Geodesic
The Möbius function of a composition poset
Journal of Algebraic Combinatorics, Tome 24 (2006) no. 2, pp. 117-136.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We determine the Möbius function of a 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. This composition poset turns out to be intimately connected with subword order, whose Möbius function was determined by Björner. We show that, using a generalization of subword order, we can obtain both Björner's results and our own as special cases.
Keywords: keywords composition, discrete Morse function, Möbius function, permutation pattern, subword order 
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Sagan, Bruce E.; Vatter, Vincent. The Möbius function of a composition poset. Journal of Algebraic Combinatorics, Tome 24 (2006) no. 2, pp. 117-136. http://geodesic.mathdoc.fr/item/JAC_2006__24_2_a4/