Why the characteristic polynomial factors

Details Why the characteristic polynomial factors Why the characteristic polynomial factors

1998-12-24

arxiv.org/abs/math/9812136v1

Bull. Amer. Math. Soc. 36 (1999), 113-134

Mathematics

Combinatorics

28 pages, 4 figures, Latex, to be published in AMS Bulletin

Scientific paper

We survey three methods for proving that the characteristic polynomial of a finite lattice factors over the nonnegative integers and indicate how they have evolved recently. The first technique uses geometric ideas and is based on Zaslavsky's theory of signed graphs. The second approach is algebraic and employs results of Saito and Terao about free hyperplane arrangements. Finally, we consider a purely combinatorial theorem of Stanley about semimodular supersolvable lattices and its generalizations.

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