{"title":"The automorphism group of the zero-divisor digraph of matrices over an antiring","authors":"David Dolvzan, Gabriel Verret","doi":"10.26493/1855-3974.2126.5b3","DOIUrl":"https://doi.org/10.26493/1855-3974.2126.5b3","url":null,"abstract":"We determine the automorphism group of the zero-divisor digraph of the semiring of matrices over an antinegative commutative semiring with a finite number of zero-divisors.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81090138","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 covering lemma and q-analogues of extremal set theory problems","authors":"Dániel Gerbner","doi":"10.26493/1855-3974.2677.b7f","DOIUrl":"https://doi.org/10.26493/1855-3974.2677.b7f","url":null,"abstract":"We prove a general lemma (inspired by a lemma of Holroyd and Talbot) about the connection of the largest cardinalities (or weight) of structures satisfying some hereditary property and substructures satisfying the same hereditary property. We use it to show how results concerning forbidden subposet problems in the Boolean poset imply analogous results in the poset of subspaces of a finite vector space. We also study generalized forbidden subposet problems in the poset of subspaces.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82746005","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":"A combinatorial problem and numerical semigroups","authors":"Aureliano M. Robles Pérez, José Carlos Rosales","doi":"10.26493/1855-3974.989.d15","DOIUrl":"https://doi.org/10.26493/1855-3974.989.d15","url":null,"abstract":"Let a = ( a 1 , …, a n ) and b = ( b 1 , …, b n ) be two n -tuples of positive integers, let X be a set of positive integers, and let g be a positive integer. In this work we show an algorithmic process in order to compute all the sets C of positive integers that fulfill the following conditions: The cardinality of C is equal to g ; If x , y ∈ ℕ {0} and x + y ∈ C , then C ∩ { x , y } ≠ ∅ ; If x ∈ C and ( x − b i ) / a i ∈ ℕ {0} for some i ∈ {1, …, n } , then ( x − b i ) / a i ∈ C ; X ∩ C = ∅ .","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89625534","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":"On zero sum-partition of Abelian groups into three sets and group distance magic labeling","authors":"S. Cichacz","doi":"10.26493/1855-3974.1054.FCD","DOIUrl":"https://doi.org/10.26493/1855-3974.1054.FCD","url":null,"abstract":"We say that a finite Abelian group Γ has the constant-sum-partition property into t sets (CSP ( t ) -property) if for every partition n = r 1 + r 2 + … + r t of n , with r i ≥ 2 for 2 ≤ i ≤ t , there is a partition of Γ into pairwise disjoint subsets A 1 , A 2 , …, A t , such that ∣ A i ∣ = r i and for some ν ∈ Γ , ∑ a ∈ A i a = ν for 1 ≤ i ≤ t . For ν = g 0 (where g 0 is the identity element of Γ ) we say that Γ has zero-sum-partition property into t sets (ZSP ( t ) -property). A Γ -distance magic labeling of a graph G = ( V , E ) with ∣ V ∣ = n is a bijection l from V to an Abelian group Γ of order n such that the weight w ( x ) = ∑ y ∈ N ( x ) l( y ) of every vertex x ∈ V is equal to the same element μ ∈ Γ , called the magic constant . A graph G is called a group distance magic graph if there exists a Γ -distance magic labeling for every Abelian group Γ of order ∣ V ( G )∣ . In this paper we study the CSP (3) -property of Γ , and apply the results to the study of group distance magic complete tripartite graphs.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73930804","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":"Distance spectrum of graph compositions","authors":"Indulal Gopalapillai","doi":"10.26493/1855-3974.103.E09","DOIUrl":"https://doi.org/10.26493/1855-3974.103.E09","url":null,"abstract":"The D -eigenvalues μ 1 , μ 2 , ..., μ p of a graph G are the eigenvalues of its distance matrix D and form the distance spectrum or the D -spectrum. In this paper we obtain the D -spectrum of the cartesian product if two distance regular graphs. The D -spectrum of the lexicographic product G [ H ] of two graphs G and H when H is regular is also obtained. The D -eigenvalues of the Hamming graphs Ham( d, n ) of diameter d and order n d and those of the C 4 nanotori, T k , m , C 4 , are determined.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2009-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73029369","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":"How Long is the Future? Working with Life-limited and Life-threatened Children","authors":"E. Brown","doi":"10.1558/IMRE.V3I1.5","DOIUrl":"https://doi.org/10.1558/IMRE.V3I1.5","url":null,"abstract":"","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2007-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86496002","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}