Journal of Algebraic Combinatorics最新文献_第5页

A standard form for scattered linearized polynomials and properties of the related translation planes 分散线性化多项式的标准形式和相关平移平面的性质

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-04-09 DOI: 10.1007/s10801-024-01317-y

Giovanni Longobardi, Corrado Zanella

{"title":"A standard form for scattered linearized polynomials and properties of the related translation planes","authors":"Giovanni Longobardi, Corrado Zanella","doi":"10.1007/s10801-024-01317-y","DOIUrl":"https://doi.org/10.1007/s10801-024-01317-y","url":null,"abstract":"In this paper, we present results concerning the stabilizer (G_f) in ({{,mathrm{{GL}},}}(2,q^n)) of the subspace (U_f={(x,f(x)):xin mathbb {F}_{q^n}}), f(x) a scattered linearized polynomial in (mathbb {F}_{q^n}[x]). Each (G_f) contains the (q-1) maps ((x,y)mapsto (ax,ay)), (ain mathbb {F}_{q}^*). By virtue of the results of Beard (Duke Math J, 39:313–321, 1972) and Willett (Duke Math J 40(3):701–704, 1973), the matrices in (G_f) are simultaneously diagonalizable. This has several consequences: (i) the polynomials such that (|G_f|>q-1) have a standard form of type (sum _{j=0}^{n/t-1}a_jx^{q^{s+jt}}) for some s and t such that ((s,t)=1), (t>1) a divisor of n; (ii) this standard form is essentially unique; (iii) for (n>2) and (q>3), the translation plane (mathcal {A}_f) associated with f(x) admits nontrivial affine homologies if and only if (|G_f|>q-1), and in that case those with axis through the origin form two groups of cardinality ((q^t-1)/(q-1)) that exchange axes and coaxes; (iv) no plane of type (mathcal {A}_f), f(x) a scattered polynomial not of pseudoregulus type, is a generalized André plane.","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140564622","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

An ultimately periodic chain in the integral Lie ring of partitions 积分列环中的终极周期链

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-04-09 DOI: 10.1007/s10801-024-01318-x

Riccardo Aragona, Roberto Civino, Norberto Gavioli

引用次数: 0

Block-transitive 3-(v, k, 1) designs on exceptional groups of Lie type 李型异常群上的块传递 3-(v, k, 1) 设计

IF 0.8 3区数学

Journal of Algebraic Combinatorics Pub Date : 2024-04-06 DOI: 10.1007/s10801-024-01315-0

引用次数: 0

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":null,"pages":null},"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":null,"pages":null},"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