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An E³ embedding of Coxeter’s regular map {8, 4 | 3} results in a regular Leonardo polyhedron 考克斯特正则图 {8, 4 | 3} 的 E³ 嵌入结果是一个正则莱昂纳多多面体
The Art of Discrete and Applied Mathematics Pub Date : 2024-05-13 DOI: 10.26493/2590-9770.1561.1e8
Jürgen Bokowski, Jörg M. Wills
{"title":"An E³ embedding of Coxeter’s regular map {8, 4 | 3} results in a regular Leonardo polyhedron","authors":"Jürgen Bokowski, Jörg M. Wills","doi":"10.26493/2590-9770.1561.1e8","DOIUrl":"https://doi.org/10.26493/2590-9770.1561.1e8","url":null,"abstract":"","PeriodicalId":382734,"journal":{"name":"The Art of Discrete and Applied Mathematics","volume":"124 42","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140985169","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
Generalizations of Cayley graphs to uniform hypergraphs 将 Cayley 图推广到均匀超图
The Art of Discrete and Applied Mathematics Pub Date : 2024-05-06 DOI: 10.26493/2590-9770.1606.28a
T. Jajcayová, R. Jajcay
{"title":"Generalizations of Cayley graphs to uniform hypergraphs","authors":"T. Jajcayová, R. Jajcay","doi":"10.26493/2590-9770.1606.28a","DOIUrl":"https://doi.org/10.26493/2590-9770.1606.28a","url":null,"abstract":"","PeriodicalId":382734,"journal":{"name":"The Art of Discrete and Applied Mathematics","volume":"1 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141006254","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
Subdiagonal and superdiagonal compositions 子对角线和超对角线构成
The Art of Discrete and Applied Mathematics Pub Date : 2023-12-13 DOI: 10.26493/2590-9770.1675.fe8
M. Archibald, A. Blecher, A. Knopfmacher, S. Wagner
{"title":"Subdiagonal and superdiagonal compositions","authors":"M. Archibald, A. Blecher, A. Knopfmacher, S. Wagner","doi":"10.26493/2590-9770.1675.fe8","DOIUrl":"https://doi.org/10.26493/2590-9770.1675.fe8","url":null,"abstract":"","PeriodicalId":382734,"journal":{"name":"The Art of Discrete and Applied Mathematics","volume":"42 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139005026","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
Symmetries of the Woolly Hat graphs 羊毛帽图的对称性
The Art of Discrete and Applied Mathematics Pub Date : 2023-10-16 DOI: 10.26493/2590-9770.1617.83c
Leah Wrenn Berman, Hiroki Koike, Elías Mochán, Alejandra Ramos-Rivera, Primož Šparl, Stephen E. Wilson
{"title":"Symmetries of the Woolly Hat graphs","authors":"Leah Wrenn Berman, Hiroki Koike, Elías Mochán, Alejandra Ramos-Rivera, Primož Šparl, Stephen E. Wilson","doi":"10.26493/2590-9770.1617.83c","DOIUrl":"https://doi.org/10.26493/2590-9770.1617.83c","url":null,"abstract":"A graph is edge-transitive if the natural action of its automorphism group on its edge set is transitive. An automorphism of a graph is semiregular if all of the orbits of the subgroup generated by this automorphism have the same length. While the tetravalent edge-transitive graphs admitting a semiregular automorphism with only one orbit are easy to determine, those that admit a semiregular automorphism with two orbits took a considerable effort and were finally classified in 2012. Of the several possible different \"types\" of potential tetravalent edge-transitive graphs admitting a semiregular automorphism with three orbits, only one \"type\" has thus far received no attention. In this paper we focus on this class of graphs, which we call the Woolly Hat graphs. We prove that there are in fact no edge-transitive Woolly Hat graphs and classify the vertex-transitive ones.","PeriodicalId":382734,"journal":{"name":"The Art of Discrete and Applied Mathematics","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136113660","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
A computer-free classification of orientably-regular maps on surfaces of genus p+1 for prime p 素数p的p+1属表面上可定向正则映射的无计算机分类
The Art of Discrete and Applied Mathematics Pub Date : 2023-10-11 DOI: 10.26493/2590-9770.1596.a23
Martin Bachratý, Marston Conder, Jana Šiagiová, Jozef Širáň
{"title":"A computer-free classification of orientably-regular maps on surfaces of genus p+1 for prime p","authors":"Martin Bachratý, Marston Conder, Jana Šiagiová, Jozef Širáň","doi":"10.26493/2590-9770.1596.a23","DOIUrl":"https://doi.org/10.26493/2590-9770.1596.a23","url":null,"abstract":"A classification of orientably-regular maps of genus p + 1 for primes p > 13 was published in 2010 by M. Conder, J. Širáň and T. Tucker. This involved a computer-free proof for primes p > 83, while for 17 ≤ p ≤ 83 it followed from computations undertaken in 2009 by M. Conder. Classification of such maps for p ≤ 7 was already available from much earlier work by others on such maps of small genus dating back to the 1930s, but without explicit proofs in a number of cases. In this paper we give a computer-free classification of orientably-regular maps of genus p + 1 for all primes p ≤ 83, complementing the 2010 work by M. Conder, J. Širáň and T. Tucker for all larger primes p.","PeriodicalId":382734,"journal":{"name":"The Art of Discrete and Applied Mathematics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136098190","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 the enumeration of leaf-labeled increasing trees with arbitrary node-degree 关于任意节点度叶标记递增树的枚举
