Titlebook: Symmetries in Graphs, Maps, and Polytopes; 5th SIGMAP Workshop, Jozef Širáň,Robert Jajcay Conference proceedings 2016 Springer Internationa

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Conference proceedings 2016ies of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d’enfant..Providing the global community of researchers in the field with the opportunity to gather, converse and present their newest findings and advances, the Symmetries In

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Paradox

On Pentagonal Geometries with Block Size 3, 4 or 5,e also prove that there exists a PENT(4, .) for . 1 (mod 8) and a PENT(5, .) for . 1 (mod 5), ., apart from nine possible exceptions. Further we construct an infinite class of pentagonal geometries PENT(.), ., and a PENT(6, 13).

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,The Grothendieck-Teichmüller Group of a Finite Group and ,-Dessins d’enfants, calculations. It turns out that the classical action of the Grothendieck-Teichmüller group on dessins d’enfants can be refined to an action on “.-dessins”, which we define, and this elucidates much of the first part.

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Powers of Skew-Morphisms,mplementary products of finite groups . with . cyclic and .. As natural generalizations of group automorphisms, they share many of their properties but proved much harder to classify. Unlike automorphisms, not all powers of skew-morphisms are skew-morphisms again. We study and classify the powers of

Inoperable

Census of Quadrangle Groups Inclusions,e and quadrangle groups forming a particular subfamily of Fuchsian groups. With two exceptions, each inclusion determines a finite bipartite map (hypermap) on a 2-dimensional spherical orbifold that encodes the complete information and gives a graphical visualisation of the inclusion. A complete des