Counting symmetry classes of dissections of a convex regular polygon
Combinatorics
2012-09-28 v1
Abstract
This paper proves explicit formulas for the number of dissections of a convex regular polygon modulo the action of the cyclic and dihedral groups. The formulas are obtained by making use of the Cauchy-Frobenius Lemma as well as bijections between rotationally symmetric dissections and simpler classes of dissections. A number of special cases of these formulas are studied. Consequently, some known enumerations are recovered and several new ones are provided.
Keywords
Cite
@article{arxiv.1209.6270,
title = {Counting symmetry classes of dissections of a convex regular polygon},
author = {Douglas Bowman and Alon Regev},
journal= {arXiv preprint arXiv:1209.6270},
year = {2012}
}