MOBIUS FUNCTIONS OF LATTICES

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 comput e and combinatorially explain the Mobius Function in various examples including non-crossing set partitions, shuffle posets, and integer par titions in dominance order. Next we present a generalization of Stanle y's theorem that the characteristic polynomial of a semimodular supers olvable lattice factors over the integers. We also give some applicati ons of this second main theorem, including the Tamari lattices. (C) 19 97 Academic Press.