Journal of Integer Sequences, Vol. 20 (2017), Article 17.7.7

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.

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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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