Sign-Graded Posets, Unimodality of $W$-Polynomials and the Charney-Davis Conjecture
Sign-Graded Posets, Unimodality of $W$-Polynomials and the Charney-Davis Conjecture
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 …