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 1 - 9 / 91 1.Decomposition of skew-morphisms of cyclic groupsIstván Kovács, Roman Nedela, 2011, original scientific articleAbstract: A skew-morphism of a group ▫$H$▫ is a permutation ▫$\sigma$▫ of its elements fixing the identity such that for every ▫$x, y \in H$▫ there exists an integer ▫$k$▫ such that ▫$\sigma (xy) = \sigma (x)\sigma k(y)$▫. It follows that group automorphisms are particular skew-morphisms. Skew-morphisms appear naturally in investigations of maps on surfaces with high degree of symmetry, namely, they are closely related to regular Cayley maps and to regular embeddings of the complete bipartite graphs. The aim of this paper is to investigate skew-morphisms of cyclic groups in the context of the associated Schur rings. We prove the following decomposition theorem about skew-morphisms of cyclic groups ▫$\mathbb Z_n$▫: if ▫$n = n_{1}n_{2}$▫ such that ▫$(n_{1}n_{2}) = 1$▫, and ▫$(n_{1}, \varphi (n_{2})) = (\varphi (n_{1}), n_{2}) = 1$▫ (▫$\varphi$▫ denotes Euler's function) then all skew-morphisms ▫$\sigma$▫ of ▫$\mathbb Z_n$▫ are obtained as ▫$\sigma = \sigma_1 \times \sigma_2$▫, where ▫$\sigma_i$▫ are skew-morphisms of ▫$\mathbb Z_{n_i}, \; i = 1, 2$▫. As a consequence we obtain the following result: All skew-morphisms of ▫$\mathbb Z_n$▫ are automorphisms of ▫$\mathbb Z_n$▫ if and only if ▫$n = 4$▫ or ▫$(n, \varphi(n)) = 1$▫.Found in: osebiKeywords: cyclic group, permutation group, skew-morphism, Schur ringPublished: 15.10.2013; Views: 1930; Downloads: 54 Full text (0,00 KB) 2.Branched cyclic regular coverings over platonic mapsRoman Nedela, Kan Hu, Naer Wang, 2014, original scientific articleFound in: osebiKeywords: zemljevidi, grafi, krov, maps, graphs, coveringPublished: 15.10.2015; Views: 1394; Downloads: 85 Full text (0,00 KB) 3.Classification of regular maps of Euler characteristic -3pMarston D. E. Conder, Roman Nedela, Jozef Širan, 2012, original scientific articleFound in: osebiKeywords: regularen zemljevid, grupa avtomorfizmov, Eulerjeva karakteristika, regular map, automorphism group, Euler characteristicsPublished: 15.10.2015; Views: 1165; Downloads: 68 Full text (0,00 KB) 4.6-decomposition of snarksRoman Nedela, Ján Karabáš, Edita Máčajová, 2013, original scientific articleFound in: osebiKeywords: dekompozicije, graf, barvanje, decompositions, graphs, coloringPublished: 15.10.2015; Views: 969; Downloads: 46 Full text (0,00 KB) 5.Maximum genus, connectivity, and Nebeský's theoremMartin Škoviera, Roman Nedela, Dan Steven Archdeacon, Michal Kotrbčík, 2015, original scientific articleFound in: osebiKeywords: maksimalen rod, Nebeskýnov rod, Bettijevo število, povezanost, maximum genus, Nebeský theorem, Betti number, connectivityPublished: 15.10.2015; Views: 1081; Downloads: 67 Full text (0,00 KB) 6.A characterization of regular embeddings of n-dimensional cubesRoman Nedela, Domenico A. Catalano, 2010, original scientific articleFound in: osebiKeywords: n-dimensional cubes, regular embedding, regular mapPublished: 15.10.2015; Views: 804; Downloads: 44 Full text (0,00 KB) 7.Regular embeddings of cycles with multiple edges revisitedMartin Škoviera, Roman Nedela, Kan Hu, Naer Wang, 2015, original scientific articleAbstract: Regularne vložitve ciklov z večkratnimi povezavami se pojavljajo v literaturi že kar nekaj časa, tako v topološki teoriji grafov kot tudi izven nje. Ta članek izriše kompletno podobo teh zemljevidov na ta način, da povsem opiše, klasificira in enumerira regularne vložitve ciklov z večkratnimi povezavami tako na orientabilnih kot tudi na neorientabilnih ploskvah. Večina rezultatov je sicer znana v tej ali oni obliki, toda tu so predstavljeni iz poenotenega zornega kota, osnovanega na teoriji končnih grup. Naš pristop daje dodatno informacijo tako o zemljevidih kot o njihovih grupah avtomorfizmov, priskrbi pa tudi dodaten vpogled v njihove odnose.Found in: osebiKeywords: regularna vložitev, večkratna povezava, Hölderjev izrek, Möbiusov zemljevid, regular embedding, multiple edge, Hölder's Theorem, Möbius mapPublished: 15.10.2015; Views: 1041; Downloads: 53 Full text (0,00 KB) 8.Classification of regular embeddings of n-dimensional cubesShao Fei Du, Marston D. E. Conder, Stephen Wilson, Roman Nedela, Domenico A. Catalano, Young Soo Kwon, 2011, original scientific articleFound in: osebiKeywords: cube, classification, regular embeddingPublished: 15.10.2015; Views: 1199; Downloads: 65 Full text (0,00 KB) 9.Archimedean maps of higher generaRoman Nedela, Ján Karabáš, 2012, original scientific articleFound in: osebiKeywords: maps, graphs, embeddingPublished: 03.04.2017; Views: 832; Downloads: 97 Full text (0,00 KB)
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