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Proceedings of the 3rd Croatian Combinatorial Days最新文献

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Matrix products of binomial coefficients and unsigned Stirling numbers 二项式系数与无符号斯特林数的矩阵积
Proceedings of the 3rd Croatian Combinatorial Days Pub Date : 2020-12-30 DOI: 10.5592/CO/CCD.2020.04
Marin Knevzevi'c, Vedran Krvcadinac, Lucija Reli'c
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引用次数: 1
A variation on the Rubik's cube 魔方的变种
Proceedings of the 3rd Croatian Combinatorial Days Pub Date : 2020-12-01 DOI: 10.5592/co/ccd.2020.03
Mathieu Dutour Sikiri'c
{"title":"A variation on the Rubik's cube","authors":"Mathieu Dutour Sikiri'c","doi":"10.5592/co/ccd.2020.03","DOIUrl":"https://doi.org/10.5592/co/ccd.2020.03","url":null,"abstract":"The Rubik's cube is a famous puzzle in which faces can be moved and the corresponding movement operations define a group. We consider here a generalization to any $3$-valent map. We prove an upper bound on the size of the corresponding group which we conjecture to be tight.","PeriodicalId":253304,"journal":{"name":"Proceedings of the 3rd Croatian Combinatorial Days","volume":"364 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122190285","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
Refinements of Euler's inequalities in plane, space and n-space 平面、空间和n空间中欧拉不等式的改进
Proceedings of the 3rd Croatian Combinatorial Days Pub Date : 1900-01-01 DOI: 10.5592/co/ccd.2020.08
D. Veljan
{"title":"Refinements of Euler's inequalities in plane, space and n-space","authors":"D. Veljan","doi":"10.5592/co/ccd.2020.08","DOIUrl":"https://doi.org/10.5592/co/ccd.2020.08","url":null,"abstract":"We improve Euler’s inequality R ≥ 2r, where R and r are triangle’s circumradius and inradius, respectively, and prove some consequences of it. We also show non-Euclidean version of this result. Next, we improve 3D analogue of Euler’s inequality for tetrahedra R ≥ 3r and discuss recursive way to improve analogues of Euler’s inequality for simplices. We end with some open problems, including possible CEEG (classical Euclidean elementary geometry) proof of Grace-Danielsson’s inequality d2 ≤ (R − 3r)(R + r), where d is the distance between the centers of the insphere and the circumsphere of a tetrahedron.","PeriodicalId":253304,"journal":{"name":"Proceedings of the 3rd Croatian Combinatorial Days","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129235860","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
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