The $m$-colored composition poset

Details The $m$-colored composition poset The $m$-colored composition poset

2005-12-15

arxiv.org/abs/math/0512369v1

Mathematics

Combinatorics

12 pages, 1 figure

Scientific paper

We generalize Bj\"{o}rner and Stanley's poset of compositions to $m$-colored compositions. Their work draws many analogies between their (1-colored) composition poset and Young's lattice of partitions, including links to (quasi-)symmetric functions and representation theory. Here we show that many of these analogies hold for any number of colors. While many of the proofs for Bj\"{o}rner and Stanley's poset were simplified by showing isomorphism with the subword order, we remark that with 2 or more colors, our posets are not isomorphic to a subword order.

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