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发件人： jcta@asu.edu (Journal) 存入地址簿 阻止发信人 加入过滤器 
收件人： chen@nankai.edu.cn 
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邮件主题： Reference Number: 1682 ---- Author: William Y. C. Chen 
发件日期： Mon, 13 Oct 2008 07:59:14 -0700 (MST) 看信件原文   打印信件 
 
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Mon Oct 13 07:58:59 MST 2008

 
Professor William Y. C. Chen

Title: The $q$-Log-convexity of the Generating Functions of the Squares of Binomial Coefficients

By: William Y. C. Chen, Robert T. Tang, Larry X. W. Wang, Arthur L. B. Yang


Dear Professor William Y. C. Chen

Thanks for submitting your paper for publication in The Journal of Combinatorial Theory, Series A, (JCT-A). We have sucessfully received your manuscript, which has been given the reference number: 1682.

Please use this number in any future correspondence with the journal.

Once I have received the referee reports for your paper I will write to you with a decision regarding publication.

In the meantime, should you have any queries, please do not hesitate to contact
me at jcta@asu.edu.

Yours sincerely,

Ole Warnaar
Managing Editor, JCTA

==================================================================
      Appended below is additional information we recorded.
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NAME 
----
William Y. C. Chen
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EMAIL 
-----
chen@nankai.edu.cn
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ADDRESS 
-------
Center for Combinatorics
Nankai University
Tianjin 300071
P. R. China
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TITLE
----- 
The $q$-Log-convexity of the Generating Functions of the Squares of Binomial Coefficients
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AUTHORS 
-------
William Y. C. Chen, Robert T. Tang, Larry X. W. Wang, Arthur L. B. Yang
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NUMBER OF PAGES
---------------
29
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ABSTRACT
--------
We prove a conjecture of Liu
and Wang on the $q$-log-convexity of the polynomial sequence
$\{\sum_{k=0}^n{n\choose k}^2q^k\}_{n\geq 0}$. By using Pieri's rule
and the Jacobi-Trudi identity for Schur functions, we obtain an
expansion of a sum of products of elementary symmetric functions in
terms of Schur functions with nonnegative coefficients. Then the
principal specialization leads to the $q$-log-convexity. We also
prove that a technical condition of Liu and Wang  holds for the
squares of the binomial coefficients. Hence we deduce that the
linear transformation with respect to the triangular array
$\{{n\choose k}^2\}_{0\leq k\leq n}$ is log-convexity preserving.
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COMMENTS
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Addressed to - no selection
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