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Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers

Jozef H. Przytycki·Adam S. Sikora
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Abstract

We give a short proof for a formula for the number of divisions of a convex (sn+2)-gon along non-crossing diagonals into (sj+2)-gons, where 1<=j<=n-1. In other words, we consider dissections of an (sn+2)-gon into pieces which can be further subdivided into (s+2)-gons. This formula generalizes the formulas for classical numbers of polygon dissections: Euler-Catalan number, Fuss number and Kirkman-Cayley number. Our proof is elementary and does not use the method of generating functions.

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Jozef H. Przytycki, Adam S. Sikora. 1998-11-13. Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers. https://arxiv.org/abs/math/9811086

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