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Proceedings of the 4th Croatian Combinatorial Days最新文献

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The Birkhoff polytope of the groups F4 and H4 基团F4和H4的Birkhoff多面体
Proceedings of the 4th Croatian Combinatorial Days Pub Date : 2023-06-01 DOI: 10.5592/co/ccd.2022.03
Mathieu Dutour Sikirić
{"title":"The Birkhoff polytope of the groups F4 and H4","authors":"Mathieu Dutour Sikirić","doi":"10.5592/co/ccd.2022.03","DOIUrl":"https://doi.org/10.5592/co/ccd.2022.03","url":null,"abstract":"We compute the set of facets of the polytope which is the convex hull of the Coxeter groups F 4 or H 4 : • For the group F 4 we found 2 orbits of facets which contradicts previous results published in [19]. • For the group H 4 we found 1063 orbits of facets which provides a coun-terexample to the conjecture of [19].","PeriodicalId":306191,"journal":{"name":"Proceedings of the 4th Croatian Combinatorial Days","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125553361","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
Planets are (very likely) in orbits of stars 行星(很可能)在恒星的轨道上运行
Proceedings of the 4th Croatian Combinatorial Days Pub Date : 2023-06-01 DOI: 10.5592/co/ccd.2022.10
D. Veljan
{"title":"Planets are (very likely) in orbits of stars","authors":"D. Veljan","doi":"10.5592/co/ccd.2022.10","DOIUrl":"https://doi.org/10.5592/co/ccd.2022.10","url":null,"abstract":"The probability that a randomly and uniformly chosen point from the circumball of a tetrahedron lies outside of the inscribed ball of the tetrahedron can be bounded very sharply from below in terms of the edge lengths of the tetrahedron. One can imagine four stars in the Universe (vertices) with known mutual distances and a small (exo-) planet orbiting between them within the circumsphere. The least probability that the planet is outside of the insphere is given in terms of the distances of the stars. The least probability occurs for the regular tetrahedron and it is 0.962962. . . . Geometrically, this is a tricky corollary of (refinements of) the famous Euler inequality: circumradius is at least three times bigger than the inradius of a tetrahedron with equality for a regular tetrahedron. The Euler inequality can be extended to Euclidean sim-plices in all dimensions and to non-Euclidean planes. The most relevant cases of 3D and 4D being in accordance with the relativity theory are considered.","PeriodicalId":306191,"journal":{"name":"Proceedings of the 4th Croatian Combinatorial Days","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122156776","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
Balanced simplicial complex associated with 1 × p polyomino 与1 × p多项式相关的平衡简单配合物
Proceedings of the 4th Croatian Combinatorial Days Pub Date : 2023-06-01 DOI: 10.5592/co/ccd.2022.01
Đorđe Barlić, Edin Liđan
{"title":"Balanced simplicial complex associated with 1 × p polyomino","authors":"Đorđe Barlić, Edin Liđan","doi":"10.5592/co/ccd.2022.01","DOIUrl":"https://doi.org/10.5592/co/ccd.2022.01","url":null,"abstract":"Balanced simplicial complexes are important objects in combinatorics and commutative algebra. A d -dimensional simplicial complex is balanced if its vertices can be coloured into d +1 colors, so there is no monochromatic edge. In this article, we establish two results concerning balanced simplicial complexes assigned to tilings of m × n board in a plane and a torus by I p -omino tile","PeriodicalId":306191,"journal":{"name":"Proceedings of the 4th Croatian Combinatorial Days","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133392135","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 divisibility properties of some binomial sums connected with the Catalan and Fibonacci numbers 关于与加泰罗尼亚数和斐波那契数有关的二项式和的可除性
Proceedings of the 4th Croatian Combinatorial Days Pub Date : 2023-06-01 DOI: 10.5592/co/ccd.2022.05
Jovan Mikić
{"title":"On divisibility properties of some binomial sums connected with the Catalan and Fibonacci numbers","authors":"Jovan Mikić","doi":"10.5592/co/ccd.2022.05","DOIUrl":"https://doi.org/10.5592/co/ccd.2022.05","url":null,"abstract":"We show that an alternating binomial sum which is connected with the Catalan numbers is divisible by n . A natural generalization of this sum is connected with the generalized Catalan numbers and also divisible by n . A new class of binomial sum is used. In Appendix A, we consider a positive binomial sum connected with Fibonacci and Lucas numbers. In Appendix B, we consider an alternating binomial sum which is also connected with Catalan numbers and divisible by ( a + 1) n + 1. Similar reasoning was already used by the author to reprove more simply Calkin’s result for divisibility of the alternating sum of powers of binomials coefficients by the central binomial coefficient.","PeriodicalId":306191,"journal":{"name":"Proceedings of the 4th Croatian Combinatorial Days","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124013471","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
