Pub Date : 2023-09-29DOI: 10.1007/s10801-023-01271-1
Subhajit Ghosh
{"title":"Cutoff phenomenon for the warp-transpose top with random shuffle","authors":"Subhajit Ghosh","doi":"10.1007/s10801-023-01271-1","DOIUrl":"https://doi.org/10.1007/s10801-023-01271-1","url":null,"abstract":"","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135131717","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 : 2023-09-23DOI: 10.1007/s10801-023-01263-1
Elad Paran
{"title":"Combinatorial Nullstellensatz over division rings","authors":"Elad Paran","doi":"10.1007/s10801-023-01263-1","DOIUrl":"https://doi.org/10.1007/s10801-023-01263-1","url":null,"abstract":"","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135959871","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/s10801-023-01259-x
J. W. Sander, T. Sander
Abstract We present a method which in principal allows to characterise all integral circulant graphs with multiplicative divisor set having a spectrum, i.e. the set of distinct eigenvalues, of any given size. We shall exemplify the method for spectra of up to four eigenvalues, also reproving some known results for three eigenvalues along the way. In particular we show that given any integral circulant graph of arbitrary order n with multiplicative divisor set and precisely four distinct eigenvalues, n necessarily is either a prime power or the product of two prime powers with explicitly given simply structured divisor set and set of eigenvalues in both cases.
{"title":"Characterisation of all integral circulant graphs with multiplicative divisor sets and few eigenvalues","authors":"J. W. Sander, T. Sander","doi":"10.1007/s10801-023-01259-x","DOIUrl":"https://doi.org/10.1007/s10801-023-01259-x","url":null,"abstract":"Abstract We present a method which in principal allows to characterise all integral circulant graphs with multiplicative divisor set having a spectrum, i.e. the set of distinct eigenvalues, of any given size. We shall exemplify the method for spectra of up to four eigenvalues, also reproving some known results for three eigenvalues along the way. In particular we show that given any integral circulant graph of arbitrary order n with multiplicative divisor set and precisely four distinct eigenvalues, n necessarily is either a prime power or the product of two prime powers with explicitly given simply structured divisor set and set of eigenvalues in both cases.","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136015935","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/s10801-023-01269-9
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。
{"title":"Saturating systems and the rank-metric covering radius","authors":"Matteo Bonini, Martino Borello, Eimear Byrne","doi":"10.1007/s10801-023-01269-9","DOIUrl":"https://doi.org/10.1007/s10801-023-01269-9","url":null,"abstract":"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 $$s_{q^m/q}(k,rho )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:msup> <mml:mi>q</mml:mi> <mml:mi>m</mml:mi> </mml:msup> <mml:mo>/</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>k</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ρ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , which is the minimum $$mathbb {F}_q$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:math> -dimension of a q -system in $$mathbb {F}_{q^m}^k$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mrow> <mml:msup> <mml:mi>q</mml:mi> <mml:mi>m</mml:mi> </mml:msup> </mml:mrow> <mml:mi>k</mml:mi> </mml:msubsup> </mml:math> that is rank- $$rho $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ρ</mml:mi> </mml:math> -saturating. This is equivalent to the covering problem in the rank metric. We obtain upper and lower bounds on $$s_{q^m/q}(k,rho )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:msup> <mml:mi>q</mml:mi> <mml:mi>m</mml:mi> </mml:msup> <mml:mo>/</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>k</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ρ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and evaluate it for certain values of k and $$rho $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ρ</mml:mi> </mml:math> . We give constructions of rank- $$rho $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ρ</mml:mi> </mml:math> -saturating systems suggested from geometry.","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136061518","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/s10801-023-01270-2
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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