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Sign-graded posets, unimodality of {\(W\)}-polynomials and the {C}harney-{D}avis conjecture
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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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).
DOI : 10.37236/1866
Classification : 06A07, 13F55
Mots-clés : sign-graded finite poset, \(W\)-polynomial, simplicial complex, polytopal sphere complex 
@article{10_37236_1866,
     author = {Petter Br\"and\'en},
     title = {Sign-graded posets, unimodality of {{\(W\)}-polynomials} and the {{C}harney-{D}avis} conjecture},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {2},
     doi = {10.37236/1866},
     zbl = {1065.06001},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1866/}
}
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Petter Brändén. Sign-graded posets, unimodality of {\(W\)}-polynomials and the {C}harney-{D}avis conjecture. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1866

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