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On noncommutative generalisations of Boolean algebras 布尔代数的非交换推广
Art Discret. Appl. Math. Pub Date : 2019-05-29 DOI: 10.26493/2590-9770.1323.ceb
A. Bucciarelli, A. Salibra
{"title":"On noncommutative generalisations of Boolean algebras","authors":"A. Bucciarelli, A. Salibra","doi":"10.26493/2590-9770.1323.ceb","DOIUrl":"https://doi.org/10.26493/2590-9770.1323.ceb","url":null,"abstract":"Skew Boolean algebras (skew BA) and Boolean-like algebras (nBA) are one-pointed and n-pointed noncommutative generalisation of Boolean algebras, respectively. We show that any nBA is a cluster of n isomorphic right-handed skew BAs, axiomatised here as the variety of skew star algebras. The variety of skew star algebras is shown to be term equivalent to the variety of nBAs. We use skew BAs in order to develop a general theory of multideals for nBAs. We also provide a representation theorem for right-handed skew BAs in terms of nBAs of n-partitions.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133248021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Groupoids on a skew lattice of objects 对象的斜格上的群
Art Discret. Appl. Math. Pub Date : 2018-10-13 DOI: 10.26493/2590-9770.1342.109
D. Fitzgerald
{"title":"Groupoids on a skew lattice of objects","authors":"D. Fitzgerald","doi":"10.26493/2590-9770.1342.109","DOIUrl":"https://doi.org/10.26493/2590-9770.1342.109","url":null,"abstract":"Motivated by some alternatives to the classical logical model of boolean algebra, this paper deals with algebraic structures which extend skew lattices by locally invertible elements. Following the meme of the Ehresmann-Schein-Nambooripad theorem, we consider a groupoid (small category of isomorphisms) in which the set of objects carries the structure of a skew lattice. The objects act on the morphisms by left and right restriction and extension mappings of the morphisms, imitating those of an inductive groupoid. Conditions are placed on the actions, from which pseudoproducts may be defined. This gives an algebra of signature (2,2,1), in which each binary operation has the structure of an orthodox semigroup. In the reverse direction, a groupoid of the kind described may be reconstructed from the algebra.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115490431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Automorphism groups of Walecki tournaments with zero and odd signatures 具有零和奇签名的Walecki锦标赛的自同构群
Art Discret. Appl. Math. Pub Date : 2018-08-26 DOI: 10.26493/2590-9770.1266.729
J. Ales
{"title":"Automorphism groups of Walecki tournaments with zero and odd signatures","authors":"J. Ales","doi":"10.26493/2590-9770.1266.729","DOIUrl":"https://doi.org/10.26493/2590-9770.1266.729","url":null,"abstract":"Walecki tournaments were defined by Alspach in 1966. They form a class of regular tournaments that posses a natural Hamilton directed cycle decomposition. It has been conjectured by Kelly in 1964 that every regular tournament possesses such a decomposition. Therefore Walecki tournaments speak in favor of the conjecture. A second interest in Walecki tournaments arises from the mapping between cycles of the complementing circular shift register and isomorphism classes of Walecki tournaments. The problem of enumerating non-isomorphic Walecki tournaments has not been solved to date. We characterize the arc structure of Walecki tournaments whose corresponding binary sequences have zero and odd signature. Automorphism groups are determined for zero signature Walecki tournaments and for odd signature Walecki tournaments with the zero signature Walecki subtournaments. \u0000Walecki tournaments possess a broad range of subtournaments isomorphic to some Walecki tournament. Subtournaments of odd signature Walecki tournaments induced by the outsets of the central vertex are proven to be either regular or almost regular.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"32 Suppl 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116359735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Axiomatic characterization of transit functions of weak hierarchies 弱层次传递函数的公理化表征
Art Discret. Appl. Math. Pub Date : 2018-08-08 DOI: 10.26493/2590-9770.1260.989
M. Changat, Prasanth G. Narasimha-Shenoi, P. Stadler
{"title":"Axiomatic characterization of transit functions of weak hierarchies","authors":"M. Changat, Prasanth G. Narasimha-Shenoi, P. Stadler","doi":"10.26493/2590-9770.1260.989","DOIUrl":"https://doi.org/10.26493/2590-9770.1260.989","url":null,"abstract":"Transit functions provide a unified approach to study notions of intervals, convexities, and betweenness. Recently, their scope has been extended to certain set systems associated with clustering. We characterize here the class of set systems that correspond to k-ary monotonic transit functions. Convexities form a subclass and are characterized in terms of transit functions by two additional axioms. We then focus on axiom systems associated with weak hierarchies as well as other generalizations of hierarchical set systems.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"183 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121938274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Maximizing general first Zagreb and sum-connectivity indices for unicyclic graphs with given independence number 给定独立数的单环图的一般第一萨格勒布和和连通性指标的最大化
Art Discret. Appl. Math. Pub Date : 2018-08-08 DOI: 10.26493/2590-9770.1262.32A
I. Tomescu
{"title":"Maximizing general first Zagreb and sum-connectivity indices for unicyclic graphs with given independence number","authors":"I. Tomescu","doi":"10.26493/2590-9770.1262.32A","DOIUrl":"https://doi.org/10.26493/2590-9770.1262.32A","url":null,"abstract":"In this paper it is shown that in the class of unicyclic graphs of order n and independence number s, the spider graph SΔ(n, s) is the unique graph maximizing general first Zagreb index 0Rα(G) for α > 1 and general sum-connectivity index χα(G) for α ≥ 1.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124247499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Reaction graphs of double Fano planes 双范诺平面的反应图
