Journal of Combinatorial Designs最新文献_第2页

3-Designs From PSL ( 2 , q ) With Cyclic Starter Blocks 从PSL （2, q）的设计与循环起动块

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-11-02 DOI: 10.1002/jcd.22014

Akihide Hanaki, Kenji Kobayashi, Akihiro Munemasa

{"title":"3-Designs From \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 PSL\u0000 \u0000 \u0000 \u0000 (\u0000 \u0000 2\u0000 ,\u0000 q\u0000 \u0000 )\u0000 \u0000 \u0000 \u0000 With Cyclic Starter Blocks","authors":"Akihide Hanaki, Kenji Kobayashi, Akihiro Munemasa","doi":"10.1002/jcd.22014","DOIUrl":"https://doi.org/10.1002/jcd.22014","url":null,"abstract":"<div>\u0000 \u0000 We consider when the projective special linear group over a finite field defines a block-transitive 3-design with a starter block which is a multiplicative subgroup of the field. For a prime power <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>q</mi>\u0000 \u0000 <mo>≡</mo>\u0000 \u0000 <mn>1</mn>\u0000 <mspace></mspace>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 \u0000 <mn>20</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, we will show that the multiplicative subgroup of order 5 is a starter block of a 3-design if and only if the multiplicative subgroup of order 10 is a starter block of a 3-design. The former is the family of 3-<math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>q</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>5</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> designs investigated by Li, Deng and Zhang, while the latter appear in a different context by Bonnecaze and Solé for the case <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>q</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mn>41</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. We also show a similar equivalence for multiplicative subgroups of orders 13 and 26 for a prime power <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>q</mi>\u0000 \u0000 <mo>≡</mo>\u0000 \u0000 <mn>1</mn>\u0000 <mspace></mspace>\u0000 \u0000 <mrow>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 2","pages":"104-114"},"PeriodicalIF":0.8,"publicationDate":"2025-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145779473","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

Binary Codes From Subset Inclusion Matrices 子集包含矩阵的二进制码

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-10-12 DOI: 10.1002/jcd.22012

Alexey D. Marin, Ivan Yu. Mogilnykh

{"title":"Binary Codes From Subset Inclusion Matrices","authors":"Alexey D. Marin, Ivan Yu. Mogilnykh","doi":"10.1002/jcd.22012","DOIUrl":"https://doi.org/10.1002/jcd.22012","url":null,"abstract":"<div>\u0000 \u0000 In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>W</mi>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, representing <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-element subsets versus <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-element subsets of an <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-element set. We provide both lower and upper bounds on the minimum distances of these codes and determine the exact values for any <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and sufficiently large <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Our study combines design and integer linear programming techniques. The codes we consider are connected to LDPC codes and combinatorial designs. Furthermore, we construct quasi-cyclic LDPC codes from inclusion matrices that exhibit performance comparable to or slightly better than MacKay-type codes when evaluated using bit flipping and min-sum algorithms.\u0000 </div>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 2","pages":"87-103"},"PeriodicalIF":0.8,"publicationDate":"2025-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145779423","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

Block-Transitive Automorphism Groups of 2- ( v , 5 , λ ) Designs 2- (v, 5, λ)设计的块传递自同构群

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-10-09 DOI: 10.1002/jcd.22010

Chuhan Lei, Xiaoqin Zhan

{"title":"Block-Transitive Automorphism Groups of 2-\u0000 \u0000 \u0000 \u0000 \u0000 (\u0000 \u0000 v\u0000 ,\u0000 5\u0000 ,\u0000 λ\u0000 \u0000 )\u0000 \u0000 \u0000 \u0000 Designs","authors":"Chuhan Lei, Xiaoqin Zhan","doi":"10.1002/jcd.22010","DOIUrl":"https://doi.org/10.1002/jcd.22010","url":null,"abstract":"<div>\u0000 \u0000 This paper investigates 2-<math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>5</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>λ</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> designs <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> admitting a block-transitive automorphism group <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. We first prove that if <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is point-imprimitive, then <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> must be one of 16, 21, or 81. We further provide a complete classification of all such designs for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mn>16</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>21</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Second, we demonstrate that if <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is point-primitive, then it must be of affine type, almost simple type, or product type. Additionally, we present a classification of pairs <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 2","pages":"53-68"},"PeriodicalIF":0.8,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145779427","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

On the Q -Polynomial Property of Bipartite Graphs Admitting a Uniform Structure 具有一致结构的二部图的Q -多项式性质

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-10-09 DOI: 10.1002/jcd.22011

Blas Fernández, Roghayeh Maleki, Štefko Miklavič, Giusy Monzillo

{"title":"On the \u0000 \u0000 \u0000 \u0000 Q\u0000 \u0000 \u0000 -Polynomial Property of Bipartite Graphs Admitting a Uniform Structure","authors":"Blas Fernández, Roghayeh Maleki, Štefko Miklavič, Giusy Monzillo","doi":"10.1002/jcd.22011","DOIUrl":"https://doi.org/10.1002/jcd.22011","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> denote a finite, connected graph with vertex set <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Fix <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>x</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mi>X</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ε</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> denote the eccentricity of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. For mutually distinct scalars <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msubsup>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <msubsup>\u0000 <mi>θ</mi>\u0000 \u0000 <mi>i</mi>\u0000 \u0000 <mo>*</mo>\u0000 </msubsup>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 \u0000 <mrow>\u0000 <mi>i</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mn>0</mn>\u0000 </mrow>\u0000 \u0000 <mi>ε</mi>\u0000 </msubsup>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> define a diagonal matrix <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>A</mi>\u0000 \u0000 <mo>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 2","pages":"69-86"},"PeriodicalIF":0.8,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.22011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145779426","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

