Journal of Algebraic Combinatorics最新文献_第6页

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

Alternating groups as products of cycle classes - II 作为周期类乘积的交替群 - II

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-02-26 DOI: 10.1007/s10801-024-01305-2

Harish Kishnani, Rijubrata Kundu, Sumit Chandra Mishra

{"title":"Alternating groups as products of cycle classes - II","authors":"Harish Kishnani, Rijubrata Kundu, Sumit Chandra Mishra","doi":"10.1007/s10801-024-01305-2","DOIUrl":"https://doi.org/10.1007/s10801-024-01305-2","url":null,"abstract":"Given integers (k,lge 2), where either l is odd or k is even, let n(k, l) denote the largest integer n such that each element of (A_n) is a product of k many l-cycles. M. Herzog, G. Kaplan and A. Lev conjectured that (lfloor frac{2kl}{3} rfloor le n(k,l)le lfloor frac{2kl}{3}rfloor +1) [Herzog et al. in J Combin Theory Ser A, 115:1235-1245 2008]. It is known that the conjecture holds when (k=2,3,4). Moreover, it is also true when (3mid l). In this article, we determine the exact value of n(k, l) when (3not mid l) and (kge 5). As an immediate consequence, we get that (n(k,l)<lfloor frac{2kl}{3}rfloor ) when (kge 5) and (3not mid l), which shows that the above conjecture is not true in general. In fact in this case, the difference between the exact value of n(k, l) and the conjectured value grows linearly in terms of k. Our results complete the determination of n(k, l) for all values of k and l.","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"41 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969121","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

Anti-dendriform algebras, new splitting of operations and Novikov-type algebras 反树枝形代数、新拆分运算和诺维科夫型代数

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-02-26 DOI: 10.1007/s10801-024-01303-4

{"title":"Anti-dendriform algebras, new splitting of operations and Novikov-type algebras","authors":"","doi":"10.1007/s10801-024-01303-4","DOIUrl":"https://doi.org/10.1007/s10801-024-01303-4","url":null,"abstract":"<h3>Abstract</h3> We introduce the notion of an anti-dendriform algebra as a new approach of splitting the associativity. It is characterized as the algebra with two multiplications giving their left and right multiplication operators, respectively, such that the opposites of these operators define a bimodule structure on the sum of these two multiplications, which is associative. This justifies the terminology due to a closely analogous characterization of a dendriform algebra. The notions of anti- ({mathcal {O}}) -operators and anti-Rota–Baxter operators on associative algebras are introduced to interpret anti-dendriform algebras. In particular, there are compatible anti-dendriform algebra structures on associative algebras with nondegenerate commutative Connes cocycles. There is an important observation that there are correspondences between certain subclasses of dendriform and anti-dendriform algebras in terms of q-algebras. As a direct consequence, we give the notion of Novikov-type dendriform algebras as an analogue of Novikov algebras for dendriform algebras, whose relationship with Novikov algebras is consistent with the one between dendriform and pre-Lie algebras. Finally, we extend to provide a general framework of introducing the notions of analogues of anti-dendriform algebras, which interprets a new splitting of operations.","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"7 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140006966","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

Resistance diameters and critical probabilities of Cayley graphs on irreducible complex reflection groups 不可还原复反射群上 Cayley 图的电阻直径和临界概率

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-02-25 DOI: 10.1007/s10801-024-01302-5

Maksim Vaskouski, Hanna Zadarazhniuk

引用次数: 0

Multi-part cross-intersecting families 多部分交叉族

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-02-25 DOI: 10.1007/s10801-024-01301-6

Yuanxiao Xi, Xiangliang Kong, Gennian Ge

引用次数: 0

Common transversals and complements in abelian groups 无边群中的公共横截面和补集

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-02-24 DOI: 10.1007/s10801-024-01299-x

引用次数: 0

Using mixed dihedral groups to construct normal Cayley graphs and a new bipartite 2-arc-transitive graph which is not a Cayley graph 利用混合二面群构建正常的 Cayley 图和一种新的非 Cayley 图的双方形 2 弧形传递图

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-02-23 DOI: 10.1007/s10801-024-01300-7

Daniel R. Hawtin, Cheryl E. Praeger, Jin-Xin Zhou

引用次数: 0

A note on “Largest independent sets of certain regular subgraphs of the derangement graph” 关于 "错乱图的某些规则子图的最大独立集 "的说明

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-02-23 DOI: 10.1007/s10801-024-01304-3

Yuval Filmus, Nathan Lindzey

引用次数: 0