Abstract
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.
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This work was partially done while B. E. Sagan was on leave at DIMACS.
Partially supported by an award from DIMACS and an NSF VIGRE grant to the Rutgers University Department of Mathematics.
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Sagan, B.E., Vatter, V. The Möbius function of a composition poset. J Algebr Comb 24, 117–136 (2006). https://doi.org/10.1007/s10801-006-0017-4
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DOI: https://doi.org/10.1007/s10801-006-0017-4