Journal of Algebraic Combinatorics最新文献_第5页

Distance spectral radii of k-uniform hypertrees with fixed diameter 具有固定直径的 k 个均匀肥大树的距离谱半径

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-04-06 DOI: 10.1007/s10801-024-01316-z

引用次数: 0

Calculations of the Euler characteristic of the Coxeter cohomology of symmetric groups 对称群 Coxeter 同调的欧拉特征计算

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-04-04 DOI: 10.1007/s10801-024-01307-0

Hayley Bertrand

{"title":"Calculations of the Euler characteristic of the Coxeter cohomology of symmetric groups","authors":"Hayley Bertrand","doi":"10.1007/s10801-024-01307-0","DOIUrl":"https://doi.org/10.1007/s10801-024-01307-0","url":null,"abstract":"This work is part of a research program to compute the Hochschild homology groups HH(_*({mathbb {C}}[x_1,ldots ,x_d]/(x_1,ldots ,x_d)^3;{mathbb {C}})) in the case (d = 2) through a lesser-known invariant called Coxeter cohomology, motivated by the isomorphism $$begin{aligned}text {HH}_i({mathbb {C}}[x_1,ldots ,x_d]/(x_1,ldots ,x_d)^3;{mathbb {C}}) cong sum _{0le j le i} H^j_C left( S_{i+j}, V^{otimes (i+j)}right) end{aligned}$$provided by Larsen and Lindenstrauss. Here, (H_C^*) denotes Coxeter cohomology, (S_{i+j}) denotes the symmetric group on (i+j) letters, and V is the standard representation of (textrm{GL}_d({mathbb {C}})) on ({mathbb {C}}^d). We compute the Euler characteristic of the Coxeter cohomology (the alternating sum of the ranks of the Coxeter cohomology groups) of several representations of (S_n). In particular, the aforementioned tensor representation, and also several classes of irreducible representations of (S_n). Although the problem and its motivation are algebraic and topological in nature, the techniques used are largely combinatorial.","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"49 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140564887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Classification of cyclic groups underlying only smooth skew morphisms 仅以光滑偏斜变形为基础的循环群的分类

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-04-03 DOI: 10.1007/s10801-024-01311-4

引用次数: 0

Weakly distance-regular digraphs whose underlying graphs are distance-regular, I 其底层图是距离规则的弱距离规则数图，I

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-04-02 DOI: 10.1007/s10801-024-01312-3

Yuefeng Yang, Qing Zeng, Kaishun Wang

引用次数: 0

Generalized non-coprime graphs of groups 群的广义非可普赖图

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-04-01 DOI: 10.1007/s10801-024-01310-5

S. Anukumar Kathirvel, Peter J. Cameron, T. Tamizh Chelvam

{"title":"Generalized non-coprime graphs of groups","authors":"S. Anukumar Kathirvel, Peter J. Cameron, T. Tamizh Chelvam","doi":"10.1007/s10801-024-01310-5","DOIUrl":"https://doi.org/10.1007/s10801-024-01310-5","url":null,"abstract":"Let G be a finite group with identity e and ( H ne {e}) be a subgroup of G. The generalized non-coprime graph (varGamma _{G,H}) of ( G ) with respect to (H) is the simple undirected graph with (G setminus {e }) as the vertex set and two distinct vertices ( x ) and ( y) are adjacent if and only if (gcd (|x|,|y|) ne 1) and either (x in H) or (y in H), where |x| is the order of (xin G). In this paper, we study certain graph theoretical properties of generalized non-coprime graphs of finite groups, concentrating on cyclic groups. More specifically, we obtain necessary and sufficient conditions for the generalized non-coprime graph of a cyclic group to be in the class of stars, paths, triangle-free, complete bipartite, complete, split, claw-free, chordal or perfect graphs. Then we show that widening the class of groups to all finite nilpotent groups gives us no new graphs, but we give as an example of contrasting behaviour the class of EPPO groups (those in which all elements have prime power order). We conclude with a connection to the Gruenberg–Kegel graph.\u0000","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140597289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Higher resonance schemes and Koszul modules of simplicial complexes 简单复数的高级共振方案和科斯祖尔模块

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-03-29 DOI: 10.1007/s10801-024-01313-2

Marian Aprodu, Gavril Farkas, Claudiu Raicu, Alessio Sammartano, Alexander I. Suciu

引用次数: 0

Matchings in matroids over abelian groups 无边群矩阵中的匹配

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-03-27 DOI: 10.1007/s10801-024-01308-z

Mohsen Aliabadi, Shira Zerbib

引用次数: 0

Bi-primitive 2-arc-transitive bi-Cayley graphs 双元 2-弧-直角双 Cayley 图形

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-03-02 DOI: 10.1007/s10801-024-01297-z

Jing Jian Li, Xiao Qian Zhang, Jin-Xin Zhou

引用次数: 0

On regular sets in Cayley graphs 关于 Cayley 图中的规则集合

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-03-02 DOI: 10.1007/s10801-024-01298-y

Xiaomeng Wang, Shou-Jun Xu, Sanming Zhou

{"title":"On regular sets in Cayley graphs","authors":"Xiaomeng Wang, Shou-Jun Xu, Sanming Zhou","doi":"10.1007/s10801-024-01298-y","DOIUrl":"https://doi.org/10.1007/s10801-024-01298-y","url":null,"abstract":"Let (Gamma = (V, E)) be a graph and a, b nonnegative integers. An (a, b)-regular set in (Gamma ) is a nonempty proper subset D of V such that every vertex in D has exactly a neighbours in D and every vertex in (V{setminus }D) has exactly b neighbours in D. A (0, 1)-regular set is called a perfect code, an efficient dominating set, or an independent perfect dominating set. A subset D of a group G is called an (a, b)-regular set of G if it is an (a, b)-regular set in some Cayley graph of G, and an (a, b)-regular set in a Cayley graph of G is called a subgroup (a, b)-regular set if it is also a subgroup of G. In this paper, we study (a, b)-regular sets in Cayley graphs with a focus on (0, k)-regular sets, where (k ge 1) is an integer. Among other things, we determine when a non-trivial proper normal subgroup of a group is a (0, k)-regular set of the group. We also determine all subgroup (0, k)-regular sets of dihedral groups and generalized quaternion groups. We obtain necessary and sufficient conditions for a hypercube or the Cartesian product of n copies of the cycle of length p to admit (0, k)-regular sets, where p is an odd prime. Our results generalize several known results from perfect codes to (0, k)-regular sets.","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"261 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Power graphs of a class of completely 0-simple semigroups 一类完全 0 简单半群的幂图

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-02-26 DOI: 10.1007/s10801-024-01306-1

Yanliang Cheng, Yong Shao, Lingli Zeng

引用次数: 0