Counting symmetry classes of dissections of a convex regular polygon
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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2012
- DOI:
- 10.48550/arXiv.1209.6270
- arXiv:
- arXiv:1209.6270
- Bibcode:
- 2012arXiv1209.6270B
- Keywords:
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- Mathematics - Combinatorics