Journal of Combinatorial Designs最新文献_第6页

Incidence-free sets and edge domination in incidence graphs 关联图中的无关联集和边支配

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2023-11-23 DOI: 10.1002/jcd.21925

Sam Spiro, Sam Adriaensen, Sam Mattheus

{"title":"Incidence-free sets and edge domination in incidence graphs","authors":"Sam Spiro, Sam Adriaensen, Sam Mattheus","doi":"10.1002/jcd.21925","DOIUrl":"10.1002/jcd.21925","url":null,"abstract":"A set of edges <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 </mrow>\u0000 <annotation> ${rm{Gamma }}$</annotation>\u0000 </semantics></math> of a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is an edge dominating set if every edge of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> intersects at least one edge of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 </mrow>\u0000 <annotation> ${rm{Gamma }}$</annotation>\u0000 </semantics></math>, and the edge domination number <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>γ</mi>\u0000 \u0000 <mi>e</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${gamma }_{e}(G)$</annotation>\u0000 </semantics></math> is the smallest size of an edge dominating set. Expanding on work of Laskar and Wallis, we study <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>γ</mi>\u0000 \u0000 <mi>e</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${gamma }_{e}(G)$</annotation>\u0000 </semantics></math> for graphs <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> which are the incidence graph of some incidence structure <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation> $D$</annotation>\u0000 </semantics></math>, with an emphasis on the case when <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation> $D$</annotation>\u0000 </semantics></math> is a symmetric design. In particular, we show in this latter case that determining <math>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 2","pages":"55-87"},"PeriodicalIF":0.7,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.21925","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

On symmetric designs with flag-transitive and point-quasiprimitive automorphism groups 关于具有旗变换群和点准三态群的对称设计

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2023-11-05 DOI: 10.1002/jcd.21924

Zhilin Zhang, Jianfu Chen, Shenglin Zhou

{"title":"On symmetric designs with flag-transitive and point-quasiprimitive automorphism groups","authors":"Zhilin Zhang, Jianfu Chen, Shenglin Zhou","doi":"10.1002/jcd.21924","DOIUrl":"10.1002/jcd.21924","url":null,"abstract":"Let <math>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>ℬ</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math> be a nontrivial symmetric <math>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>k</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>λ</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math>-design with <math>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mn>100</mn>\u0000 </mrow></math>, and let <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> be a flag-transitive automorphism group of <math>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow></math>. In this paper, we show that if <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is quasiprimitive on <math>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow></math>, then <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is of holomorph affine or almost simple type. Moreover, if <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is imprimitive on <math>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow></math>, then <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is of almost simple type. According to this observation and to the classification of the finite simple groups we determine all such symmetric designs and the corresponding automorphism groups. We conclude with two open problems and a conjecture.","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 3","pages":"107-126"},"PeriodicalIF":0.7,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135726222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Dual incidences and t-designs in vector spaces 向量空间中的对偶关联和t-设计

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2023-10-13 DOI: 10.1002/jcd.21922

Kristijan Tabak

{"title":"Dual incidences and t-designs in vector spaces","authors":"Kristijan Tabak","doi":"10.1002/jcd.21922","DOIUrl":"https://doi.org/10.1002/jcd.21922","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 <annotation> $V$</annotation>\u0000 </semantics></math> be an <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation> $n$</annotation>\u0000 </semantics></math>-dimensional vector space over <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <mi>q</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{mathbb{F}}}_{q}$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> ${rm{ {mathcal H} }}$</annotation>\u0000 </semantics></math> is any set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-dimensional subspaces of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 <annotation> $V$</annotation>\u0000 </semantics></math>. We construct two incidence structures <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>D</mi>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mi>a</mi>\u0000 \u0000 <mi>x</mi>\u0000 </mrow>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>H</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${{mathscr{D}}}_{max}({rm{ {mathcal H} }})$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>D</mi>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mi>i</mi>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>H</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${{mathscr{D}}}_{min}({rm{ {mathcal H} }})$</annotation>\u0000 </semantics></math> using subspaces from <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> ${rm{ {mathcal H} }}$</annotation>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 1","pages":"46-52"},"PeriodicalIF":0.7,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134805714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Completing the solution of the directed Oberwolfach problem with cycles of equal length 完成了等长环有向Oberwolfach问题的求解

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2023-09-25 DOI: 10.1002/jcd.21918

Alice Lacaze-Masmonteil

{"title":"Completing the solution of the directed Oberwolfach problem with cycles of equal length","authors":"Alice Lacaze-Masmonteil","doi":"10.1002/jcd.21918","DOIUrl":"https://doi.org/10.1002/jcd.21918","url":null,"abstract":"In this paper, we give a solution to the last outstanding case of the directed Oberwolfach problem with tables of uniform length. Namely, we address the two-table case with tables of equal odd length. We prove that the complete symmetric digraph on <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation> $2m$</annotation>\u0000 </semantics></math> vertices, denoted <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>K</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <mo>*</mo>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation> ${K}_{2m}^{* }$</annotation>\u0000 </semantics></math>, admits a resolvable decomposition into directed cycles of odd length <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation> $m$</annotation>\u0000 </semantics></math>. This completely settles the directed Oberwolfach problem with tables of uniform length.","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 1","pages":"5-30"},"PeriodicalIF":0.7,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.21918","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134880386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3

