Proper partitions of a polygon and k-Catalan numbers

Bruce Sagan

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arXiv · math/0407280

Proper partitions of a polygon and k-Catalan numbers

Bruce Sagan

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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.

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BibTeX RIS

Bruce Sagan. 2004-07-15. Proper partitions of a polygon and k-Catalan numbers. https://arxiv.org/abs/math/0407280

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