The m-Colored Composition Poset

We define a partial order on colored compositions with many properties analogous to Young’s lattice. We show that saturated chains correspond to colored permutations, and that covering relations correspond to a Pieri-type rule for colored quasi-symmetric functions. We also show that the poset is CL-shellable. In the case of a single color, we recover the subword order on binary words.

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Brian Drake, T. Kyle Petersen
• Keywords: COMBINATORICS 2007, Partial Order, Pieri-type Rule, Quasi-symmetric Functions