2005/07/22 by Bruce E. Sagan, Bruce Sagan, Sagan, Bruce +2 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Topological and Geometric Data Analysis #math.AT #math.CO #msc:05E25 #msc:06A07 #msc:68R15
paper · pdf · doi:10.48550/arxiv.math/0507485
20 pager, 4 figures, for related papers see http://www.math.msu.edu/~sagan and http://math.rutgers.edu/~vatter
arxiv created 2005/07/22 · arxiv updated 2009/12/01
We determine the Möbius 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 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.