2005/12/15 by Brian Drake, Drake, Brian, T. Kyle Petersen +1
Mathematics · #52B22 #Combinatorics (math.CO) #FOS: Mathematics #Primary 06A07 #Secondary 05A99 #math.CO #msc:05A99 #msc:06A07 #msc:52B22
paper · pdf · doi:10.48550/arxiv.math/0512369
12 pages, 1 figure
arxiv created 2005/12/15 · arxiv updated 2009/12/01
We generalize Björner 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 Björner 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.