{"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}
{"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}
{"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}
{"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}
{"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}
{"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}
{"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}
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}
{"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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