Orthogonal cycle systems with cycle length less than 10 周期长度小于10的正交循环系

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2023-09-25 DOI: 10.1002/jcd.21921

Selda Küçükçifçi, Emine Şule Yazıcı

{"title":"Orthogonal cycle systems with cycle length less than 10","authors":"Selda Küçükçifçi, Emine Şule Yazıcı","doi":"10.1002/jcd.21921","DOIUrl":"https://doi.org/10.1002/jcd.21921","url":null,"abstract":"An <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>-decomposition of a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is a partition of the edge set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> into subsets, where each subset induces a copy of the graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>. A <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-orthogonal <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>-decomposition of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is a set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>-decompositions of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> such that any two copies of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math> in distinct <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>-decompositions intersect in at most one edge. When <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mi>v</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> $G={K}_{v}$</annotation>\u0000 </semantics></math>, we call the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>-decompositi","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 1","pages":"31-45"},"PeriodicalIF":0.7,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134814340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Generalizations of some Nordhaus–Gaddum-type results on spectral radius 谱半径上某些Nordhaus–Gaddum型结果的推广

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2023-09-21 DOI: 10.1002/jcd.21919

Junying Lu, Lanchao Wang, Yaojun Chen

{"title":"Generalizations of some Nordhaus–Gaddum-type results on spectral radius","authors":"Junying Lu, Lanchao Wang, Yaojun Chen","doi":"10.1002/jcd.21919","DOIUrl":"https://doi.org/10.1002/jcd.21919","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> be a simple graph and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $lambda (G)$</annotation>\u0000 </semantics></math> the spectral radius of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>. For <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation> $kge 2$</annotation>\u0000 </semantics></math>, a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-edge decomposition <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>H</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>…</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>H</mi>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation> $({H}_{1},{rm{ldots }},{H}_{k})$</annotation>\u0000 </semantics></math> is <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math> spanning subgraphs such that their edge sets form a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-partition of the edge set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>. In this paper, we obtain some sharp lower and upper bounds for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 12","pages":"701-712"},"PeriodicalIF":0.7,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50153173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Construction of rank 4 self-dual association schemes inducing three partial geometric designs 诱导三个局部几何设计的秩为4的自对偶关联方案的构造

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2023-09-05 DOI: 10.1002/jcd.21917

Akihide Hanaki

引用次数: 0

proper partial geometries with an automorphism group acting primitively on points and lines 自同构群初始作用于点和线的适当局部几何

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2023-08-31 DOI: 10.1002/jcd.21914

Wendi Di

{"title":"proper partial geometries with an automorphism group acting primitively on points and lines","authors":"Wendi Di","doi":"10.1002/jcd.21914","DOIUrl":"https://doi.org/10.1002/jcd.21914","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation> ${mathscr{S}}$</annotation>\u0000 </semantics></math> be a finite proper partial geometry pg<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>t</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>α</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $(s,t,alpha )$</annotation>\u0000 </semantics></math> not isomorphic to the van Lint–Schrijver partial geometry pg<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mn>5</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>5</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $(5,5,2)$</annotation>\u0000 </semantics></math> and let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> be a group of automorphisms of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation> ${mathscr{S}}$</annotation>\u0000 </semantics></math> acting primitively on both points and lines of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation> ${mathscr{S}}$</annotation>\u0000 </semantics></math>, we show that if <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mn>60</mn>\u0000 </mrow>\u0000 <annotation> $alpha le 60$</annotation>\u0000 </semantics></math> then <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> must be almost simple.","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 11","pages":"642-664"},"PeriodicalIF":0.7,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50148812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

P℘N functions, complete mappings and quasigroup difference sets P℘N函数、完备映射与拟群差集

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2023-08-23 DOI: 10.1002/jcd.21916

Nurdagül Anbar, Tekgül Kalaycı, Wilfried Meidl, Constanza Riera, Pantelimon Stănică

{"title":"P℘N functions, complete mappings and quasigroup difference sets","authors":"Nurdagül Anbar, Tekgül Kalaycı, Wilfried Meidl, Constanza Riera, Pantelimon Stănică","doi":"10.1002/jcd.21916","DOIUrl":"https://doi.org/10.1002/jcd.21916","url":null,"abstract":"We investigate pairs of permutations <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $F,G$</annotation>\u0000 </semantics></math> of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <msup>\u0000 <mi>p</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msup>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{mathbb{F}}}_{{p}^{n}}$</annotation>\u0000 </semantics></math> such that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mi>a</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>G</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>x</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $F(x+a)-G(x)$</annotation>\u0000 </semantics></math> is a permutation for every <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>a</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <msup>\u0000 <mi>p</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msup>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> $ain {{mathbb{F}}}_{{p}^{n}}$</annotation>\u0000 </semantics></math>. We show that, in that case, necessarily <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>x</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mi>℘</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>x</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 12","pages":"667-690"},"PeriodicalIF":0.7,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50141470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1

On the directed Oberwolfach problem for complete symmetric equipartite digraphs and uniform-length cycles 关于完全对称等分有向图和一致长环的有向Oberwolfach问题

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2023-08-22 DOI: 10.1002/jcd.21913

Nevena Francetić, Mateja Šajna

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引用次数: 0