2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71911Let 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.16 pages, 2 figures, Latex, see related papers at http://www.math.msu.edu/~saganCombinatorics05A10 (Primary) 05A05, 05A15, 05A19, 05C05 (Secondary)text