SIGNS IN THE cd-INDEX OF EULERIAN PARTIALLY ORDERED SETS

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Issue Date
2000-12-28Author
Bayer, Margaret M.
Publisher
American Mathematical Society
Type
Article
Article Version
Scholarly/refereed, publisher version
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Show full item recordAbstract
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 ag vector can be encoded efficiently in the cd-index. The cd-index of a polytope has all positive entries. An important open problem is to give the broadest natural class of Eulerian posets having nonnegative cd-index. This paper completely determines which entries of the cd-index are nonnegative for all Eulerian posets. It also shows that there are no other lower or upper bounds on cd-coefficients (except for the coefficient of cn).
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Citation
Bayer, Margaret M. "SIGNS IN THE cd-INDEX OF EULERIAN PARTIALLY ORDERED SETS." Proceedings of the American Mathematical Society vol 129, number 8 pages 2219-2225. http://dx.doi.org/10.1090/S0002-9939-00-05831-7
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