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Archimedean maps of higher genera
Názov Archimedean maps of higher genera Aut.údaje Ján Karabáš, Roman Nedela Autor Karabáš Ján 1977- (50%) UMBFP12 - Inštitút matematiky a informatiky
Spoluautori Nedela Roman 1960- (50%) UMBFP12 - Inštitút matematiky a informatiky
Zdroj.dok. Mathematics of Computation. Vol. 81, no. 277 (2012), pp. 569-583. - Providence : American Mathematical Society, 2012 Kľúč.slová polyhedron Archimedean solid surfaces groups graph embedding regular maps Cayley maps genus Jazyk dok. angličtina Krajina Spojené štáty Systematika 51 Anotácia The paper focuses on the classification of vertex-transitive polyhedral maps of genus from 2 to 4. These maps naturally generalise the spherical maps associated with the classical Archimedean solids. Our analysis is based on the fact that each Archimedean map on an orientable surface projects onto a one- or a two-vertex quotient map. For a given genus g>= 2 the number of quotients to consider is bounded by a function of g. All Archimedean maps of genus g can be reconstructed from these quotients as regular covers with covering transformation group isomorphic to a group G from a set of g-admissible groups. Since the lists of groups acting on surfaces of genus 2,3, and 4 are known, the problem can be solved by a computer-aided case-to-case analysis Kategória publikačnej činnosti ADC Číslo archívnej kópie 22535 Kategória ohlasu PISANSKI, Tomaz - WILLIAMS, Gordon - BERMAN, Leah Wrenn. Operations on oriented maps. In Symmetry (Basel). ISSN 2073-8994, 2017, vol. 9, no. 11, art. no. 274, pp. 1-14.
LEOPOLD, Undine. Vertex-transitive polyhedra of higher genus, I. In Discrete and computational geometry. ISSN 0179-5376, 2017, vol. 57, no. 1, pp. 125-151.
GÉVAY, Gabor - SCHULTE, Egon - WILLS, Joerg M. The regular Grunbaum polyhedron of genus 5. In Advances in geometry. ISSN 1615-715X, 2014, vol. 14, no. 3, pp. 465-482.
PELLICER, Daniel. Vertex-transitive maps with Schlafli type {3,7}. In Discrete mathematics. ISSN 0012-365X, 2014, vol. 317, pp. 53-74.
UPADHYAY, Ashish K. - TIWARI, Anand K. - MAITY, Dipendu. Semi-equivelar maps. In Beiträge zur Algebra und Geometrie. ISSN 0138-4821, 2014, vol. 55, no. 1, pp. 229-242.
TIWARI, Anand Kumar - UPADHYAY, Ashish Kumar. Semi-equivelar maps on the surface of Euler characteristic - 1. In Note di matematica. ISSN 1123-2536, 2017, vol. 37, no. 2, pp. 91-102.
MAITI, Arun. Quasi-vertex-transitive maps on the plane. In Disctere mathematics. ISSN 0012-365X, 2020, vol. 343, no. 7, art. no. 111911, pp. 1-8.
DATTA, Basudeb - MAITY, Dipendu. Correction to: Semi-equivelar and vertex-transitive maps on the torus. In Beiträge zur Algebra und Geometrie. ISSN 0138-4821, 2020, vol. 61, no. 1, pp. 187-188.
TIWARI, Anand K. - TRIPATHI, Amit - SINGH, Yogendra - GUPTA, Punam. Doubly semiequivelar maps on Torus and Klein bottle. In Journal of mathematics. ISSN 2314-4629, 2020, vol. 2020, art. no. 5674172.
DATTA, Basudeb - GUPTA, Subhojoy. Semi-regular tilings of the hyperbolic plane. In Discrete and computational geometry. ISSN 0179-5376, 2021, vol. 65, no. 2, pp. 531-553.
UPADHYAY, Ashish Kumar. Symmetries of maps on surfaces. In Complex Symmetries. 1. vyd. Cham : Birkhäuser, 2021. ISBN 978-3-030-88058-3, pp. 35-42.
SINGH, Yogendra - TIWARI, Anand Kumar. Doubly semi-equivelar maps on the plane and the torus. In AKCE international journal of graphs and combinatorics. ISSN 0972-8600, 2022, vol. 19, no. 3, pp. 296-310.
BHOWMIK, Debashis - UPADHYAY, Ashish Kumar. Some semi-equivelar maps of Euler characteristics-2. In National Academy Science letters. ISSN 0250-541X, 2021, vol. 44, no. 5, pp. 433-436.
MELINON, Patrice. Vitreous carbon, geometry and topology : a hollistic approach. In Nanomaterials. ISSN 2079-4991, 2021, vol. 11, no. 7, pp. 1-40.
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