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Mathematics > Combinatorics

arXiv:1411.3397 (math)
[Submitted on 12 Nov 2014 (v1), last revised 30 Apr 2015 (this version, v2)]

Title:The $γ$-positivity of basic Eulerian polynomials via group actions

Authors:Zhicong Lin, Jiang Zeng
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Abstract:We provide combinatorial interpretation for the $\gamma$-coefficients of the basic Eulerian polynomials that enumerate permutations by the excedance statistic and the major index as well as the corresponding $\gamma$-coefficients for derangements. Our results refine the classical $\gamma$-positivity results for the Eulerian polynomials and the derangement polynomials. The main tools are Brändén's modified Foata--Strehl action on permutations and the recent triple statistic (des, rix,aid) equidistibuted with (exc, fix, maj).
Comments: 16 pages, 2 figures, final version for publication in Journal of Combinatorial Theory, Series A
Subjects: Combinatorics (math.CO)
Cite as: arXiv:1411.3397 [math.CO]
  (or arXiv:1411.3397v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1411.3397

Submission history

From: Jiang Zeng [view email]
[v1] Wed, 12 Nov 2014 23:44:29 UTC (15 KB)
[v2] Thu, 30 Apr 2015 14:03:32 UTC (15 KB)
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