Pub Date : 2023-09-22DOI: 10.1007/s10801-023-01269-9
Matteo Bonini, Martino Borello, Eimear Byrne
Abstract We introduce the concept of a rank-saturating system and outline its correspondence to a rank-metric code with a given covering radius. We consider the problem of finding the value of $$s_{q^m/q}(k,rho )$$ sqm/q(k,ρ) , which is the minimum $$mathbb {F}_q$$ Fq -dimension of a q -system in $$mathbb {F}_{q^m}^k$$ Fqmk that is rank- $$rho $$ ρ -saturating. This is equivalent to the covering problem in the rank metric. We obtain upper and lower bounds on $$s_{q^m/q}(k,rho )$$ sqm/q(k,ρ) and evaluate it for certain values of k and $$rho $$ ρ . We give constructions of rank- $$rho $$ ρ -saturating systems suggested from geometry.
摘要引入了秩饱和系统的概念，并概述了它与给定覆盖半径的秩度量码的对应关系。我们考虑寻找$$s_{q^m/q}(k,rho )$$ s q m / q (k， ρ)的值的问题，它是$$mathbb {F}_{q^m}^k$$ F q m k中秩- $$rho $$ ρ -饱和的q -系统的最小$$mathbb {F}_q$$ F q -维。这相当于秩度量中的覆盖问题。我们得到了$$s_{q^m/q}(k,rho )$$ s q m / q (k， ρ)的上界和下界，并对k和$$rho $$ ρ的某些值进行了计算。我们给出了秩- $$rho $$ ρ -饱和系统的构造。
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Pub Date : 2023-09-22DOI: 10.1007/s10801-023-01270-2
Lu Zheng, Bo Zhou
{"title":"The closeness eigenvalues of graphs","authors":"Lu Zheng, Bo Zhou","doi":"10.1007/s10801-023-01270-2","DOIUrl":"https://doi.org/10.1007/s10801-023-01270-2","url":null,"abstract":"","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136059162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-22DOI: 10.1007/s10801-023-01267-x
Sayyed Heidar Jafari, Samir Zahirović
{"title":"Power graphs of all nilpotent groups","authors":"Sayyed Heidar Jafari, Samir Zahirović","doi":"10.1007/s10801-023-01267-x","DOIUrl":"https://doi.org/10.1007/s10801-023-01267-x","url":null,"abstract":"","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136059286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-21DOI: 10.1007/s10801-023-01260-4
Xueyi Huang, Lu Lu, Katja Mönius
{"title":"Splitting fields of mixed Cayley graphs over abelian groups","authors":"Xueyi Huang, Lu Lu, Katja Mönius","doi":"10.1007/s10801-023-01260-4","DOIUrl":"https://doi.org/10.1007/s10801-023-01260-4","url":null,"abstract":"","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136101792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-14DOI: 10.1007/s10801-023-01257-z
Daniel Gonçalves, Virgínia Silva Rodrigues, Yolanda Cabrera Casado
{"title":"Special Issue: CIMPA Floripa: from dynamics to algebra and representation theory and back","authors":"Daniel Gonçalves, Virgínia Silva Rodrigues, Yolanda Cabrera Casado","doi":"10.1007/s10801-023-01257-z","DOIUrl":"https://doi.org/10.1007/s10801-023-01257-z","url":null,"abstract":"","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135208522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-15DOI: 10.1007/s10801-023-01236-4
M. Orel
{"title":"The core of a complementary prism","authors":"M. Orel","doi":"10.1007/s10801-023-01236-4","DOIUrl":"https://doi.org/10.1007/s10801-023-01236-4","url":null,"abstract":"","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"58 1","pages":"589 - 609"},"PeriodicalIF":0.8,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43612480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-13DOI: 10.1007/s10801-023-01248-0
José Martínez-Bernal, Oscar A. Pizá-Morales, Miguel A. Valencia-Bucio
{"title":"Nonvanishing Betti numbers of edge ideals of weakly chordal graphs","authors":"José Martínez-Bernal, Oscar A. Pizá-Morales, Miguel A. Valencia-Bucio","doi":"10.1007/s10801-023-01248-0","DOIUrl":"https://doi.org/10.1007/s10801-023-01248-0","url":null,"abstract":"","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"58 1","pages":"279 - 290"},"PeriodicalIF":0.8,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45306922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-13DOI: 10.1007/s10801-023-01251-5
Badriah Al-Juaid, M. Jackson, James Koussas, T. Kowalski
{"title":"Edge colourings and qualitative representations of chromatic algebras","authors":"Badriah Al-Juaid, M. Jackson, James Koussas, T. Kowalski","doi":"10.1007/s10801-023-01251-5","DOIUrl":"https://doi.org/10.1007/s10801-023-01251-5","url":null,"abstract":"","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"58 1","pages":"157 - 182"},"PeriodicalIF":0.8,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47914295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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