Solving the dimer problem on Apollonian gasket 解决阿波罗垫圈上的二聚体问题
Proceedings of the 4th Croatian Combinatorial Days Pub Date : 2023-06-01 DOI: 10.5592/co/ccd.2022.02
T. Došlić, Luka Podrug
{"title":"Solving the dimer problem on Apollonian gasket","authors":"T. Došlić, Luka Podrug","doi":"10.5592/co/ccd.2022.02","DOIUrl":"https://doi.org/10.5592/co/ccd.2022.02","url":null,"abstract":"For any three circles in the plane where each circle is tangent to the other two, the Descartes’ theorem yields the existence of a fourth circle tangent to the starting three. Continuing this process by adding a new circle between any three tangent circles leads to Apollonian packings. The fractal structures resulting from infinite continuation of such processes are known as Apollonian gaskets. Close-packed dimer configurations on such structures are well modeled by perfect matchings in the corresponding graphs. We consider Apollonian gaskets for several types of initial configurations and present explicit expressions for the number of perfect matchings in such graphs","PeriodicalId":306191,"journal":{"name":"Proceedings of the 4th Croatian Combinatorial Days","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126551127","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
Extended abstract on Local Irregularity Conjecture and cactus graphs 局部不规则猜想与仙人掌图的扩展摘要
Proceedings of the 4th Croatian Combinatorial Days Pub Date : 2023-06-01 DOI: 10.5592/co/ccd.2022.08
J. Sedlar, R. Škrekovski
{"title":"Extended abstract on Local Irregularity Conjecture and cactus graphs","authors":"J. Sedlar, R. Škrekovski","doi":"10.5592/co/ccd.2022.08","DOIUrl":"https://doi.org/10.5592/co/ccd.2022.08","url":null,"abstract":",","PeriodicalId":306191,"journal":{"name":"Proceedings of the 4th Croatian Combinatorial Days","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133896890","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
Complexity function for a variant of Flory model on a ladder 阶梯上Flory模型变体的复杂度函数
Proceedings of the 4th Croatian Combinatorial Days Pub Date : 2023-06-01 DOI: 10.5592/co/ccd.2022.07
Mate Puljiz, Stjepan Šebek, Josip Žubrinić
{"title":"Complexity function for a variant of Flory model on a ladder","authors":"Mate Puljiz, Stjepan Šebek, Josip Žubrinić","doi":"10.5592/co/ccd.2022.07","DOIUrl":"https://doi.org/10.5592/co/ccd.2022.07","url":null,"abstract":"In this article, we compare the famous Flory model with its variant that was recently introduced by the authors. Instead of looking at these models on a one-dimensional lattice, we consider a two-row ladder. For both models we compute the complexity function, and we analyze the differences of static and dynamic versions of these models.","PeriodicalId":306191,"journal":{"name":"Proceedings of the 4th Croatian Combinatorial Days","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116069559","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
Grids of equidistant walks 等距行走的网格
Proceedings of the 4th Croatian Combinatorial Days Pub Date : 2023-06-01 DOI: 10.5592/co/ccd.2022.04
Biserka Kolarec
{"title":"Grids of equidistant walks","authors":"Biserka Kolarec","doi":"10.5592/co/ccd.2022.04","DOIUrl":"https://doi.org/10.5592/co/ccd.2022.04","url":null,"abstract":",","PeriodicalId":306191,"journal":{"name":"Proceedings of the 4th Croatian Combinatorial Days","volume":"29 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132237718","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 circumradius equations of cyclic polygons 关于循环多边形的环半径方程
Proceedings of the 4th Croatian Combinatorial Days Pub Date : 2023-06-01 DOI: 10.5592/co/ccd.2022.09
D. Svrtan
{"title":"On circumradius equations of cyclic polygons","authors":"D. Svrtan","doi":"10.5592/co/ccd.2022.09","DOIUrl":"https://doi.org/10.5592/co/ccd.2022.09","url":null,"abstract":",","PeriodicalId":306191,"journal":{"name":"Proceedings of the 4th Croatian Combinatorial Days","volume":"197 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122369773","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 a linear recurrence relation of the divide-and-conquer type 分治式的线性递推关系
Proceedings of the 4th Croatian Combinatorial Days Pub Date : 2023-06-01 DOI: 10.5592/co/ccd.2022.06
Daniele Parisse
{"title":"On a linear recurrence relation of the divide-and-conquer type","authors":"Daniele Parisse","doi":"10.5592/co/ccd.2022.06","DOIUrl":"https://doi.org/10.5592/co/ccd.2022.06","url":null,"abstract":",","PeriodicalId":306191,"journal":{"name":"Proceedings of the 4th Croatian Combinatorial Days","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129072020","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
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