The Art of Discrete and Applied Mathematics Pub Date : 2023-10-05 DOI: 10.26493/2590-9770.1589.7e1
Johannes Wirtz
{"title":"On the enumeration of leaf-labeled increasing trees with arbitrary node-degree","authors":"Johannes Wirtz","doi":"10.26493/2590-9770.1589.7e1","DOIUrl":"https://doi.org/10.26493/2590-9770.1589.7e1","url":null,"abstract":"We consider the counting problem of the number of leaf-labeled increasing trees, where internal nodes may have an arbitrary number of descendants. The set of all such trees is a discrete representation of the genealogies obtained under certain population-genetical models such as multiple-merger coalescents. While the combinatorics of the binary trees among those are well understood, for the number of all trees only an approximate asymptotic formula is known. In this work, we validate this formula up to constant terms and compare the asymptotic behavior of the number of all leaf-labeled increasing trees to that of binary, ternary and quaternary trees.","PeriodicalId":382734,"journal":{"name":"The Art of Discrete and Applied Mathematics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134947730","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
Realizations of higher rank toroids 更高级别环面的实现
The Art of Discrete and Applied Mathematics Pub Date : 2023-09-21 DOI: 10.26493/2590-9770.1595.d70
Barry Monson
{"title":"Realizations of higher rank toroids","authors":"Barry Monson","doi":"10.26493/2590-9770.1595.d70","DOIUrl":"https://doi.org/10.26493/2590-9770.1595.d70","url":null,"abstract":"The Art of Discrete and Applied Mathematics (ADAM) is a modern, dynamic, platinum open access, electronic journal that will publish high-quality articles of arbitrary length in contemporary discrete and applied mathematics in which neither the authors nor the readers incur any costs.","PeriodicalId":382734,"journal":{"name":"The Art of Discrete and Applied Mathematics","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136154803","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
Grand Dyck paths with air pockets 有气囊的大堤路
The Art of Discrete and Applied Mathematics Pub Date : 2023-09-18 DOI: 10.26493/2590-9770.1587.b2a
Jean-Luc Baril, Sergey Kirgizov, Rémi Maréchal, Vincent Vajnovszki
{"title":"Grand Dyck paths with air pockets","authors":"Jean-Luc Baril, Sergey Kirgizov, Rémi Maréchal, Vincent Vajnovszki","doi":"10.26493/2590-9770.1587.b2a","DOIUrl":"https://doi.org/10.26493/2590-9770.1587.b2a","url":null,"abstract":"Grand Dyck paths with air pockets (GDAP) are a generalization of Dyck paths with air pockets by allowing them to go the x-axis. We present enumerative results on GDAP (or their prefixes) subject to various restrictions such as maximal/minimal height, ordinate of the last point and particular first return decomposition. In some special cases we give bijections with other known combinatorial classes.","PeriodicalId":382734,"journal":{"name":"The Art of Discrete and Applied Mathematics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135109332","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
The core of a vertex transitive complementary prism of a lexicographic product 一个字典积的顶点传递互补棱镜的核心
The Art of Discrete and Applied Mathematics Pub Date : 2023-08-16 DOI: 10.26493/2590-9770.1623.7f0
Marko Orel
{"title":"The core of a vertex transitive complementary prism of a lexicographic product","authors":"Marko Orel","doi":"10.26493/2590-9770.1623.7f0","DOIUrl":"https://doi.org/10.26493/2590-9770.1623.7f0","url":null,"abstract":"The complementary prism of a graph Γ is the graph ΓΓ̄, which is formed from the union of Γ and its complement Γ̄ by adding an edge between each pair of identical vertices in Γ and Γ̄. Vertex-transitive self-complementary graphs provide vertex-transitive complementary prisms. It was recently proved by the author that ΓΓ̄ is a core, i.e. all its endomorphisms are automorphisms, whenever Γ is vertex-transitive, self-complementary, and either Γ is a core or its core is a complete graph. In this paper the same conclusion is obtained for some other classes of vertex-transitive self-complementary graphs that can be decomposed as a lexicographic product Γ = Γ1[Γ2]. In the process some new results about the homomorphisms of a lexicographic product are obtained.","PeriodicalId":382734,"journal":{"name":"The Art of Discrete and Applied Mathematics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136337528","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
Optimal orientations of strong products of paths 路径强乘积的最优方向
The Art of Discrete and Applied Mathematics Pub Date : 2018-08-08 DOI: 10.26493/2590-9770.1246.99c
Tjaša Paj Erker
{"title":"Optimal orientations of strong products of paths","authors":"Tjaša Paj Erker","doi":"10.26493/2590-9770.1246.99c","DOIUrl":"https://doi.org/10.26493/2590-9770.1246.99c","url":null,"abstract":"","PeriodicalId":382734,"journal":{"name":"The Art of Discrete and Applied Mathematics","volume":"105 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":"123082185","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: 3
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