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On the Charney-Davis and Neggers-Stanley Conjectures  (Make Corrections)  
Victor Reiner, Volkmar Welker



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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)

Active bibliography (related documents):   More   All
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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A Homological Lower Bound For Order Dimension Of Lattices - Reiner, Welker   (Correct)
On Some Instances Of The Generalized Baues Problem - Reiner   (Correct)
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