Proper partitions of a polygon and k-Catalan numbers
Combinatorics
2007-05-23 v1
Abstract
Let P be a polygon whose vertices have been colored (labeled) cyclically with the numbers 1,2,...,c. Motivated by conjectures of Propp, we are led to consider partitions of P into k-gons which are proper in the sense that each k-gon contains all c colors on its vertices. Counting the number of proper partitions involves a generalization of the k-Catalan numbers. We also show that in certain cases, any proper partition can be obtained from another by a sequence of moves called flips.
Cite
@article{arxiv.math/0407280,
title = {Proper partitions of a polygon and k-Catalan numbers},
author = {Bruce Sagan},
journal= {arXiv preprint arXiv:math/0407280},
year = {2007}
}
Comments
16 pages, 2 figures, Latex, see related papers at http://www.math.msu.edu/~sagan