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Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers | | Jozef H. Przytycki
; Adam S. Sikora
; | | Date: |
13 Nov 1998 | | Subject: | Combinatorics MSC-class: 05A | math.CO | | 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. | | Source: | arXiv, math.CO/9811086 | | Services: | Forum | Review | PDF | Favorites | |
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