Art Discret. Appl. Math. Pub Date : 2018-08-06 DOI: 10.26493/2590-9770.1239.E1F
Mariusz Meszka, A. Rosa
{"title":"Reaction graphs of double Fano planes","authors":"Mariusz Meszka, A. Rosa","doi":"10.26493/2590-9770.1239.E1F","DOIUrl":"https://doi.org/10.26493/2590-9770.1239.E1F","url":null,"abstract":"We consider various reaction graphs on the set of distinct double Fano planes.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133143713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On silver and golden optical orthogonal codes 对银和金光学正交码
Art Discret. Appl. Math. Pub Date : 2018-08-03 DOI: 10.26493/2590-9770.1236.CE4
M. Buratti
{"title":"On silver and golden optical orthogonal codes","authors":"M. Buratti","doi":"10.26493/2590-9770.1236.CE4","DOIUrl":"https://doi.org/10.26493/2590-9770.1236.CE4","url":null,"abstract":"It is several years that no theoretical construction for optimal (v, k, 1) optical orthogonal codes (OOCs) with new parameters has been discovered. In particular, the literature almost completely lacks optimal (v, k, 1)-OOCs with k > 3 which are not regular. In this paper we will show how some elementary difference multisets allow to obtain three new classes of optimal but not regular (3p, 4, 1)-, (5p, 5, 1)-, and (2p, 4, 1)-OOCs which are describable in terms of Pell and Fibonacci numbers. The OOCs of the first two classes (resp. third class) will be called silver (resp. golden) since they exist provided that the square of a silver element (resp. golden element) of ℤp is a primitive square of ℤp.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"130 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115894959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Subspace restrictions and affine composition for covering perfect hash families 覆盖完美哈希族的子空间限制和仿射组成
Art Discret. Appl. Math. Pub Date : 2018-08-03 DOI: 10.26493/2590-9770.1220.3A1
C. Colbourn, Erin Lanus
{"title":"Subspace restrictions and affine composition for covering perfect hash families","authors":"C. Colbourn, Erin Lanus","doi":"10.26493/2590-9770.1220.3A1","DOIUrl":"https://doi.org/10.26493/2590-9770.1220.3A1","url":null,"abstract":"Covering perfect hash families provide a very compact representation of a useful family of covering arrays, leading to the best asymptotic upper bounds and fast, effective algorithms. Their compactness implies that an additional row in the hash family leads to many new rows in the covering array. In order to address this, subspace restrictions constrain covering perfect hash family so that a predictable set of many rows in the covering array can be removed without loss of coverage. Computing failure probabilities for random selections that must, or that need not, satisfy the restrictions, we identify a set of restrictions on which to focus. We use existing algorithms together with one novel method, affine composition, to accelerate the search. We report on a set of computational constructions for covering arrays to demonstrate that imposing restrictions often improves on previously known upper bounds.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128511527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Self-dual, self-Petrie-dual and Möbius regular maps on linear fractional groups 线性分数群上的自对偶，自皮特对偶和Möbius正则映射
Art Discret. Appl. Math. Pub Date : 2018-07-30 DOI: 10.26493/2590-9770.1263.86e
G. Erskine, Katarína Hriňáková, Olivia Jeans
{"title":"Self-dual, self-Petrie-dual and Möbius regular maps on linear fractional groups","authors":"G. Erskine, Katarína Hriňáková, Olivia Jeans","doi":"10.26493/2590-9770.1263.86e","DOIUrl":"https://doi.org/10.26493/2590-9770.1263.86e","url":null,"abstract":"Regular maps on linear fractional groups $PSL(2,q)$ and $PGL(2,q$) have been studied for many years and the theory is well-developed, including generating sets for the asscoiated groups. This paper studies the properties of self-duality, self-Petrie-duality and Mobius regularity in this context, providing necessary and sufficient conditions for each case. We also address the special case for regular maps of type (5,5). The final section includes an enumeration of the $PSL(2,q)$ maps for $qle81$ and a list of all the $PSL(2,q)$ maps which have any of these special properties for $qle49$.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130823607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The number of independent sets in a connected graph and its complement 连通图及其补中的独立集的数目
Art Discret. Appl. Math. Pub Date : 2018-07-26 DOI: 10.26493/2590-9770.1258.C2B
Yarong Wei, Yumei Hu
{"title":"The number of independent sets in a connected graph and its complement","authors":"Yarong Wei, Yumei Hu","doi":"10.26493/2590-9770.1258.C2B","DOIUrl":"https://doi.org/10.26493/2590-9770.1258.C2B","url":null,"abstract":"For a connected graph G, the total number of independent vertex sets (including the empty vertex set) is denoted by i(G). In this paper, we consider Nordhaus-Gaddum-type inequalities for the number of independent sets of a connected graph with connected complement. First we define a transformation on a graph that increases i(G) and i(G). Next, we obtain the minimum and maximum value of i(G) + i(G), where graph G is a tree T with connected complement and a unicyclic graph G with connected complement, respectively. In each case, we characterize the extremal graphs. Finally, we establish an upper bound on the i(G) in terms of the Wiener polarity index.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123423880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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