发布求助
文献互助 智能选刊 最新文献

SIAM J. Discret. Math.最新文献

筛选
英文 中文
Rank-Metric Codes, Semifields, and the Average Critical Problem 等级-度量码、半域和平均临界问题
SIAM J. Discret. Math. Pub Date : 2023-06-15 DOI: 10.1137/22m1486893
Anina Gruica, A. Ravagnani, John Sheekey, Ferdinando Zullo
{"title":"Rank-Metric Codes, Semifields, and the Average Critical Problem","authors":"Anina Gruica, A. Ravagnani, John Sheekey, Ferdinando Zullo","doi":"10.1137/22m1486893","DOIUrl":"https://doi.org/10.1137/22m1486893","url":null,"abstract":"We investigate two fundamental questions intersecting coding theory and combinatorial geometry, with emphasis on their connections. These are the problem of computing the asymptotic density of MRD codes in the rank metric, and the Critical Problem for combinatorial geometries by Crapo and Rota. Using methods from semifield theory, we derive two lower bounds for the density function of full-rank, square MRD codes. The first bound is sharp when the matrix size is a prime number and the underlying field is sufficiently large, while the second bound applies to the binary field. We then take a new look at the Critical Problem for combinatorial geometries, approaching it from a qualitative, often asymptotic, viewpoint. We illustrate the connection between this very classical problem and that of computing the asymptotic density of MRD codes. Finally, we study the asymptotic density of some special families of codes in the rank metric, including the symmetric, alternating and Hermitian ones. In particular, we show that the optimal codes in these three contexts are sparse.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"11 1","pages":"1079-1117"},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74703849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On the Parameterized Complexity of Counting Small-Sized Minimum (boldsymbol{(S,T)})-Cuts 计算小尺寸最小值的参数化复杂度(boldsymbol{(S,T)}) -Cuts
SIAM J. Discret. Math. Pub Date : 2023-06-13 DOI: 10.1137/21m1398203
Pierre Bergé, Wassim Bouaziz, Arpad Rimmel, J. Tomasik
{"title":"On the Parameterized Complexity of Counting Small-Sized Minimum (boldsymbol{(S,T)})-Cuts","authors":"Pierre Bergé, Wassim Bouaziz, Arpad Rimmel, J. Tomasik","doi":"10.1137/21m1398203","DOIUrl":"https://doi.org/10.1137/21m1398203","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"1 1","pages":"964-996"},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77238233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Colorful Matchings 彩色拼毛
SIAM J. Discret. Math. Pub Date : 2023-06-12 DOI: 10.1137/21m139997x
A. Arman, V. Rödl, M. Sales
{"title":"Colorful Matchings","authors":"A. Arman, V. Rödl, M. Sales","doi":"10.1137/21m139997x","DOIUrl":"https://doi.org/10.1137/21m139997x","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"23 1","pages":"925-950"},"PeriodicalIF":0.0,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77778001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
(boldsymbol{H})-Games Played on Vertex Sets of Random Graphs (boldsymbol{H})-在随机图的顶点集上玩的游戏
SIAM J. Discret. Math. Pub Date : 2023-06-09 DOI: 10.1137/20m1375991
Gal Kronenberg, Adva Mond, A. Naor
{"title":"(boldsymbol{H})-Games Played on Vertex Sets of Random Graphs","authors":"Gal Kronenberg, Adva Mond, A. Naor","doi":"10.1137/20m1375991","DOIUrl":"https://doi.org/10.1137/20m1375991","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"10 1","pages":"864-916"},"PeriodicalIF":0.0,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75506236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Density of (boldsymbol{mathbb{Z}_3}) -Flow-Critical Graphs 论(boldsymbol{mathbb{Z}_3}) -流临界图的密度
SIAM J. Discret. Math. Pub Date : 2023-06-01 DOI: 10.1137/22m1496529
Z. Dvořák, B. Mohar
{"title":"On Density of (boldsymbol{mathbb{Z}_3}) -Flow-Critical Graphs","authors":"Z. Dvořák, B. Mohar","doi":"10.1137/22m1496529","DOIUrl":"https://doi.org/10.1137/22m1496529","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"1 1","pages":"699-717"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76129444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Parameterized Counting and Cayley Graph Expanders 参数化计数和Cayley图展开器
