The $m$-Colored Composition Poset

Abstract

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.