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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Why the characteristic polynomial factors
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by Bruce E. Sagan PDF
Bull. Amer. Math. Soc. 36 (1999), 113-133 Request permission


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
  • MR Author ID: 152890
  • Email:
  • 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
  • © Copyright 1999 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 36 (1999), 113-133
  • MSC (1991): Primary 06A07; Secondary 05C15, 20F55, 06C10, 52B30
  • DOI:
  • MathSciNet review: 1659875