期刊：
JOURNAL OF GROUP THEORY,2024年27(1):61-88 ISSN：1433-5883
通讯作者：
Gang Chen
作者机构：
[Chen, Gang; Ren, Qing] School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China;[Ponomarenko, Ilia] Steklov Institute of Mathematics at St. Petersburg, St. Petersburg, Russia
通讯机构：
[Gang Chen] S;School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China
摘要：
For any finite group 𝐺 and a positive integer 𝑚, we define and study a Schur ring over the direct power G m , which gives an algebraic interpretation of the partition of G m obtained by the 𝑚-dimensional Weisfeiler–Leman algorithm. It is proved that this ring determines the group 𝐺 up to isomorphism if m ≥ 3 , and approaches the Schur ring associated with the group Aut ( G ) acting on G m naturally if 𝑚 increases. It turns out that the problem of finding this limit ring is polynomial-time equivalent to the group isomorphism problem.
摘要：
Schur rings over the infinite dihedral group Z (sic) Z(2) are studied according to properties of Schur rings over infinite groups and the classification of Schur rings over infinite cyclic groups. Schur rings over Z (sic) Z(2) are classified under the assumption that Z is an A-subgroup. Those Schur rings are proved to be traditional.
期刊：
Applied Mathematics and Computation,2023年445:127842 ISSN：0096-3003
通讯作者：
Zhang, Shunzhe(shunzhezhang@hubu.edu.cn)
作者机构：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Chen, Yuan] Wuhan Text Univ, Res Ctr Nonlinear Sci, Sch Math & Phys Sci, Wuhan 430073, Peoples R China.;[Hu, Zhiquan] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Zhang, Shunzhe] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.
通讯机构：
[Shunzhe Zhang] H;Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, PR China
摘要：
In this paper, we study fusion categories which contain a proper fusion subcategory with maximal rank. They are generalizations of near-group fusion categories. We first prove that they admit spherical structure. We then classify those which are non-degenerate or symmetric. Finally, we classify such fusion categories of rank 4. (c) 2022 Elsevier Inc. All rights reserved.
摘要：
Let G be a finite group, H be a proper subgroup of G, and S be a unitary subring of C. The kernel of the restriction map S[Irr(G)] → S[Irr(H)] as a ring homomorphism is studied. As a corollary, the main result in [Isaacs, I. M. and Navarro, G., Injective restriction of characters, Arch. Math., 108, 2017, 437–439] is reproved.
作者机构：
[Chen, Gang; Ponomarenko, Ilia] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Ponomarenko, Ilia] Steklov Inst Math St Petersburg, St Petersburg, Russia.;[Ponomarenko, Ilia] Sobolev Inst Math, Novosibirsk, Russia.
通讯机构：
[Gang Chen] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, China
摘要：
A Cartesian decomposition of a coherent configuration
$${\cal X}$$
is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of
$${\cal X}$$
comes from a certain Cartesian decomposition. It is proved that if the coherent configuration
$${\cal X}$$
is thick, then there is a unique maximal Cartesian decomposition of
$${\cal X}$$
, i.e., there is exactly one internal tensor decomposition of
$${\cal X}$$
into indecomposable components. In particular, this implies an analog of the Krull-Schmidt theorem for the thick coherent configurations. A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.
期刊：
Journal of Algebraic Combinatorics,2021年53(2):435-454 ISSN：0925-9899
通讯作者：
Xu, Bangteng
作者机构：
[Chen, Gang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Xu, Bangteng] Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
通讯机构：
[Xu, Bangteng] E;Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
关键词：
Association schemes;Thin residues;Automorphism groups;Schurian schemes;\(O^{\vartheta }\)(S)-feasible association schemes
摘要：
The schurity of association schemes has been studied in many papers. One of the major topics is to investigate the schurity of those association schemes whose thin residues are thin. A difficult case is that the thin residue is an elementary abelian p-group of rank 2. A class of these association schemes has played an important role in the study of p-schemes of order
$$p^3$$
. In this paper, we study the automorphism groups and schurity problem of this class of association schemes. In particular, we will establish very simple sufficient (and necessary) conditions for these association schemes to be schurian. As an application, we obtain two infinite families of schurian association schemes.
