Geodesic
Number of dissections of the regular $n$-gon by diagonals
Journal of integer sequences, Tome 20 (2017) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 05C25, 05C69
Keywords: n-gon, dissection, dihedral group 
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     author = {Buloron, Joris N. and Corcino, Roberto B. and Ontolan, Jay M.},
     title = {Number of dissections of the regular $n$-gon by diagonals},
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Buloron, Joris N.; Corcino, Roberto B.; Ontolan, Jay M. Number of dissections of the regular $n$-gon by diagonals. Journal of integer sequences, Tome 20 (2017) no. 7. http://geodesic.mathdoc.fr/item/JIS_2017__20_7_a1/