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Séminaire Lotharingien de Combinatoire, B35a (1995), 20pp.

# Bruce Sagan

# Why the Characteristic Polynomial Factors

**Abstract.**
We survey three methods for proving that the characteristic polynomial
of a finite ranked lattice factors over the nonnegative integers and
indicate how they have evolved recently. The first
technique uses geometric ideas and is
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 supersolvable lattices
and its generalizations.

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