Journal of Combinatorial Theory Series A最新文献_第8页

Flag-transitive automorphism groups of 2-designs with λ ≥ (r,λ)2 are not product type λ≥(r,λ)2的2-设计的旗跨自形群不是积型的

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-06-19 DOI: 10.1016/j.jcta.2024.105923

Huiling Li , Zhilin Zhang , Shenglin Zhou

引用次数: 0

Intersection density of imprimitive groups of degree pq pq 度冒号群的交集密度

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-06-12 DOI: 10.1016/j.jcta.2024.105922

Angelot Behajaina , Roghayeh Maleki , Andriaherimanana Sarobidy Razafimahatratra

{"title":"Intersection density of imprimitive groups of degree pq","authors":"Angelot Behajaina , Roghayeh Maleki , Andriaherimanana Sarobidy Razafimahatratra","doi":"10.1016/j.jcta.2024.105922","DOIUrl":"https://doi.org/10.1016/j.jcta.2024.105922","url":null,"abstract":"<div>A subset <math><mi>F</mi></math> of a finite transitive group <math><mi>G</mi><mo>≤</mo><mi>Sym</mi><mo>(</mo><mi>Ω</mi><mo>)</mo></math> is intersecting if any two elements of <math><mi>F</mi></math> agree on an element of Ω. The intersection density of G is the number<math><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>max</mi><mo>⁡</mo><mrow><mo>{</mo><mrow><mo>|</mo><mi>F</mi><mo>|</mo></mrow><mo>/</mo><mo>|</mo><msub><mrow><mi>G</mi></mrow><mrow><mi>ω</mi></mrow></msub><mo>|</mo><mo>|</mo><mi>F</mi><mo>⊂</mo><mi>G</mi><mtext> is intersecting</mtext><mo>}</mo></mrow><mo>,</mo></math> where <math><mi>ω</mi><mo>∈</mo><mi>Ω</mi></math> and <math><msub><mrow><mi>G</mi></mrow><mrow><mi>ω</mi></mrow></msub></math> is the stabilizer of ω in G. It is known that if <math><mi>G</mi><mo>≤</mo><mi>Sym</mi><mo>(</mo><mi>Ω</mi><mo>)</mo></math> is an imprimitive group of degree a product of two odd primes <math><mi>p</mi><mo>></mo><mi>q</mi></math> admitting a block of size p or two complete block systems, whose blocks are of size q, then <math><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mn>1</mn></math>.In this paper, we analyze the intersection density of imprimitive groups of degree pq with a unique block system with blocks of size q based on the kernel of the induced action on blocks. For those whose kernels are non-trivial, it is proved that the intersection density is larger than 1 whenever there exists a cyclic code C with parameters <math><msub><mrow><mo>[</mo><mi>p</mi><mo>,</mo><mi>k</mi><mo>]</mo></mrow><mrow><mi>q</mi></mrow></msub></math> such that any codeword of C has weight at most <math><mi>p</mi><mo>−</mo><mn>1</mn></math>, and under some additional conditions on the cyclic code, it is a proper rational number. For those that are quasiprimitive, we reduce the cases to almost simple groups containing <math><mi>Alt</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> or a projective special linear group. We give some examples where the latter has intersection density equal to 1, under some restrictions on p and q.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"208 ","pages":"Article 105922"},"PeriodicalIF":1.1,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S009731652400061X/pdfft?md5=4600ca58b59525e76de9f361f9c870b7&pid=1-s2.0-S009731652400061X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141308391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Remarks on MacMahon's q-series 关于麦克马洪 Q 系列的评论

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-06-03 DOI: 10.1016/j.jcta.2024.105921

Ken Ono, Ajit Singh

引用次数: 0

A multiparametric Murnaghan-Nakayama rule for Macdonald polynomials 麦克唐纳多项式的多参数穆纳汉-中山规则

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-05-29 DOI: 10.1016/j.jcta.2024.105920

Naihuan Jing , Ning Liu

{"title":"A multiparametric Murnaghan-Nakayama rule for Macdonald polynomials","authors":"Naihuan Jing , Ning Liu","doi":"10.1016/j.jcta.2024.105920","DOIUrl":"https://doi.org/10.1016/j.jcta.2024.105920","url":null,"abstract":"<div>We introduce a new family of operators as multi-parameter deformation of the one-row Macdonald polynomials. The matrix coefficients of these operators acting on the space of symmetric functions with rational coefficients in two parameters <math><mi>q</mi><mo>,</mo><mi>t</mi></math> (denoted by <math><mi>Λ</mi><mo>(</mo><mi>q</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>) are computed by assigning some values to skew Macdonald polynomials in λ-ring notation. The new rule is utilized to provide new iterative formulas and also recover various existing formulas in a unified manner. Specifically the following applications are discussed: (i) A <math><mo>(</mo><mi>q</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-Murnaghan-Nakayama rule for Macdonald functions is given as a generalization of the q-Murnaghan-Nakayama rule; (ii) An iterative formula for the <math><mo>(</mo><mi>q</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-Green polynomial is deduced; (iii) A simple proof of the Murnaghan-Nakayama rule for the Hecke algebra and the Hecke-Clifford algebra is offered; (iv) A combinatorial inversion of the Pieri rule for Hall-Littlewood functions is derived with the help of the vertex operator realization of the Hall-Littlewood functions; (v) Two iterative formulae for the <math><mo>(</mo><mi>q</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-Kostka polynomials <math><msub><mrow><mi>K</mi></mrow><mrow><mi>λ</mi><mi>μ</mi></mrow></msub><mo>(</mo><mi>q</mi><mo>,</mo><mi>t</mi><mo>)</mo></math> are obtained from the dual version of our multiparametric Murnaghan-Nakayama rule, one of which yields an explicit formula for arbitrary λ and μ in terms of the generalized <math><mo>(</mo><mi>q</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-binomial coefficient introduced independently by Lassalle and Okounkov.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"207 ","pages":"Article 105920"},"PeriodicalIF":1.1,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141163388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

