Journal of Combinatorial Designs最新文献

筛选
英文 中文
On the equivalence of certain quasi-Hermitian varieties 关于某些拟Hermitian变种的等价性
IF 0.7 4区 数学
Journal of Combinatorial Designs Pub Date : 2022-12-07 DOI: 10.1002/jcd.21870
Angela Aguglia, Luca Giuzzi
{"title":"On the equivalence of certain quasi-Hermitian varieties","authors":"Angela Aguglia, Luca Giuzzi","doi":"10.1002/jcd.21870","DOIUrl":"https://doi.org/10.1002/jcd.21870","url":null,"abstract":"<p>By Aguglia et al., new quasi-Hermitian varieties <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>ℳ</mi>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>,</mo>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{rm{ {mathcal M} }}}_{alpha ,beta }$</annotation>\u0000 </semantics></math> in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mtext>PG</mtext>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>,</mo>\u0000 <msup>\u0000 <mi>q</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $text{PG}(r,{q}^{2})$</annotation>\u0000 </semantics></math> depending on a pair of parameters <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>,</mo>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 <annotation> $alpha ,beta $</annotation>\u0000 </semantics></math> from the underlying field <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mtext>GF</mtext>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>q</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $text{GF}({q}^{2})$</annotation>\u0000 </semantics></math> have been constructed. In the present paper we study the structure of the lines contained in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>ℳ</mi>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>,</mo>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{rm{ {mathcal M} }}}_{alpha ,beta }$</annotation>\u0000 </semantics></math> and consequently determine the projective equivalence classes of such varieties for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation> $q$</annotation>\u0000 </semantics></math> odd and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>=</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation> $r=3$</annotation>\u0000 </semantics></math>. As a byproduct, we also prove that the collinearity graph of <math>\u0000 <semantics>\u0000 <mrow>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 2","pages":"124-138"},"PeriodicalIF":0.7,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50123664","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: 3
Projective planes of order 12 do not have a collineation group of order 4 12阶的投影平面不具有4阶的共线群
IF 0.7 4区 数学
Journal of Combinatorial Designs Pub Date : 2022-12-05 DOI: 10.1002/jcd.21869
Kenzi Akiyama, Chihiro Suetake, Masaki Tanaka
{"title":"Projective planes of order 12 do not have a collineation group of order 4","authors":"Kenzi Akiyama,&nbsp;Chihiro Suetake,&nbsp;Masaki Tanaka","doi":"10.1002/jcd.21869","DOIUrl":"https://doi.org/10.1002/jcd.21869","url":null,"abstract":"<p>In this paper, we prove that there are no projective planes of order 12 admitting a collineation group of order 4. This yields that the order of any collineation group of a projective plane of order 12 is 1, 2, or 3.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 2","pages":"87-123"},"PeriodicalIF":0.7,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50115602","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
Tight globally simple nonzero sum Heffter arrays and biembeddings 紧全局简单非零和Heffter数组和biembeddings
IF 0.7 4区 数学
Journal of Combinatorial Designs Pub Date : 2022-11-15 DOI: 10.1002/jcd.21866
Lorenzo Mella, Anita Pasotti
{"title":"Tight globally simple nonzero sum Heffter arrays and biembeddings","authors":"Lorenzo Mella,&nbsp;Anita Pasotti","doi":"10.1002/jcd.21866","DOIUrl":"https://doi.org/10.1002/jcd.21866","url":null,"abstract":"&lt;p&gt;Square relative nonzero sum Heffter arrays, denoted by &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 \u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${rm{N}}{{rm{H}}}_{t}(n;k)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, have been introduced as a variant of the classical concept of Heffter array. An &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 \u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${rm{N}}{{rm{H}}}_{t}(n;k)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is an &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $ntimes n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; partially filled array with elements in &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${{mathbb{Z}}}_{v}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 \u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 \u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $v=2nk+t$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, whose rows and whose columns contain &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; filled cells, suc","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 1","pages":"41-83"},"PeriodicalIF":0.7,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50151154","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: 6
The existence of irrational most perfect magic squares 非理性最完美幻方的存在性
IF 0.7 4区 数学
Journal of Combinatorial Designs Pub Date : 2022-11-09 DOI: 10.1002/jcd.21865
Jingyuan Chen, Jinwei Wu, Dianhua Wu
