Journal of Algebraic Combinatorics

, Volume 26, Issue 4, pp 507–527

F-actions and parallel-product decomposition of reflexible maps

Article

DOI: 10.1007/s10801-007-0069-0

Cite this article as:
Orbanić, A. J Algebr Comb (2007) 26: 507. doi:10.1007/s10801-007-0069-0

Abstract

The parallel product of two rooted maps was introduced by S.E. Wilson in 1994. The main question of this paper is whether for a given reflexible map M one can decompose the map into a parallel product of two reflexible maps. This can be achieved if and only if the monodromy (or the automorphism) group of the map has at least two minimal normal subgroups. All reflexible maps up to 100 edges, which are not parallel-product decomposable, are calculated and presented. For this purpose, all degenerate and slightly-degenerate reflexible maps are classified.

In this paper the theory of F-actions is developed including a classification of quotients and parallel-product decomposition. Projections and lifts of automorphisms for quotients and for parallel products are studied. The theory can be immediately applied on rooted maps and rooted hypermaps as they are special cases of F-actions.

Keywords

Rooted map F-Action Map quotients Normal quotient Parallel product Reflexible map Parallel-product decomposition 

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Faculty of Mathematics and Physics, Department of MathematicsUniversity of LjubljanaLjubljanaSlovenia

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