Bruce Sagan, Vincent Vatter
Published 2005-07-22Version 1
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.
Comments: 20 pager, 4 figures, for related papers see http://www.math.msu.edu/~sagan and http://math.rutgers.edu/~vatter
Groebner basis degree bounds on $\Tor^{k[Λ ]}_\bullet(k,k)_\bullet$ and discrete Morse theory for posets
The Möbius Function of a Restricted Composition Poset
The Möbius function of generalized subword order
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