Journal of Combinatorial Designs最新文献_第3页

There Exist Steiner Systems S ( 2 , 8 , 225 ) and S ( 2 , 9 , 289 ) 存在Steiner系统S (2,8，225)和S （2,9,289）

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2026-04-13 Epub Date: 2026-03-26 DOI: 10.1002/jcd.70011

Ivan Hetman

{"title":"There Exist Steiner Systems \u0000 \u0000 \u0000 \u0000 S\u0000 \u0000 (\u0000 \u0000 2\u0000 ,\u0000 8\u0000 ,\u0000 225\u0000 \u0000 )\u0000 \u0000 \u0000 \u0000 and \u0000 \u0000 \u0000 \u0000 S\u0000 \u0000 (\u0000 \u0000 2\u0000 ,\u0000 9\u0000 ,\u0000 289\u0000 \u0000 )","authors":"Ivan Hetman","doi":"10.1002/jcd.70011","DOIUrl":"https://doi.org/10.1002/jcd.70011","url":null,"abstract":"<div>\u0000 \u0000 In this note, six Steiner systems <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>S</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>8</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>225</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and four Steiner systems <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>S</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>9</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>289</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> are presented. This resolves two of 129 undecided cases for block designs with block length 8 and 9, mentioned in the Handbook of Combinatorial Designs.</div>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 6","pages":"259-261"},"PeriodicalIF":0.8,"publicationDate":"2026-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686282","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

Untouchable Sets of Size 2 q ± 1 in P G ( 2 , q ) pg （2, q）中2 q±1的不可触集

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2026-03-11 Epub Date: 2026-01-20 DOI: 10.1002/jcd.70007

Jeremy M. Dover

{"title":"Untouchable Sets of Size \u0000 \u0000 \u0000 \u0000 2\u0000 q\u0000 ±\u0000 1\u0000 \u0000 \u0000 in \u0000 \u0000 \u0000 \u0000 P\u0000 G\u0000 \u0000 (\u0000 \u0000 2\u0000 ,\u0000 q\u0000 \u0000 )","authors":"Jeremy M. Dover","doi":"10.1002/jcd.70007","DOIUrl":"https://doi.org/10.1002/jcd.70007","url":null,"abstract":"<div>\u0000 \u0000 An untouchable set in a projective plane is a set of points such that no line of the plane meets the set in exactly one point. Recently, Héger and Nagy (Avoiding Secants of Given Size in Finite Projective Planes, J. Combin. Des. 33:83–93, 2024.) provided a generalization of untouchable sets to <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-avoiding sets, and addressed the issue of the spectrum of sizes that such sets can attain in finite planes. In the case of untouchable sets, the authors state as an open question the existence of untouchable sets of size <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>q</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>q</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. We answer this question in the affirmative for Desarguesian planes of even order, and provide a construction of untouchable sets of size <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>q</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> in <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>q</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>q</mi>\u0000 \u0000 <mo>≡</mo>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 5","pages":"228-231"},"PeriodicalIF":0.8,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567395","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 Regular Quaternary Hadamard Matrices 关于正则四元Hadamard矩阵

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2026-03-11 Epub Date: 2026-01-20 DOI: 10.1002/jcd.70006

Hadi Kharaghani, Behruz Tayfeh-Rezaie, Vlad Zaitsev

引用次数: 0

Recursive and Cyclic Constructions for Double-Change Covering Designs 双变化覆盖设计的递归和循环结构

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-12-28 DOI: 10.1002/jcd.70000

Amanda Lynn Chafee, Brett Stevens

{"title":"Recursive and Cyclic Constructions for Double-Change Covering Designs","authors":"Amanda Lynn Chafee, Brett Stevens","doi":"10.1002/jcd.70000","DOIUrl":"https://doi.org/10.1002/jcd.70000","url":null,"abstract":"A double-change covering design (DCCD) is a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-set <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and an ordered list <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>b</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> blocks of size <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> where every pair from <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> must occur in at least one block and each pair of consecutive blocks differs by exactly two elements. It is minimal if it has the fewest blocks possible and circular when the first and last blocks also differ by two elements. We give a recursive construction that uses 1-factorizations of complete graphs and expansion sets to construct a DCCD(<math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mfrac>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mi>k</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 \u0000 <mo>,<","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 4","pages":"198-209"},"PeriodicalIF":0.8,"publicationDate":"2025-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.70000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146223971","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

Subsquares in Random Latin Squares and Rectangles 随机拉丁方块和矩形中的子方块

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-12-18 DOI: 10.1002/jcd.70004

Alexander Divoux, Tom Kelly, Camille Kennedy, Jasdeep Sidhu

{"title":"Subsquares in Random Latin Squares and Rectangles","authors":"Alexander Divoux, Tom Kelly, Camille Kennedy, Jasdeep Sidhu","doi":"10.1002/jcd.70004","DOIUrl":"https://doi.org/10.1002/jcd.70004","url":null,"abstract":"A <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> partial Latin rectangle is <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>C</mi>\u0000 \u0000 <mo>-</mo>\u0000 \u0000 <mi>sparse</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> if the number of nonempty entries in each row and column is at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and each symbol is used at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> times. We prove that the probability a uniformly random <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> Latin rectangle, where <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\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 <mi>α</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, contains a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>β</mi>\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 4","pages":"184-197"},"PeriodicalIF":0.8,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.70004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146224501","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

