Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers
Abstract
We give a short proof for a formula for the number of divisions of a convex (sn+2)gon along noncrossing diagonals into (sj+2)gons, where 1<=j<=n1. 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: EulerCatalan number, Fuss number and KirkmanCayley number. Our proof is elementary and does not use the method of generating functions.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 1998
 DOI:
 10.48550/arXiv.math/9811086
 arXiv:
 arXiv:math/9811086
 Bibcode:
 1998math.....11086P
 Keywords:

 Combinatorics;
 05A
 EPrint:
 9 pages, 4 figures