Signs in the -index of Eulerian partially ordered sets

Author:
Margaret M. Bayer

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2219-2225

MSC (2000):
Primary 06A07

Published electronically:
December 28, 2000

MathSciNet review:
1823903

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

A graded partially ordered set is Eulerian if every interval has the same number of elements of even rank and of odd rank. Face lattices of convex polytopes are Eulerian. For Eulerian partially ordered sets, the flag vector can be encoded efficiently in the -index. The -index of a polytope has all positive entries. An important open problem is to give the broadest natural class of Eulerian posets having nonnegative -index. This paper completely determines which entries of the -index are nonnegative for all Eulerian posets. It also shows that there are no other lower or upper bounds on -coefficients (except for the coefficient of ).

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Additional Information

**Margaret M. Bayer**

Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-2142

Email:
bayer@math.ukans.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05831-7

Keywords:
Eulerian poset,
flag vector,
$cd$-index

Received by editor(s):
October 22, 1999

Received by editor(s) in revised form:
December 21, 1999

Published electronically:
December 28, 2000

Communicated by:
John R. Stembridge

Article copyright:
© Copyright 2000
American Mathematical Society