New Difference Triangle Sets by a Field-Programmable Gate Array-Based Search Technique 基于现场可编程门阵列搜索技术的新差分三角集

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-10-02 DOI: 10.1002/jcd.22009

Mohannad Shehadeh, William Kingsford, Frank R. Kschischang

引用次数: 0

Completing Multi-Latin Rectangles via Factors With Prescribed Degrees in Bipartite Graphs 用二部图中规定度数的因子补全多拉丁矩形

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-09-28 DOI: 10.1002/jcd.22008

Amin Bahmanian

{"title":"Completing Multi-Latin Rectangles via Factors With Prescribed Degrees in Bipartite Graphs","authors":"Amin Bahmanian","doi":"10.1002/jcd.22008","DOIUrl":"https://doi.org/10.1002/jcd.22008","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Q</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be an <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> array whose top left <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <mi>s</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> sub-array <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is filled with a set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> different symbols such that each cell of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> contains <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> symbols. In this note, we find conditions under which each empty cell of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Q</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> can be filled with <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> symbols in such a way that the total number of occurrences of each symbol is prescribed and that each symbol occurs at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 1","pages":"31-36"},"PeriodicalIF":0.8,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.22008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533770","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

Variations on Bollobás Systems of d -Partitions d -Partitions的Bollobás系统的变体

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-09-24 DOI: 10.1002/jcd.22007

Yu Fang, Xiaomiao Wang, Tao Feng

{"title":"Variations on Bollobás Systems of \u0000 \u0000 \u0000 d\u0000 \u0000 -Partitions","authors":"Yu Fang, Xiaomiao Wang, Tao Feng","doi":"10.1002/jcd.22007","DOIUrl":"https://doi.org/10.1002/jcd.22007","url":null,"abstract":"<div>\u0000 \u0000 This paper investigates five kinds of systems of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </semantics></math>-partitions of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, including symmetric Bollobás systems, strong Bollobás systems, Bollobás systems, skew Bollobás systems, and weak Bollobás systems. Many known results on variations of Bollobás systems are unified. Especially, we give a negative answer to a conjecture on Bollobás systems of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </semantics></math>-partitions of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> that was presented by Hegedüs and Frankl (European J. Comb., 120 [2024], 103983). Even though this conjecture does not hold for general Bollobás systems, we show that it holds for strong Bollobás systems of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </semantics></math>-partitions of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>.\u0000 </div>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 1","pages":"15-30"},"PeriodicalIF":0.8,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533702","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

Steiner Triple Systems With High Discrepancy 高差异斯坦纳三系

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-09-09 DOI: 10.1002/jcd.22004

Lior Gishboliner, Stefan Glock, Amedeo Sgueglia

{"title":"Steiner Triple Systems With High Discrepancy","authors":"Lior Gishboliner, Stefan Glock, Amedeo Sgueglia","doi":"10.1002/jcd.22004","DOIUrl":"https://doi.org/10.1002/jcd.22004","url":null,"abstract":"In this paper, we initiate the study of discrepancy questions for combinatorial designs. Specifically, we show that, for every fixed <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>≡</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>3</mn>\u0000 <mspace></mspace>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 \u0000 <mn>6</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, any <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-colouring of the triples on <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> admits a Steiner triple system of order <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> with discrepancy <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <msup>\u0000 <mi>n</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 1","pages":"5-14"},"PeriodicalIF":0.8,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.22004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533679","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

Maximum Shattering 最大破碎

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-08-29 DOI: 10.1002/jcd.22005

Noga Alon, Varun Sivashankar, Daniel G. Zhu

{"title":"Maximum Shattering","authors":"Noga Alon, Varun Sivashankar, Daniel G. Zhu","doi":"10.1002/jcd.22005","DOIUrl":"https://doi.org/10.1002/jcd.22005","url":null,"abstract":"A family <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of subsets of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>]</mo>\u0000 </mrow>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mo>…</mo>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> shatters a set <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>A</mi>\u0000 \u0000 <mo>⊆</mo>\u0000 \u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> if for every <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>A</mi>\u0000 \u0000 <mo>′</mo>\u0000 </msup>\u0000 \u0000 <mo>⊆</mo>\u0000 \u0000 <mi>A</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, there is an <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>F</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mi>ℱ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semant","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"33 12","pages":"456-470"},"PeriodicalIF":0.8,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.22005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145273063","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

Completing Partial k -Star Designs 完成部分k星设计

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-08-17 DOI: 10.1002/jcd.22003

Ajani De Vas Gunasekara, Daniel Horsley

{"title":"Completing Partial \u0000 \u0000 \u0000 \u0000 k\u0000 \u0000 \u0000 -Star Designs","authors":"Ajani De Vas Gunasekara, Daniel Horsley","doi":"10.1002/jcd.22003","DOIUrl":"https://doi.org/10.1002/jcd.22003","url":null,"abstract":"A <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-star is a complete bipartite graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mrow>\u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. A partial <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-star design of order <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a pair <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>A</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> where <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> vertices and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a set of edge-disjoint <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"33 12","pages":"446-455"},"PeriodicalIF":0.8,"publicationDate":"2025-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.22003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272800","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}

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