The Ramanujan Journal

, Volume 27, Issue 3, pp 297–304 | Cite as

Partially 2-colored permutations and the Boros–Moll polynomials

  • William Y. C. Chen
  • Sabrina X. M. Pang
  • Ellen X. Y. Qu
Article
First Online:
Received:
Accepted:

Abstract

We find a combinatorial setting for the coefficients of the Boros–Moll polynomials P m (a) in terms of partially 2-colored permutations. Using this model, we give a combinatorial proof of a recurrence relation on the coefficients of P m (a). This approach enables us to give a combinatorial interpretation of the log-concavity of P m (a) which was conjectured by Moll and confirmed by Kauers and Paule.

Keywords

Partially 2-colored permutation Boros–Moll polynomial Rising factorial Log-concavity Bijection 

Mathematics Subject Classification (2000)

05A05 05A10 05A20 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • William Y. C. Chen
    • 1
  • Sabrina X. M. Pang
    • 2
  • Ellen X. Y. Qu
    • 3
  1. 1.Center for Combinatorics, LPMC-TJKLCNankai UniversityTianjinP.R. China
  2. 2.College of Mathematics and StatisticsHebei University of Economics and BusinessShijiazhuangP.R. China
  3. 3.School of Mathematical SciencesOcean University of ChinaQingdaoP.R. China

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