Mobius functions of lattices

Details Mobius functions of lattices Mobius functions of lattices

1998-01-02

arxiv.org/abs/math/9801009v1

Adv. in Math. 127 (1997), 94-123

Mathematics

Combinatorics

29 pages, 6 figures, Latex, see related papers at http://www.math.msu.edu/~sagan

Scientific paper

We introduce the concept of a bounded below set in a lattice. This can be used to give a generalization of Rota's broken circuit theorem to any finite lattice. We then show how this result can be used to compute and combinatorially explain the M\"obius function in various examples including non-crossing set partitions, shuffle posets, and integer partitions in dominance order. Next we present a generalization of Stanley's theorem that the characteristic polynomial of a semimodular supersolvable lattice factors over the integers. We also give some applications of this second main theorem, including the Tamari lattices.

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