A characterisation of edge-affine 2-arc-transitive covers of K2n,2n K2n,2n的边缘-参数2-弧-传递盖的特性描述

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-05-29 DOI: 10.1016/j.jcta.2024.105919

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

引用次数: 0

Power-free complementary binary morphisms 无幂次互补二元态式

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-05-22 DOI: 10.1016/j.jcta.2024.105910

Jeffrey Shallit , Arseny Shur , Stefan Zorcic

{"title":"Power-free complementary binary morphisms","authors":"Jeffrey Shallit , Arseny Shur , Stefan Zorcic","doi":"10.1016/j.jcta.2024.105910","DOIUrl":"https://doi.org/10.1016/j.jcta.2024.105910","url":null,"abstract":"<div>We revisit the topic of power-free morphisms, focusing on the properties of the class of complementary morphisms. Such morphisms are defined over a 2-letter alphabet, and map the letters 0 and 1 to complementary words. We prove that every prefix of the famous Thue–Morse word t gives a complementary morphism that is <math><msup><mrow><mn>3</mn></mrow><mrow><mo>+</mo></mrow></msup></math>-free and hence α-free for every real number <math><mi>α</mi><mo>></mo><mn>3</mn></math>. We also describe, using a 4-state binary finite automaton, the lengths of all prefixes of t that give cubefree complementary morphisms. Next, we show that 3-free (cubefree) complementary morphisms of length k exist for all <math><mi>k</mi><mo>∉</mo><mo>{</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>}</mo></math>. Moreover, if k is not of the form <math><mn>3</mn><mo>⋅</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></math>, then the images of letters can be chosen to be factors of t. Finally, we observe that each cubefree complementary morphism is also α-free for some <math><mi>α</mi><mo><</mo><mn>3</mn></math>; in contrast, no binary morphism that maps each letter to a word of length 3 (resp., a word of length 6) is α-free for any <math><mi>α</mi><mo><</mo><mn>3</mn></math>.In addition to more traditional techniques of combinatorics on words, we also rely on the Walnut theorem-prover. Its use and limitations are discussed.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"207 ","pages":"Article 105910"},"PeriodicalIF":1.1,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141083216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Spectra of power hypergraphs and signed graphs via parity-closed walks 通过奇偶封闭行走的幂超图和有符号图谱

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-05-22 DOI: 10.1016/j.jcta.2024.105909

Lixiang Chen , Edwin R. van Dam , Changjiang Bu

{"title":"Spectra of power hypergraphs and signed graphs via parity-closed walks","authors":"Lixiang Chen , Edwin R. van Dam , Changjiang Bu","doi":"10.1016/j.jcta.2024.105909","DOIUrl":"https://doi.org/10.1016/j.jcta.2024.105909","url":null,"abstract":"<div>The k-power hypergraph <math><msup><mrow><mi>G</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math> is the k-uniform hypergraph that is obtained by adding <math><mi>k</mi><mo>−</mo><mn>2</mn></math> new vertices to each edge of a graph G, for <math><mi>k</mi><mo>≥</mo><mn>3</mn></math>. A parity-closed walk in G is a closed walk that uses each edge an even number of times. In an earlier paper, we determined the eigenvalues of the adjacency tensor of <math><msup><mrow><mi>G</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math> using the eigenvalues of signed subgraphs of G. Here, we express the entire spectrum (that is, we determine all multiplicities and the characteristic polynomial) of <math><msup><mrow><mi>G</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math> in terms of parity-closed walks of G. Moreover, we give an explicit expression for the multiplicity of the spectral radius of <math><msup><mrow><mi>G</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math>. As a side result, we show that the number of parity-closed walks of given length is the corresponding spectral moment averaged over all signed graphs with underlying graph G. By extrapolating the characteristic polynomial of <math><msup><mrow><mi>G</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math> to <math><mi>k</mi><mo>=</mo><mn>2</mn></math>, we introduce a pseudo-characteristic function which is shown to be the geometric mean of the characteristic polynomials of all signed graphs on G. This supplements a result by Godsil and Gutman that the arithmetic mean of the characteristic polynomials of all signed graphs on G equals the matching polynomial of G.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"207 ","pages":"Article 105909"},"PeriodicalIF":1.1,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141078251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Maximum flag-rank distance codes 最大旗阶距离编码

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-05-20 DOI: 10.1016/j.jcta.2024.105908

Gianira N. Alfarano , Alessandro Neri , Ferdinando Zullo

引用次数: 0

Linkage of graphs with flows 图形与流量的联系

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-05-03 DOI: 10.1016/j.jcta.2024.105907

Alex Abreu , Marco Pacini , Matheus Secco

引用次数: 0

The enumeration of equivalent classes of minimal general dihedral group codes 最小一般二面群编码等价类的枚举