SIAM J. Discret. Math. Pub Date : 2023-04-26 DOI: 10.1137/22m1479804
N. Peyerimhoff, M. Roth, Johannes Schmitt, J. Stix, A. Vdovina, Philip Wellnitz
{"title":"Parameterized Counting and Cayley Graph Expanders","authors":"N. Peyerimhoff, M. Roth, Johannes Schmitt, J. Stix, A. Vdovina, Philip Wellnitz","doi":"10.1137/22m1479804","DOIUrl":"https://doi.org/10.1137/22m1479804","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"100 1","pages":"405-486"},"PeriodicalIF":0.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73616417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On the girth and diameter of generalized Johnson graphs 关于广义Johnson图的周长和直径
SIAM J. Discret. Math. Pub Date : 2023-04-06 DOI: 10.1016/j.disc.2017.08.022
Louis Anthony Agong, Carmen Amarra, IV JohnS.Caughman, Ari J. Herman, Tai Terada
{"title":"On the girth and diameter of generalized Johnson graphs","authors":"Louis Anthony Agong, Carmen Amarra, IV JohnS.Caughman, Ari J. Herman, Tai Terada","doi":"10.1016/j.disc.2017.08.022","DOIUrl":"https://doi.org/10.1016/j.disc.2017.08.022","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"10 1","pages":"138-142"},"PeriodicalIF":0.0,"publicationDate":"2023-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90332329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Improved Bound for the Gerver-Ramsey Collinearity Problem Gerver-Ramsey共线性问题的改进界
SIAM J. Discret. Math. Pub Date : 2023-03-25 DOI: 10.48550/arXiv.2303.14579
T. Lidbetter
{"title":"Improved Bound for the Gerver-Ramsey Collinearity Problem","authors":"T. Lidbetter","doi":"10.48550/arXiv.2303.14579","DOIUrl":"https://doi.org/10.48550/arXiv.2303.14579","url":null,"abstract":"Let $S$ be a finite subset of $mathbb{Z}^n$. A vector sequence $(mathbf{z}_i)$ is an $S$-walk if and only if $mathbf{z}_{i+1} - mathbf{z}_i$ is an element of $S$ for all $i$. Gerver and Ramsey showed in 1979 that for $Ssubset mathbb{Z}^3$ there exists an infinite $S$-walk in which no $5^{11} + 1=48{small,}828{small,}126$ points are collinear. Here, we use the same general approach, but with the aid of a computer search, to improve the bound to $189$.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"72 1","pages":"113718"},"PeriodicalIF":0.0,"publicationDate":"2023-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82115736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Graph Parameters, Implicit Representations and Factorial Properties 图参数，隐式表示和阶乘性质
SIAM J. Discret. Math. Pub Date : 2023-03-08 DOI: 10.1007/978-3-031-06678-8_5
Bogdan Alecu, V. E. Alekseev, A. Atminas, V. Lozin, V. Zamaraev
{"title":"Graph Parameters, Implicit Representations and Factorial Properties","authors":"Bogdan Alecu, V. E. Alekseev, A. Atminas, V. Lozin, V. Zamaraev","doi":"10.1007/978-3-031-06678-8_5","DOIUrl":"https://doi.org/10.1007/978-3-031-06678-8_5","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"5 1","pages":"113573"},"PeriodicalIF":0.0,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88214647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Recoloring Planar Graphs of Girth at Least Five 周长至少为5的平面图重新上色
SIAM J. Discret. Math. Pub Date : 2023-02-21 DOI: 10.1137/21m1463598
Valentin Bartier, N. Bousquet, Carl Feghali, Marc Heinrich, B. Moore, Théo Pierron
{"title":"Recoloring Planar Graphs of Girth at Least Five","authors":"Valentin Bartier, N. Bousquet, Carl Feghali, Marc Heinrich, B. Moore, Théo Pierron","doi":"10.1137/21m1463598","DOIUrl":"https://doi.org/10.1137/21m1463598","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"10 1","pages":"332-350"},"PeriodicalIF":0.0,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72930481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
首页 上一页 下一页 尾页
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
现在去查看 取消
×
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：481959085
Book学术官方微信