作者机构：
[Hao, Yanli; Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Hao, Yanli] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Yanli Hao] D;Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA<&wdkj&>Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China
关键词：
Dense random graphs;Gallai's path partition conjecture;k-degenerate graph;Linear arboricity conjecture
摘要：
A graph is a linear forest if each of its components is a path. Given a graph G with maximum degree Delta(G), motivated by the famous linear arboricity conjecture and Lovasz's classic result on partitioning the edge set of a graph into paths, we call a partition F:=F-1 vertical bar...vertical bar F-k of the edge set of G an exact linear forest partition if each F-i induces a linear forest, k <= left perpendicular Delta(G)+1/2right perpendicular, and every vertex v is an element of V(G) is on at most left perpendiculardG(v)+1/2right perpendicular non-trivial paths belonging to F. In this paper, we prove the following two results. Every 2-degenerate graph has an exact linear forest partition, and so does every series-parallel graph, every outerplanar graph, and every subdivision of any graph provided each edge of the original graph is subdivided at least once. Let p is an element of(0,1) be a constant. If G similar to G(n,p), then a.a.s. G has an exact linear forest partition. (C) 2021 Elsevier B.V. All rights reserved.
期刊：
ARS MATHEMATICA CONTEMPORANEA,2021年21(1) ISSN：1855-3966
通讯作者：
Ponomarenko, I.
作者机构：
[He, Jiawei; Chen, Gang] School of Mathematics and Statistics, Central China Normal University, Wuhan, China;Steklov Institute of Mathematics, St. Petersburg, Russian Federation;Sobolev Institute of Mathematics, Novosibirsk, Russian Federation;School of Mathematics, Statistics of Central China Normal University, Wuhan, China;Novosibirsk State University, Novosibirsk, Russian Federation
通讯机构：
[Ponomarenko, I.] S;Steklov Institute of MathematicsRussian Federation
关键词：
Association schemes;Coherent configurations;Groups
期刊：
JOURNAL OF COMBINATORIAL THEORY SERIES B,2019年139:128-162 ISSN：0095-8956
通讯作者：
Jing, Guangming
作者机构：
[Chen, Guantao; Jing, Guangming] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Chen, Guantao] Cent China Normal Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.
通讯机构：
[Jing, Guangming] G;Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.
关键词：
Chromatic index;Graph density;Critical chromatic graph;Tashkinov tree
摘要：
Let G be a graph with possible multiple edges but no loops. The density of G, denoted by rho(G) , is defined as max(H subset of G, vertical bar V(H)vertical bar >= 2) inverted right perpendicular vertical bar E(H)vertical bar/left perpendicular vertical bar V(H)vertical bar/2 right perpendicular inverted left perpendicular. Goldberg (1973) and Seymour (1974) independently conjectured that if the chromatic index chi'(G) satisfies chi'(G) >= Delta(G) + 2 then chi'(G) = rho(G), which is commonly regarded as Goldberg's conjecture. An equivalent conjecture, usually credited to Jakobsen, states that for any odd integer m >= 3, if chi'(G) >= m Delta(G)/m-1 + m-3/m-1 then chi'(G) = rho(G). The Tashkinov tree technique, a common generalization of Vizing fans and Kierstead paths for multigraphs, has emerged as the main tool to attack these two conjectures. On the other hand, Asplund and McDonald recently showed that there is a limitation to this method. In this paper, we will go beyond Tashkinov trees and provide a much larger extended structure, using which we see hope to tackle the conjecture. Applying this new technique, we show that the Goldberg's conjecture holds for graphs with Delta(G) <= 39, or vertical bar V(G)vertical bar <= 39 and the Jakobsen Conjecture holds for m <= 39, where the previously known best bound is 23. We also improve a number of other related results. (C) 2019 Elsevier Inc. All rights reserved.
