By Jozef Širáň, Robert Jajcay
This quantity comprises seventeen of the simplest papers introduced on the SIGMAP Workshop 2014, representing the latest advances within the box of symmetries of discrete items and constructions, with a specific emphasis on connections among maps, Riemann surfaces and dessins d’enfant.
Read or Download Symmetries in Graphs, Maps, and Polytopes: 5th SIGMAP Workshop, West Malvern, UK, July 2014 PDF
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Extra info for Symmetries in Graphs, Maps, and Polytopes: 5th SIGMAP Workshop, West Malvern, UK, July 2014
First note that the coset-preserving skew-morphisms of abelian groups giving rise to regular Cayley maps have an even more restricted structure. Lemma 6 If ϕ is a coset-preserving skew-morphism of an abelian group A that gives rise to a regular Cayley map C M(A, X, P), then ϕ is either t-balanced or a group automorphism of A. Proof If a coset-preserving skew-morphism ϕ possesses a generating orbit X that is closed under inverses, all elements of X belong to the same coset of ker ϕ, and have therefore the same power function value t.
Tucker, Regular Cayley maps for cyclic groups, Trans. Amer. Math. Soc. 366 no. 7, 3585–3609 (2014). 4. R. Feng, R. Jajcay and Y. Wang, Regular t-balanced Cayley maps for abelian groups, Discrete Math. 311, 2309–2316 (2011). 5. V. Horoševskiˇı, Automorphisms of finite groups, Math. USSR Sbornik 22, 584–594 (1974). 6. R. Jajcay, On a new product of groups, European J. Combin. 15, 251–252 (1994). 7. R. Jajcay and R. Nedela, Half-regular Cayley maps, Graphs and Combinatorics 31, 1003–1018 (2015). 8.
Koviera, Regular Maps from Cayley Graphs II. Antibalanced Cayley Maps, Discrete Math. 124, 179–191 (1994). 20. Y. -Q. Feng, Regular balanced Cayley maps for cyclic, dihedral and generalized quaternion groups, Acta Math. Sin. (Engl. ) 21, no. 4, 773–778 (2005). 21. -Y. Zhang, A classification of regular Cayley maps with trivial Cayley-core for dihedral groups, to appear in Discrete Math. Census of Quadrangle Groups Inclusions António Breda d’Azevedo, Domenico A. Catalano, Ján Karabáš and Roman Nedela Abstract In a classical result of 1972 Singerman classifies the inclusions between triangle groups.