liaison for toric ideals of graphs 图的几何顶点分解与环向理想联络

Algebraic Combinatorics Pub Date : 2022-07-13 DOI: 10.5802/alco.295

Mike Cummings, S. Silva, Jenna Rajchgot, A. Tuyl

{"title":"Geometric vertex decomposition and liaison for toric ideals of graphs","authors":"Mike Cummings, S. Silva, Jenna Rajchgot, A. Tuyl","doi":"10.5802/alco.295","DOIUrl":"https://doi.org/10.5802/alco.295","url":null,"abstract":"The geometric vertex decomposability property for polynomial ideals is an ideal-theoretic generalization of the vertex decomposability property for simplicial complexes. Indeed, a homogeneous geometrically vertex decomposable ideal is radical and Cohen-Macaulay, and is in the Gorenstein liaison class of a complete intersection (glicci). In this paper, we initiate an investigation into when the toric ideal $I_G$ of a finite simple graph $G$ is geometrically vertex decomposable. We first show how geometric vertex decomposability behaves under tensor products, which allows us to restrict to connected graphs. We then describe a graph operation that preserves geometric vertex decomposability, thus allowing us to build many graphs whose corresponding toric ideals are geometrically vertex decomposable. Using work of Constantinescu and Gorla, we prove that toric ideals of bipartite graphs are geometrically vertex decomposable. We also propose a conjecture that all toric ideals of graphs with a square-free degeneration with respect to a lexicographic order are geometrically vertex decomposable. As evidence, we prove the conjecture in the case that the universal Gr\"obner basis of $I_G$ is a set of quadratic binomials. We also prove that some other families of graphs have the property that $I_G$ is glicci.","PeriodicalId":36046,"journal":{"name":"Algebraic Combinatorics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44752809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

A tensor-cube version of the Saxl conjecture Saxl猜想的张量立方体版本

Algebraic Combinatorics Pub Date : 2022-06-28 DOI: 10.5802/alco.267

Nate Harman, Christopher Ryba

引用次数: 1

Strong cospectrality in trees 树的强共谱性

Algebraic Combinatorics Pub Date : 2022-06-07 DOI: 10.5802/alco.288

G. Coutinho, Emanuel Juliano, Thomás Jung Spier

引用次数: 1

Fusions of tensor powers of Johnson schemes Johnson格式张量幂的融合

Algebraic Combinatorics Pub Date : 2022-05-23 DOI: 10.5802/alco.271

Sean Eberhard, M. Muzychuk

引用次数: 1

Arkhipov’s theorem, graph minors, and linear system nonlocal games Arkhipov定理，图子和线性系统非局部对策

Algebraic Combinatorics Pub Date : 2022-05-10 DOI: 10.5802/alco.292

Connor Paddock, Vincent Russo, Turner Silverthorne, William Slofstra

{"title":"Arkhipov’s theorem, graph minors, and linear system nonlocal games","authors":"Connor Paddock, Vincent Russo, Turner Silverthorne, William Slofstra","doi":"10.5802/alco.292","DOIUrl":"https://doi.org/10.5802/alco.292","url":null,"abstract":"The perfect quantum strategies of a linear system game correspond to certain representations of its solution group. We study the solution groups of graph incidence games, which are linear system games in which the underlying linear system is the incidence system of a (non-properly) two-coloured graph. While it is undecidable to determine whether a general linear system game has a perfect quantum strategy, for graph incidence games this problem is solved by Arkhipov's theorem, which states that the graph incidence game of a connected graph has a perfect quantum strategy if and only if it either has a perfect classical strategy, or the graph is nonplanar. Arkhipov's criterion can be rephrased as a forbidden minor condition on connected two-coloured graphs. We extend Arkhipov's theorem by showing that, for graph incidence games of connected two-coloured graphs, every quotient closed property of the solution group has a forbidden minor characterization. We rederive Arkhipov's theorem from the group theoretic point of view, and then find the forbidden minors for two new properties: finiteness and abelianness. Our methods are entirely combinatorial, and finding the forbidden minors for other quotient closed properties seems to be an interesting combinatorial problem.","PeriodicalId":36046,"journal":{"name":"Algebraic Combinatorics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44410792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Explicit spherical designs 显式球面设计

Algebraic Combinatorics Pub Date : 2022-05-05 DOI: 10.5802/alco.213

Ziqing Xiang

引用次数: 2