On symmetric quadrangulations

Details On symmetric quadrangulations On symmetric quadrangulations

2011-03-18

arxiv.org/abs/1103.3657v1

Mathematics

Combinatorics

Supported by the European project ExploreMaps ERC StG 208471

Scientific paper

This note gathers observations on symmetric quadrangulations, with enumerative consequences. In the first part a new method for the enumeration of rooted simple quadrangulations is presented, based on quotienting symmetric simple quadrangulations in two different ways (one standard, the other one new). In the second part, based on results of Bouttier, Di Francesco and Guitter and on quotient and substitution operations, the series of several families of symmetric quadrangular dissections (general, without multiple edges, without nonfacial 4-cycle, respectively) are computed, with control on the distance from the central vertex to the outer boundary.

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