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Title Archimedean maps of higher genera Author info Ján Karabáš, Roman Nedela Author Karabáš Ján 1977- (50%) UMBFP12 - Inštitút matematiky a informatiky
Co-authors Nedela Roman 1960- (50%) UMBFP12 - Inštitút matematiky a informatiky
Source document Mathematics of Computation. Vol. 81, no. 277 (2012), pp. 569-583. - Providence : American Mathematical Society, 2012 Keywords polyhedron Archimedean solid surfaces groups graph embedding regular maps Cayley maps genus Language English Country United States of America systematics 51 Annotation 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 Public work category ADC No. of Archival Copy 22535 Repercussion category PISANSKI, Tomaz - WILLIAMS, Gordon - BERMAN, Leah Wrenn. Operations on oriented maps. In Symmetry-basel. ISSN 2073-8994, 2017, vol. 9, no. 11.
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 Beitrage 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.
DATTA, Basudeb - MAITY, Dipendu. Semi-equivelar and vertex-transitive maps on the torus (vol 58, pg 617, 2017). In Beitrage zur algebra und geometrie-contributions to algebra and geometry. 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 & computational geometry. ISSN 0179-5376, 2019, DOI: 10.1007/s00454-019-00156-0.
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.
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, pp. 187–188.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References (1) - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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Title Archimedean solids of genus two Par.title Archimedove telesá bodu dva Author info Ján Karabáš, Roman Nedela Author Karabáš Ján 1977- UMBUV01 - Ústav vedy a výskumu
Co-authors Nedela Roman 1960- UMBFP10 - Katedra matematiky
Source document Electronic Notes in Discrete Mathematics. No. 28(2007), pp. 331-339. - Amsterdam : Elsevier, 2007 Note abstrakt In: Electronic Notes in Discrete Mathematics. - Č. 28 (2007), s. [1 s.]. - Amsterdam : Elsevier B. V., 2007. - Bibl.: s. 338-339 Keywords archimedovské teleso grupy mapy - maps Archimedean solid groups graph embedding surfaces Language English Country Netherlands systematics 51 Annotation Res. angl. Public work category ADE No. of Archival Copy 4823 Repercussion category PELLICER, Daniel. Vertex-transitive maps with Schlafli type {3,7}. In Discrete mathematics. ISSN 0012-365X, 2014, vol. 317, pp. 53-74.
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.
KUMAR TIWARI, Anand - KUMAR UPADHYAY, Ashish. Semi-equivelar maps on the torus and the Klein bottle with few vertices. In Mathematica Slovaca. ISSN 0139-9918, 2017, vol. 67, no. 2, pp. 519-532.
UPADHYAY, Ashish K. - TIWARI, Anand K. - MAITY, Dipendu. Semi-equivelar maps. In Beitrage zur Algebra und Geometrie. ISSN 0138-4821, 2014, vol. 55, no. 1, pp. 229-242.
ŠUCH, O. Vertex-transitive maps on a torus. In Acta Mathematica Universitatis Comenianae. ISSN 0862-9544, 2011, vol. 80, no. 1, pp. 1-30.
UPADHYAY, A.K. - TAWARI A.K. - MAITY, D. Some semi-equivelar maps. In arXiv:1101.0671 [math.GT] [online]. New York : Cornell Univerisity Library, 2011, pp. [1-20] [cit. 2018-22-02]. Dostupné na: https://arxiv.org/pdf/1101.0671.pdf
JENDROĽ, Stanislav - ŠKRABUĽÁKOVÁ, Erika. Facial non-repetitive edge colouring of semiregular polyhedra. In Acta Universitatis Matthiae Belii : series Mathematics. Banská Bystrica : Ústav vedy a výskumu Univerzity Mateja Bela v Banskej Bystrici, 2009. ISBN 978-80-8083-906-2, s. 37-52.
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.
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.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ 
article
Title Archimedean solids of genus two Author info Ján Karabáš, Roman Nedela Author Karabáš Ján 1977- (50%) UMBUV01 - Ústav vedy a výskumu
Co-authors Nedela Roman 1960- (50%) UMBFP10 - Katedra matematiky
Source document Electronic Notes in Discrete Mathematics. Č. 28 (2007), s. [1 s.]. - Amsterdam : Elsevier B. V., 2007 Keywords Archimedean solid mapy - maps surfaces groups graph embedding Language English URL http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B75GV-4N5M9FJ-1P&_user=3838381&_coverDate=03%2F01%2F2007&_alid=652089114&_rdoc=2&_fmt=summary&_orig=search&_cdi=13104&_sort=d&_docanchor=&view=c&_ct=6&_acct=C000061505&_version=1&_urlVersion=0&_userid=3838381&md5=a02e7b64292f0adf4785e661fd66f011 Public work category AFG Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ unrecognised