Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers

1998/11/13 by Jozef H. Przytycki, Przytycki, Jozef H., Adam S. Sikora +1 · 1 citation
Mathematics · #05A #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A

paper · pdf · doi:10.48550/arxiv.math/9811086

9 pages, 4 figures

arxiv created 1998/11/13 · arxiv updated 2009/11/30

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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• On weighted partial triangulations of convex polygons

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