The M\"obius function of the composition poset
Combinatorics
2007-05-23 v1 Algebraic Topology
Abstract
We determine the M\"obius function of the poset of compositions of an integer. In fact we give two proofs of this formula, one using an involution and one involving discrete Morse theory. The composition poset turns out to be intimately connected with subword order, whose M\"obius function was determined by Bj\"orner. We show that using a generalization of subword order, we can obtain both Bj\"orner's results and our own as special cases.
Keywords
Cite
@article{arxiv.math/0507485,
title = {The M\"obius function of the composition poset},
author = {Bruce Sagan and Vincent Vatter},
journal= {arXiv preprint arXiv:math/0507485},
year = {2007}
}
Comments
20 pager, 4 figures, for related papers see http://www.math.msu.edu/~sagan and http://math.rutgers.edu/~vatter