Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers
Jozef H. Przytycki, Adam S. Sikora
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.
Create a lesson
Related papers
Graded Ehrhart theory for hypersimplices
Nathaniel Libman, Weston Miller
Closing the gap and settling the problem of queens on an n× n board, each attacking at most one other
Kristina Ago, Bojan Bašić, Radojka Ciganović
Leading term strandings for webs
Michael Bo, Madelyn Burns, Junyang Chen et al.
Refutation of the Non-Cancelling-Intersections Conjecture
Hermann Wilhelm
Asymptotic Bounds for Online Ramsey Numbers of Stars versus Long Paths and Cycles
Sam Beilis, Israel R. Curbelo, Elizabeth R. Koizumi
The Erdos--Gallai bound for consecutive even cycle lengths
Yaobin Chen, Hong Liu, Xia Wang et al.