Number of Dissections of the Regular n-gon by Diagonals
Joris N. Buloron, Roberto B. Corcino, and Jay M. Ontolan
Cebu Normal University
Cebu City, Philippines
This paper presents a formula for the distinct dissections by diagonals
of a regular n-gon modulo the action of the dihedral group. This
counting includes dissection with intersecting or non-intersecting
diagonals. We utilize a corollary of the Cauchy-Frobenius theorem,
which involves counting of cycles. We also give an explicit formula for
the prime number case. We give as a remark the number of distinct
dissections, modulo the action of the cyclic group of finite order.
Full version: pdf,
Received September 13 2016; revised version received May 9 2016; June 30 2017; July 18 2017.
Published in Journal of Integer Sequences, July 29 2017.
Minor revision, August 14 2017.
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