Geodesic
Number of dissections of the regular \(n\)-gon by diagonals
Journal of integer sequences, Tome 20 (2017) no. 7
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 
@article{JIS_2017__20_7_a1,
     author = {Buloron,  Joris N. and Corcino,  Roberto B. and Ontolan,  Jay M.},
     title = {Number of dissections of the regular \(n\)-gon by diagonals},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {7},
     zbl = {1368.05067},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_7_a1/}
}
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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/