{"title":"The existence of irrational most perfect magic squares","authors":"Jingyuan Chen,&nbsp;Jinwei Wu,&nbsp;Dianhua Wu","doi":"10.1002/jcd.21865","DOIUrl":"https://doi.org/10.1002/jcd.21865","url":null,"abstract":"&lt;p&gt;Let &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;≡&lt;/mo&gt;\u0000 \u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;mod&lt;/mi&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 \u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:10638539:media:jcd21865:jcd21865-math-0001\" wiley:location=\"equation/jcd21865-math-0001.png\"&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;unicode{x02261}&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mspace width=\"0.3em\"/&gt;&lt;mrow&gt;&lt;mo class=\"MathClass-open\"&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;mod&lt;/mi&gt;&lt;mspace width=\"0.3em\"/&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mo class=\"MathClass-close\"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a positive integer, &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;msub&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:10638539:media:jcd21865:jcd21865-math-0002\" wiley:location=\"equation/jcd21865-math-0002.png\"&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo class=\"MathClass-open\"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo class=\"MathClass-close\"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a magic square, where &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 \u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 \u0000 &lt;msub&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 1","pages":"23-40"},"PeriodicalIF":0.7,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50126745","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 large partial ovoids of symplectic and Hermitian polar spaces 关于辛和Hermitian极空间的大偏卵形
IF 0.7 4区 数学
Journal of Combinatorial Designs Pub Date : 2022-11-06 DOI: 10.1002/jcd.21864
Michela Ceria, Jan De Beule, Francesco Pavese, Valentino Smaldore
{"title":"On large partial ovoids of symplectic and Hermitian polar spaces","authors":"Michela Ceria,&nbsp;Jan De Beule,&nbsp;Francesco Pavese,&nbsp;Valentino Smaldore","doi":"10.1002/jcd.21864","DOIUrl":"https://doi.org/10.1002/jcd.21864","url":null,"abstract":"&lt;p&gt;In this paper we provide constructive lower bounds on the sizes of the largest partial ovoids of the symplectic polar spaces &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${mathscr{W}}(3,q)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $q$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; odd square, &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 \u0000 &lt;mo&gt;≢&lt;/mo&gt;\u0000 \u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;mod&lt;/mi&gt;\u0000 \u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $qnotequiv 0(mathrm{mod}3)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;5&lt;/mn&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${mathscr{W}}(5,q)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and of the Hermitian polar spaces &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℋ&lt;/mi&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;msup&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 \u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; ${rm{ {mathcal H} }}(4,{q}^{2})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 1","pages":"5-22"},"PeriodicalIF":0.7,"publicationDate":"2022-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50123308","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
An alternative construction of the Hermitian unital 2-(28, 4, 1) design Hermitian酉2-(28, 4. 1) 设计
IF 0.7 4区 数学
Journal of Combinatorial Designs Pub Date : 2022-09-26 DOI: 10.1002/jcd.21861
Koichi Inoue
{"title":"An alternative construction of the Hermitian unital 2-(28, 4, 1) design","authors":"Koichi Inoue","doi":"10.1002/jcd.21861","DOIUrl":"https://doi.org/10.1002/jcd.21861","url":null,"abstract":"<p>In this paper, we give an alternative construction of the Hermitian unital 2-(28, 4, 1) design in such a way that it is constructed on the isotropic vectors in a unitary geometry of dimension 3 over the field <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <mn>4</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{mathbb{F}}}_{4}$</annotation>\u0000 </semantics></math>. As a corollary, we can construct a unique 3-(10, 4, 1) design (namely, the Witt system <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <msub>\u0000 <mi>W</mi>\u0000 \u0000 <mn>10</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${{boldsymbol{W}}}_{{bf{10}}}$</annotation>\u0000 </semantics></math>).</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"30 12","pages":"752-759"},"PeriodicalIF":0.7,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72166349","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
An alternative construction of the Hermitian unital 2‐(28, 4, 1) design 厄米单位2‐(28,4,1)设计的另一种结构
IF 0.7 4区 数学
Journal of Combinatorial Designs Pub Date : 2022-09-26 DOI: 10.1002/jcd.21861
Koichi Inoue
{"title":"An alternative construction of the Hermitian unital 2‐(28, 4, 1) design","authors":"Koichi Inoue","doi":"10.1002/jcd.21861","DOIUrl":"https://doi.org/10.1002/jcd.21861","url":null,"abstract":"In this paper, we give an alternative construction of the Hermitian unital 2‐(28, 4, 1) design in such a way that it is constructed on the isotropic vectors in a unitary geometry of dimension 3 over the field F 4 ${{mathbb{F}}}_{4}$ . As a corollary, we can construct a unique 3‐(10, 4, 1) design (namely, the Witt system W 10 ${{boldsymbol{W}}}_{{bf{10}}}$ ).","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"6 1","pages":"753 - 759"},"PeriodicalIF":0.7,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86699161","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
