Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers
Combinatorics
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/9811086,
title = {Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers},
author = {Jozef H. Przytycki and Adam S. Sikora},
journal= {arXiv preprint arXiv:math/9811086},
year = {2007}
}
Comments
9 pages, 4 figures