Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers

Details Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers

1998-11-13

arxiv.org/abs/math/9811086v1

Mathematics

Combinatorics

9 pages, 4 figures

Scientific paper

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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