1998/01/02 by Andreas Blass, Bruce E. Sagan
Mathematics · #math.CO #msc:06A07 #msc:06B99 #msc:05A17 #msc:05A18
published as Adv. in Math. 127 (1997), 94-123 · 29 pages, 6 figures, Latex, see related papers at http://www.math.msu.edu/~sagan
arxiv created 1998/01/02 · arxiv updated 2009/11/30
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 Möbius 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.