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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The limiting distribution of the coefficients of the $q$-Catalan numbers
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by William Y. C. Chen, Carol J. Wang and Larry X. W. Wang PDF
Proc. Amer. Math. Soc. 136 (2008), 3759-3767 Request permission

Abstract:

We show that the limiting distributions of the coefficients of the $q$-Catalan numbers and the generalized $q$-Catalan numbers are normal. Despite the fact that these coefficients are not unimodal for small $n$, we conjecture that for sufficiently large $n$, the coefficients are unimodal and even log-concave except for a few terms of the head and tail.
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Additional Information
  • William Y. C. Chen
  • Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
  • MR Author ID: 232802
  • Email: chen@nankai.edu.cn
  • Carol J. Wang
  • Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
  • Email: wangjian@cfc.nankai.edu.cn
  • Larry X. W. Wang
  • Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
  • MR Author ID: 845775
  • Email: wxw@cfc.nankai.edu.cn
  • Received by editor(s): August 20, 2007
  • Published electronically: July 3, 2008
  • Additional Notes: The authors are grateful to the referee for valuable suggestions. Thanks are also due to Barbara Margolius and Helmut Prodinger for helpful comments. This work was supported by the 973 Project, the PCSIRT Project of the Ministry of Education, the Ministry of Science and Technology, and the National Science Foundation of China.
  • Communicated by: Jim Haglund
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3759-3767
  • MSC (2000): Primary 05A16, 60C05
  • DOI: https://doi.org/10.1090/S0002-9939-08-09464-1
  • MathSciNet review: 2425713