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FPT-Algorithms for the (ell) -Matchoid Problem with a Coverage Objective 具有覆盖目标的(ell) -匹配问题的fpt算法
SIAM J. Discret. Math. Pub Date : 2023-06-15 DOI: 10.1137/21m1442267
Chien-Chung Huang, Justin Ward
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引用次数: 0
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Erdős Matching Conjecture for almost perfect matchings Erdős匹配猜想几乎完美匹配
SIAM J. Discret. Math. Pub Date : 2023-04-01 DOI: 10.48550/arXiv.2206.01526
D. Kolupaev, A. Kupavskii
{"title":"Erdős Matching Conjecture for almost perfect matchings","authors":"D. Kolupaev, A. Kupavskii","doi":"10.48550/arXiv.2206.01526","DOIUrl":"https://doi.org/10.48550/arXiv.2206.01526","url":null,"abstract":"","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76438784","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
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":null,"pages":null},"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
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