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On certain combinatorial expansions of the Eulerian polynomials

✍ Scribed by Chak-On Chow


Book ID
108047125
Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
247 KB
Volume
41
Category
Article
ISSN
0196-8858

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We prove combinatorially that the W-polynomials of naturally labeled graded posets of rank 1 or 2 (an antichain has rank 0) are unimodal, thus providing further supporting evidence for the Neggers Stanley conjecture. For such posets we also obtain a combinatorial proof that the W-polynomials are sym