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Abstract: For a graded naturally labelled poset P , it is shown that the P -Eulerian polynomial counting linear extensions of P by their number of descents has symmetric and unimodal coefficient sequence, verifying the motivating consequence of the Neggers-Stanley conjecture on real zeroes for W (P, t) in these cases. The result is deduced from McMullen's g-Theorem, by exhibiting a simplicial polytopal sphere whose h-polynomial is W (P, t). Whenever this is... (Update)
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9.2: On the Charney-Davis and Neggers-Stanley Conjectures - Reiner, Welker (Correct)
1.0: Positivity Problems and Conjectures in Algebraic Combinatorics - Stanley (1999) (Correct)
0.7: The Charney-Davis Quantity for Certain Graded Posets - Reiner, Stanton, Welker (2003) (Correct)
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BibTeX entry: (Update)
@misc{ reiner-charneydavis,
author = "Victor Reiner and Volkmar Welker",
title = "On the {C}harney--{D}avis and {N}eggers--{S}tanley Conjectures",
url = "citeseer.ist.psu.edu/621291.html" }
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