Sign-graded posets, unimodality of W-polynomials and the Charney-Davis conjecture
2004 (English)In: The Electronic Journal of Combinatorics, ISSN 1077-8926, Vol. 11, no 2Article in journal (Refereed) Published
We generalize the notion of graded posets to what we call sign-graded (labeled) posets. We prove that the W-polynomial of a sign-graded poset is symmetric and unimodal. This extends a recent result of Reiner and Welker who proved it for graded posets by associating a simplicial polytopal sphere to each graded poset. By proving that the W-polynomials of sign-graded posets has the right sign at -1, we are able to prove the Charney-Davis Conjecture for these spheres (whenever they are flag).
Place, publisher, year, edition, pages
2004. Vol. 11, no 2
IdentifiersURN: urn:nbn:se:kth:diva-23892ISI: 000225248000001OAI: oai:DiVA.org:kth-23892DiVA: diva2:342591
QC 201005252010-08-102010-08-10Bibliographically approved