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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Why the characteristic polynomial factors


Author: Bruce E. Sagan
Journal: Bull. Amer. Math. Soc. 36 (1999), 113-133
MSC (1991): Primary 06A07; Secondary 05C15, 20F55, 06C10, 52B30
Published electronically: February 16, 1999
MathSciNet review: 1659875
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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 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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Additional Information

Bruce E. Sagan
Affiliation: Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027
Email: sagan@math.msu.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-99-00775-2
PII: S 0273-0979(99)00775-2
Keywords: Characteristic polynomial, free arrangement, M\"obius function, partially ordered set, signed graph, subspace arrangement, supersolvable lattice
Received by editor(s): June 30, 1996
Received by editor(s) in revised form: November 30, 1998
Published electronically: February 16, 1999
Additional Notes: Presented at the 35th meeting of the Séminaire Lotharingien de Combinatoire, October 4–6, 1995
Article copyright: © Copyright 1999 American Mathematical Society