Pub Date : 2019-08-13DOI: 10.26493/1855-3974.2126.5b3
David Dolvzan, Gabriel Verret
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.
在有限个零因子的反交换半环上，确定了矩阵的半环的零因子有向图的自同构群。
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Pub Date : 2019-05-16DOI: 10.26493/1855-3974.2677.b7f
Dániel Gerbner
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.
{"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}
Pub Date : 2018-06-25DOI: 10.26493/1855-3974.989.d15
Aureliano M. Robles Pérez, José Carlos Rosales
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 = ∅ .
{"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}
Pub Date : 2017-05-09DOI: 10.26493/1855-3974.1054.FCD
S. Cichacz
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.
我们说一个有限阿贝尔群Γconstant-sum-partition属性为t集(CSP (t)财产)如果为每个分区n = 1 + r 2 + ... + r t (n, 2 r≥2≤≤t,我有一个分区Γ两两不相交的子集1,2,…,t,这样∣我∣= r和一些ν∈Γ,∑∈一我=ν1≤≤t。对于ν = g 0(其中g 0是Γ的单位元)，我们说Γ具有零和划分属性，分为t个集合(ZSP (t) -属性)。图G = (V, E)，∣V∣= n的Γ -距离幻标号是一个从V到n阶阿贝尔群Γ的双射l，使得每个顶点x∈V的权w (x) =∑y∈n (x) l(y)等于同一个元素μ∈Γ，称为幻常数。如果对于每个阶为∣V (G)∣的阿别群Γ存在一个Γ -距离幻标，则图G称为群距离幻图。本文研究了Γ的CSP(3) -性质，并将结果应用于群距离幻完全三部图的研究。
{"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}
Pub Date : 2009-06-02DOI: 10.26493/1855-3974.103.E09
Indulal Gopalapillai
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.
{"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}
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