Journal of Combinatorial Designs最新文献_第9页

The maximum number of columns in E ( s 2 ) $,E({s}^{2})$ -optimal supersaturated designs with 16 rows and s max = 4 ${s}_{{rm{max }}}=4$ is 60 E（s 2）$中的最大列数，E（｛s｝^｛2｝）$—具有16行且s最大=4的最优过饱和设计${s}_｛｛rm｝｝＝4$等于60

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2023-01-09 DOI: 10.1002/jcd.21873

Luis B. Morales

{"title":"The maximum number of columns in \u0000 \u0000 \u0000 \u0000 E\u0000 \u0000 (\u0000 \u0000 s\u0000 2\u0000 \u0000 )\u0000 \u0000 \u0000 $,E({s}^{2})$\u0000 -optimal supersaturated designs with 16 rows and \u0000 \u0000 \u0000 \u0000 s\u0000 max\u0000 \u0000 =\u0000 4\u0000 \u0000 ${s}_{{rm{max }}}=4$\u0000 is 60","authors":"Luis B. Morales","doi":"10.1002/jcd.21873","DOIUrl":"https://doi.org/10.1002/jcd.21873","url":null,"abstract":"We show that the maximum number of columns in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mspace></mspace>\u0000 <mi>E</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>s</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $,E({s}^{2})$</annotation>\u0000 </semantics></math>-optimal supersaturated designs (SSDs) with 16 rows and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>s</mi>\u0000 <mi>max</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation> ${s}_{{rm{max }}}=4$</annotation>\u0000 </semantics></math> is 60 by showing that there exists no resolvable 2-(16, 8, 35) design such that any two blocks from different parallel classes intersect in 3, 5, or 4 points. This is accomplished by an exhaustive computer search that uses the parallel class intersection pattern method to reduce the search space. We also classify all nonisomorphic <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mspace></mspace>\u0000 <mi>E</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>s</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $,E({s}^{2})$</annotation>\u0000 </semantics></math>-optimal 5-circulant SSDs with 16 rows and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>s</mi>\u0000 <mi>max</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mn>8</mn>\u0000 </mrow>\u0000 <annotation> ${s}_{{rm{max }}}=8$</annotation>\u0000 </semantics></math>.","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 4","pages":"165-178"},"PeriodicalIF":0.7,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50143087","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

Euclidean designs obtained from spherical embedding of coherent configurations 相干配置球面嵌入的欧氏设计

IF 0.7 4区数学

Journal of Combinatorial Designs Pub Date : 2022-12-19 DOI: 10.1002/jcd.21871

Aiguo Wang, Yan Zhu

{"title":"Euclidean designs obtained from spherical embedding of coherent configurations","authors":"Aiguo Wang, Yan Zhu","doi":"10.1002/jcd.21871","DOIUrl":"https://doi.org/10.1002/jcd.21871","url":null,"abstract":"Coherent configurations are a generalization of association schemes. Motivated by the recent study of Q-polynomial coherent configurations, in this paper, we study the spherical embedding of a Q-polynomial coherent configuration into some eigenspace by a primitive idempotent. We present a necessary and sufficient condition when the embedding becomes a Euclidean <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $t$</annotation>\u0000 </semantics></math>-design (on two concentric spheres) in terms of the Krein numbers for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation> $tle 4$</annotation>\u0000 </semantics></math>. In addition, we obtain some Euclidean 2- or 3-designs from spherical embedding of coherent configurations including tight relative 4- or 5-designs in binary Hamming schemes and the union of derived designs of a tight 4-design in Hamming schemes.","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 3","pages":"143-161"},"PeriodicalIF":0.7,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50137509","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 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":"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

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, Anita Pasotti","doi":"10.1002/jcd.21866","DOIUrl":"https://doi.org/10.1002/jcd.21866","url":null,"abstract":"Square relative nonzero sum Heffter arrays, denoted by <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 \u0000 <msub>\u0000 <mi>H</mi>\u0000 \u0000 <mi>t</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>;</mo>\u0000 \u0000 <mi>k</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${rm{N}}{{rm{H}}}_{t}(n;k)$</annotation>\u0000 </semantics></math>, have been introduced as a variant of the classical concept of Heffter array. An <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 \u0000 <msub>\u0000 <mi>H</mi>\u0000 \u0000 <mi>t</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>;</mo>\u0000 \u0000 <mi>k</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${rm{N}}{{rm{H}}}_{t}(n;k)$</annotation>\u0000 </semantics></math> is an <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation> $ntimes n$</annotation>\u0000 </semantics></math> partially filled array with elements in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>Z</mi>\u0000 \u0000 <mi>v</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{mathbb{Z}}}_{v}$</annotation>\u0000 </semantics></math>, where <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mn>2</mn>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mi>k</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $v=2nk+t$</annotation>\u0000 </semantics></math>, whose rows and whose columns contain <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math> 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, Jinwei Wu, Dianhua Wu","doi":"10.1002/jcd.21865","DOIUrl":"https://doi.org/10.1002/jcd.21865","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>≡</mo>\u0000 \u0000 <mn>0</mn>\u0000 <mspace></mspace>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <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\"><mrow><mrow><mi>n</mi><mo>unicode{x02261}</mo><mn>0</mn><mspace width=\"0.3em\"/><mrow><mo class=\"MathClass-open\">(</mo><mrow><mi>mod</mi><mspace width=\"0.3em\"/><mn>4</mn></mrow><mo class=\"MathClass-close\">)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> be a positive integer, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>M</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <msub>\u0000 <mi>m</mi>\u0000 \u0000 <mrow>\u0000 <mi>i</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>j</mi>\u0000 </mrow>\u0000 </msub>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <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\"><mrow><mrow><mi>M</mi><mo>=</mo><mrow><mo class=\"MathClass-open\">(</mo><msub><mi>m</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo class=\"MathClass-close\">)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> be a magic square, where <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <msub>\u0000 <mi>m</mi>\u0000 \u0000 <mrow>\u0000 <mi>i</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>j</mi>\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, Jan De Beule, Francesco Pavese, Valentino Smaldore","doi":"10.1002/jcd.21864","DOIUrl":"https://doi.org/10.1002/jcd.21864","url":null,"abstract":"In this paper we provide constructive lower bounds on the sizes of the largest partial ovoids of the symplectic polar spaces <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>W</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>3</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>q</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${mathscr{W}}(3,q)$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation> $q$</annotation>\u0000 </semantics></math> odd square, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 \u0000 <mo>≢</mo>\u0000 \u0000 <mn>0</mn>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>mod</mi>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $qnotequiv 0(mathrm{mod}3)$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>W</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>5</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>q</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${mathscr{W}}(5,q)$</annotation>\u0000 </semantics></math> and of the Hermitian polar spaces <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℋ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>4</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msup>\u0000 <mi>q</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${rm{ {mathcal H} }}(4,{q}^{2})$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 <","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

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

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, Stefano Della Fiore","doi":"10.1002/jcd.21862","DOIUrl":"https://doi.org/10.1002/jcd.21862","url":null,"abstract":"A subset <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $A$</annotation>\u0000 </semantics></math> of an abelian group <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is sequenceable if there is an ordering <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>a</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mtext>…</mtext>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>a</mi>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $({a}_{1},ldots ,{a}_{k})$</annotation>\u0000 </semantics></math> of its elements such that the partial sums <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>s</mi>\u0000 \u0000 <mn>0</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>s</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mtext>…</mtext>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>s</mi>\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