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

New results on orthogonal arrays OA(3,5,4n + 2) 关于正交阵列 OA（3,5,4n + 2）的新成果

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-01-24 DOI: 10.1016/j.jcta.2024.105864

Dongliang Li, Haitao Cao

引用次数: 0

q-Supercongruences from Jackson's ϕ78 summation and Watson's ϕ78 transformation 从杰克逊的ϕ78求和与沃森的ϕ78变换中得出的q-超级共轭关系

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2024-01-12 DOI: 10.1016/j.jcta.2023.105853

Chuanan Wei

引用次数: 0

Nowhere-zero 3-flows in Cayley graphs on supersolvable groups 超可溶群上 Cayley 图中的无处零 3 流

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2023-12-28 DOI: 10.1016/j.jcta.2023.105852

Junyang Zhang , Sanming Zhou

引用次数: 0

Neighbour-transitive codes in Kneser graphs 克奈瑟图中的邻接变换码

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2023-12-14 DOI: 10.1016/j.jcta.2023.105850

Dean Crnković, Daniel R. Hawtin, Nina Mostarac, Andrea Švob

{"title":"Neighbour-transitive codes in Kneser graphs","authors":"Dean Crnković, Daniel R. Hawtin, Nina Mostarac, Andrea Švob","doi":"10.1016/j.jcta.2023.105850","DOIUrl":"10.1016/j.jcta.2023.105850","url":null,"abstract":"<div>A code C is a subset of the vertex set of a graph and C is s-neighbour-transitive if its automorphism group <math><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>C</mi><mo>)</mo></math> acts transitively on each of the first <math><mi>s</mi><mo>+</mo><mn>1</mn></math> parts <math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>s</mi></mrow></msub></math> of the distance partition <math><mo>{</mo><mi>C</mi><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>}</mo></math>, where ρ is the covering radius of C. While codes have traditionally been studied in the Hamming and Johnson graphs, we consider here codes in the Kneser graphs. Let Ω be the underlying set on which the Kneser graph <math><mi>K</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></math> is defined. Our first main result says that if C is a 2-neighbour-transitive code in <math><mi>K</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></math> such that C has minimum distance at least 5, then <math><mi>n</mi><mo>=</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn></math> (i.e., C is a code in an odd graph) and C lies in a particular infinite family or is one particular sporadic example. We then prove several results when C is a neighbour-transitive code in the Kneser graph <math><mi>K</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></math>. First, if <math><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>C</mi><mo>)</mo></math> acts intransitively on Ω we characterise C in terms of certain parameters. We then assume that <math><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>C</mi><mo>)</mo></math> acts transitively on Ω, first proving that if C has minimum distance at least 3 then either <math><mi>K</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></math> is an odd graph or <math><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>C</mi><mo>)</mo></math> has a 2-homogeneous (and hence primitive) action on Ω. We then assume that C is a code in an odd graph and <math><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>C</mi><mo>)</mo></math> acts imprimitively on Ω and characterise C in terms of certain parameters. We give examples in each of these cases and pose several open problems.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"204 ","pages":"Article 105850"},"PeriodicalIF":1.1,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138634436","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

Algebraic approach to the completeness problem for (k,n)-arcs in planes over finite fields 用代数方法解决有限域上平面中 (k,n)-arc 的完备性问题

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2023-12-13 DOI: 10.1016/j.jcta.2023.105851

Gábor Korchmáros , Gábor P. Nagy , Tamás Szőnyi

引用次数: 0

Asymptotics for real monotone double Hurwitz numbers 实单调双赫尔维茨数的渐近线

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2023-12-08 DOI: 10.1016/j.jcta.2023.105848

Yanqiao Ding, Qinhao He

{"title":"Asymptotics for real monotone double Hurwitz numbers","authors":"Yanqiao Ding, Qinhao He","doi":"10.1016/j.jcta.2023.105848","DOIUrl":"10.1016/j.jcta.2023.105848","url":null,"abstract":"<div>In recent years, monotone double Hurwitz numbers were introduced as a naturally combinatorial modification of double Hurwitz numbers. Monotone double Hurwitz numbers share many structural properties with their classical counterparts, such as piecewise polynomiality, while the quantitative properties of these two numbers are quite different. We consider real analogues of monotone double Hurwitz numbers and study the asymptotics for these real analogues. The key ingredient is an interpretation of real tropical covers with arbitrary splittings as factorizations in the symmetric group which generalizes the result from Guay-Paquet et al. (2016) [18]. By using the above interpretation, we consider three types of real analogues of monotone double Hurwitz numbers: real monotone double Hurwitz numbers relative to simple splittings, relative to arbitrary splittings and real mixed double Hurwitz numbers. Under certain conditions, we find lower bounds for these real analogues, and obtain logarithmic asymptotics for real monotone double Hurwitz numbers relative to arbitrary splittings and real mixed double Hurwitz numbers. In particular, under given conditions real mixed double Hurwitz numbers are logarithmically equivalent to complex double Hurwitz numbers. We construct a family of real tropical covers and use them to show that real monotone double Hurwitz numbers relative to simple splittings are logarithmically equivalent to monotone double Hurwitz numbers with specific conditions. This is consistent with the logarithmic equivalence of real double Hurwitz numbers and complex double Hurwitz numbers.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"204 ","pages":"Article 105848"},"PeriodicalIF":1.1,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138550931","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

