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2008

Proper Partitions of a Polygon and k-Catalan Numbers

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Proper Partitions of a Polygon and k-Catalan Numbers
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.
Bruce E. Sagan
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2008
Where ARSCOM
Authors Bruce E. Sagan
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