Proper partitions of a polygon and k-Catalan numbers

Details Proper partitions of a polygon and k-Catalan numbers Proper partitions of a polygon and k-Catalan numbers

2004-07-15

arxiv.org/abs/math/0407280v1

Mathematics

Combinatorics

16 pages, 2 figures, Latex, see related papers at http://www.math.msu.edu/~sagan

Scientific paper

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.

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