The Maximal Cardinality of Quantum Latin Squares and Quantum Latin Cubes 量子拉丁平方和量子拉丁立方的最大基数

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-12-15 DOI: 10.1002/jcd.70002

Yuyuan Zhang, Yiwen Zhang, Mingzhen Lv, Haitao Cao

{"title":"The Maximal Cardinality of Quantum Latin Squares and Quantum Latin Cubes","authors":"Yuyuan Zhang, Yiwen Zhang, Mingzhen Lv, Haitao Cao","doi":"10.1002/jcd.70002","DOIUrl":"https://doi.org/10.1002/jcd.70002","url":null,"abstract":"<div>\u0000 \u0000 In this paper, by extending the classical singular direct product construction to the quantum setting we resolve the existence problem for quantum Latin squares with maximal cardinality except for 11 possible exceptions. We also prove that there exists a quantum Latin cube of order <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> with maximal cardinality for all positive integers <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, except when <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a prime or <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mi>p</mi>\u0000 \u0000 <mi>q</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, where <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>p</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>q</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> are prime numbers and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>p</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>q</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>≠</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>.</","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 4","pages":"169-183"},"PeriodicalIF":0.8,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146217381","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

Code Construction of Some Quasi-Unbiased Weighing Matrices 一类拟无偏加权矩阵的编码构造

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-11-25 DOI: 10.1002/jcd.70001

Masaaki Harada

{"title":"Code Construction of Some Quasi-Unbiased Weighing Matrices","authors":"Masaaki Harada","doi":"10.1002/jcd.70001","DOIUrl":"10.1002/jcd.70001","url":null,"abstract":"<div>\u0000 \u0000 We construct pairs of quasi-unbiased weighing matrices for parameters <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>10</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>8</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>4</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>16</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>16</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>14</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>4</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>49</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>18</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>16</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>4</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>64</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>32</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>30</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <m","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 3","pages":"157-166"},"PeriodicalIF":0.8,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146058069","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

Completely (Quasi-)Uniform Nested Boolean Steiner Quadruple Systems 完全（拟）一致嵌套布尔斯坦纳四重系统

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-11-13 DOI: 10.1002/jcd.22016

Xiao-Nan Lu

{"title":"Completely (Quasi-)Uniform Nested Boolean Steiner Quadruple Systems","authors":"Xiao-Nan Lu","doi":"10.1002/jcd.22016","DOIUrl":"10.1002/jcd.22016","url":null,"abstract":"<div>\u0000 \u0000 Nested Steiner quadruple systems are designs derived from Steiner quadruple systems (SQSs) by partitioning each block into pairs. A nested SQS is completely uniform if every possible pair appears with equal multiplicity, and completely quasi-uniform if every pair appears with multiplicities that differ by at most one. An explicit construction on the Boolean SQS of order <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mn>2</mn>\u0000 \u0000 <mi>m</mi>\u0000 </msup>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is presented, producing a nested SQS<math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <msup>\u0000 <mn>2</mn>\u0000 \u0000 <mi>m</mi>\u0000 </msup>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> that is completely uniform when <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is odd and completely quasi-uniform when <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is even for each integer <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. These results resolve two open problems posed by Chee et al. (2025). The notion of completely uniform pairings is further generalized for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-designs with <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. As an application, completely uniform nested 2-<math>\u0000 <semantics>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 3","pages":"139-156"},"PeriodicalIF":0.8,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146083212","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

Simple 3-Designs of PSL ( 2 , 2 n ) With Block Size 13 块大小为13的PSL （2,2 n）的简单3-设计

IF 0.8 4区数学

Journal of Combinatorial Designs Pub Date : 2025-11-13 DOI: 10.1002/jcd.22015

Takara Kondo, Yuto Nogata

{"title":"Simple 3-Designs of \u0000 \u0000 \u0000 \u0000 PSL\u0000 \u0000 (\u0000 \u0000 2\u0000 ,\u0000 \u0000 2\u0000 n\u0000 \u0000 \u0000 )\u0000 \u0000 \u0000 \u0000 With Block Size 13","authors":"Takara Kondo, Yuto Nogata","doi":"10.1002/jcd.22015","DOIUrl":"10.1002/jcd.22015","url":null,"abstract":"This paper focuses on the investigation of simple 3-<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mn>2</mn>\u0000 \u0000 <mi>n</mi>\u0000 </msup>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>13</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 admitting <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mtext>PSL</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msup>\u0000 <mn>2</mn>\u0000 \u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> as an automorphism group. Such designs arise from the orbits of 13-element subsets under the action of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mtext>PSL</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msup>\u0000 <mn>2</mn>\u0000 \u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> on the project","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"34 3","pages":"119-138"},"PeriodicalIF":0.8,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.22015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146091227","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

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}

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