Chiral polytopes whose smallest regular cover is a polytope 最小正则封面为多面体的手性多面体

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2023-12-08 DOI: 10.1016/j.jcta.2023.105839

Gabe Cunningham

引用次数: 0

A further look at the sum of the parts with the same parity in the partitions of n 再看看 n 的分区中奇偶校验相同的部分之和。

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2023-12-08 DOI: 10.1016/j.jcta.2023.105849

George E. Andrews , Mircea Merca

引用次数: 0

The method of constant terms and k-colored generalized Frobenius partitions 常项法与k色广义Frobenius划分

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2023-12-01 DOI: 10.1016/j.jcta.2023.105837

Su-Ping Cui , Nancy S.S. Gu , Dazhao Tang

{"title":"The method of constant terms and k-colored generalized Frobenius partitions","authors":"Su-Ping Cui , Nancy S.S. Gu , Dazhao Tang","doi":"10.1016/j.jcta.2023.105837","DOIUrl":"10.1016/j.jcta.2023.105837","url":null,"abstract":"<div>In his 1984 AMS memoir, Andrews introduced the family of k-colored generalized Frobenius partition functions. For any positive integer k, let <math><mi>c</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math> denote the number of k-colored generalized Frobenius partitions of n. Among many other things, Andrews proved that for any <math><mi>n</mi><mo>≥</mo><mn>0</mn></math>, <math><mi>c</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mn>5</mn><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo><mo>≡</mo><mn>0</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>5</mn><mo>)</mo></math>. Since then, many scholars subsequently considered congruence properties of various k-colored generalized Frobenius partition functions, typically with a small number of colors.In 2019, Chan, Wang and Yang systematically studied arithmetic properties of <math><mtext>C</mtext><msub><mrow><mi>Φ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math> with <math><mn>2</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>17</mn></math> by employing the theory of modular forms, where <math><mtext>C</mtext><msub><mrow><mi>Φ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math> denotes the generating function of <math><mi>c</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math>. We notice that many coefficients in the expressions of <math><mtext>C</mtext><msub><mrow><mi>Φ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math> are not integers. In this paper, we first observe that <math><mtext>C</mtext><msub><mrow><mi>Φ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math> is related to the constant term of a family of bivariable functions, then establish a general symmetric and recurrence relation on the coefficients of these bivariable functions. Based on this relation, we next derive many bivariable identities. By extracting and computing the constant terms of these bivariable identities, we establish the expressions of <math><mtext>C</mtext><msub><mrow><mi>Φ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math> with integral coefficients. As an immediate consequence, we prove some infinite families of congruences satisfied by <math><mi>c</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math>, where k is allowed to grow arbitrary large.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"203 ","pages":"Article 105837"},"PeriodicalIF":1.1,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138468997","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

Monochromatic arithmetic progressions in automatic sequences with group structure 群结构自动数列中的单色等差数列

IF 1.1 2区数学

Journal of Combinatorial Theory Series A Pub Date : 2023-12-01 DOI: 10.1016/j.jcta.2023.105831

Ibai Aedo , Uwe Grimm , Neil Mañibo , Yasushi Nagai , Petra Staynova

{"title":"Monochromatic arithmetic progressions in automatic sequences with group structure","authors":"Ibai Aedo , Uwe Grimm , Neil Mañibo , Yasushi Nagai , Petra Staynova","doi":"10.1016/j.jcta.2023.105831","DOIUrl":"https://doi.org/10.1016/j.jcta.2023.105831","url":null,"abstract":"<div>We determine asymptotic growth rates for lengths of monochromatic arithmetic progressions in certain automatic sequences. In particular, we look at (one-sided) fixed points of aperiodic, primitive, bijective substitutions and spin substitutions, which are generalisations of the Thue–Morse and Rudin–Shapiro substitutions, respectively. For such infinite words, we show that there exists a subsequence <math><mo>{</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></math> of differences along which the maximum length <math><mi>A</mi><mo>(</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math> of a monochromatic arithmetic progression (with fixed difference <math><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub></math>) grows at least polynomially in <math><msub><mrow><mi>d</mi></mrow><mrow><mi>n</mi></mrow></msub></math>. Explicit upper and lower bounds for the growth exponent can be derived from a finite group associated to the substitution. As an application, we obtain bounds for a van der Waerden-type number for a class of colourings parametrised by the size of the alphabet and the length of the substitution.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"203 ","pages":"Article 105831"},"PeriodicalIF":1.1,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138466156","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: 3