Weak sequenceability in cyclic groups 循环群中的弱序列性
IF 0.7 4区 数学
Journal of Combinatorial Designs Pub Date : 2022-09-26 DOI: 10.1002/jcd.21862
Simone Costa, Stefano Della Fiore
{"title":"Weak sequenceability in cyclic groups","authors":"Simone Costa,&nbsp;Stefano Della Fiore","doi":"10.1002/jcd.21862","DOIUrl":"https://doi.org/10.1002/jcd.21862","url":null,"abstract":"&lt;p&gt;A subset &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $A$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of an abelian group &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is &lt;i&gt;sequenceable&lt;/i&gt; if there is an ordering &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 \u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mtext&gt;…&lt;/mtext&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;msub&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 \u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 \u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt; $({a}_{1},ldots ,{a}_{k})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of its elements such that the partial sums &lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 \u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 \u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;msub&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 \u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;mtext&gt;…&lt;/mtext&gt;\u0000 \u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 \u0000 &lt;msub&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"30 12","pages":"735-751"},"PeriodicalIF":0.7,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.21862","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72166654","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: 4
Completing the spectrum of semiframes with block size three 完成块大小为3的半帧频谱
IF 0.7 4区 数学
Journal of Combinatorial Designs Pub Date : 2022-09-13 DOI: 10.1002/jcd.21856
H. Cao, D. Xu, Hao Zheng
{"title":"Completing the spectrum of semiframes with block size three","authors":"H. Cao, D. Xu, Hao Zheng","doi":"10.1002/jcd.21856","DOIUrl":"https://doi.org/10.1002/jcd.21856","url":null,"abstract":"A k ‐semiframe of type g u is a k ‐GDD of type g u ( X , G , ℬ ) , in which the collection of blocks ℬ can be written as a disjoint union ℬ = P ∪ Q , where P is partitioned into parallel classes of X and Q is partitioned into holey parallel classes, each holey parallel class being a partition of X G for some G ∈ G . In this paper, we will introduce a new concept of t ‐perfect semiframe and use it to prove the existence of a 3‐semiframe of type g u with even group size. This completes the proof of the existence of 3‐semiframes with uniform group size.","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"5 1","pages":"716 - 732"},"PeriodicalIF":0.7,"publicationDate":"2022-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76964572","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
Completing the spectrum of semiframes with block size three 完成块大小为3的半帧的谱
IF 0.7 4区 数学
Journal of Combinatorial Designs Pub Date : 2022-09-13 DOI: 10.1002/jcd.21856
H. Cao, D. Xu, H. Zheng
{"title":"Completing the spectrum of semiframes with block size three","authors":"H. Cao,&nbsp;D. Xu,&nbsp;H. Zheng","doi":"10.1002/jcd.21856","DOIUrl":"https://doi.org/10.1002/jcd.21856","url":null,"abstract":"<p>A <math>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow></math>-semiframe of type <math>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>g</mi>\u0000 \u0000 <mi>u</mi>\u0000 </msup>\u0000 </mrow></math> is a <math>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow></math>-GDD of type <math>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>g</mi>\u0000 \u0000 <mi>u</mi>\u0000 </msup>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>X</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>ℬ</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math>, in which the collection of blocks <math>\u0000 \u0000 <mrow>\u0000 <mi>ℬ</mi>\u0000 </mrow></math> can be written as a disjoint union <math>\u0000 \u0000 <mrow>\u0000 <mi>ℬ</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mi>P</mi>\u0000 \u0000 <mo>∪</mo>\u0000 \u0000 <mi>Q</mi>\u0000 </mrow></math>, where <math>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow></math> is partitioned into parallel classes of <math>\u0000 \u0000 <mrow>\u0000 <mi>X</mi>\u0000 </mrow></math> and <math>\u0000 \u0000 <mrow>\u0000 <mi>Q</mi>\u0000 </mrow></math> is partitioned into holey parallel classes, each holey parallel class being a partition of <math>\u0000 \u0000 <mrow>\u0000 <mi>X</mi>\u0000 \u0000 <mo></mo>\u0000 \u0000 <mi>G</mi>\u0000 </mrow></math> for some <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mi>G</mi>\u0000 </mrow></math>. In this paper, we will introduce a new concept of <math>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow></math>-perfect semiframe and use it to prove the existence of a 3-semiframe of type <math>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>g</mi>\u0000 \u0000 <mi>u</mi>\u0000 </msup>\u0000 </mrow></math> with even group size. This completes the proof of the existence of 3-semiframes with uniform group size.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"30 11","pages":"716-732"},"PeriodicalIF":0.7,"publicationDate":"2022-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72169121","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
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信