作者机构：
[Chen, Gang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Xu, Bangteng] Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
通讯机构：
[Xu, Bangteng] E;Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
关键词：
Character tables;Closed subsets;Generalized wreath products;Table algebras;Association schemes
摘要：
Graph edge coloring has a rich theory, many applications and beautiful conjectures, and it is studied not only by mathematicians, but also by computer scientists. In this survey, written for the non-expert, we shall describe some main results and techniques and state some of the many popular conjectures in the theory. Besides known results a new basic result about brooms is obtained.
期刊：
Communications in Algebra,2018年46(8):3510-3519 ISSN：0092-7872
通讯作者：
Xu, Bangteng
作者机构：
[Chen, Gang] Cent China Normal Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.;[Xu, Bangteng] Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
通讯机构：
[Xu, Bangteng] E;Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
关键词：
Character tables;closed subsets;dual C-algebras;finite groups;generalized wreath products;table algebras
期刊：
Journal of Algebra,2017年488:201-229 ISSN：0021-8693
通讯作者：
Ponomarenko, Ilia
作者机构：
[Chen, Gang] Cent China Normal Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.;[Ponomarenko, Ilia] Steklov Inst Math, St Petersburg, Russia.
通讯机构：
[Ponomarenko, Ilia] S;Steklov Inst Math, St Petersburg, Russia.
摘要：
Let X be a coherent configuration associated with a transitive group G. In terms of the intersection numbers of X, a necessary condition for the point stabilizer of G to be a TI-subgroup, is established. Furthermore, under this condition, X is determined up to isomorphism by the intersection numbers. It is also proved that asymptotically, this condition is also sufficient. More precisely, an arbitrary homogeneous coherent configuration satisfying this condition is associated with a transitive group, the point stabilizer of which is a TI-subgroup. As a byproduct of the developed theory, recent results on pseudocyclic and quasi-thin association schemes are generalized and improved. In particular, it is shown that any scheme of prime degree p and valency k is associated with a transitive group, whenever p > 1 + 6k(k - 1)(2). (C) 2017 Elsevier Inc. All rights reserved.
期刊：
SIAM JOURNAL ON DISCRETE MATHEMATICS,2017年31(4):2429-2439 ISSN：0895-4801
通讯作者：
Chen, Guantao
作者机构：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Chen, Guantao] Cent China Normal Univ, Fac Math & Stat, Wuhan, Hubei, Peoples R China.;[Enomoto, Hikoe] Waseda Univ, Grad Sch Econ, Tokyo 1698050, Japan.;[Ozeki, Kenta] Yokohama Natl Univ, Fac Environm & Informat Sci, Yokohama, Kanagawa 2408501, Japan.;[Tsuchiya, Shoichi] Senshu Univ, Sch Network & Informat, Kawasaki, Kanagawa 2148580, Japan.
通讯机构：
[Chen, Guantao] G;[Chen, Guantao] C;Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;Cent China Normal Univ, Fac Math & Stat, Wuhan, Hubei, Peoples R China.
作者机构：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Chen, Guantao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Chen, Xiaodong] Liaoning Univ Technol, Coll Sci, Jinzhou 121001, Peoples R China.;[Zhao, Yue] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA.
期刊：
Graphs and Combinatorics,2017年33(5):1321-1345 ISSN：0911-0119
通讯作者：
Tsuchiya, Shoichi
作者机构：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Chen, Guantao] Cent China Normal Univ, Fac Math & Stat, Wuhan, Hubei, Peoples R China.;[Han, Jie] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, Brazil.;[Suil, O.] SUNY, Dept Appl Math & Stat, Incheon 21985, South Korea.;[Shan, Songling] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA.
