English

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}
}