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Article overview
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Schur Positivity and the $q$-Log-convexity of the Narayana Polynomials | William Y. C. Chen
; Larry X.W. Wang
; Arthur L. B. Yang
; | Date: |
10 Jun 2008 | Abstract: | Using Schur positivity and the principal specialization of Schur functions,
we provide a proof of a recent conjecture of Liu and Wang on the
$q$-log-convexity of the Narayana polynomials, and a proof of the second
conjecture that the Narayana transformation preserves the log-convexity. Based
on a formula of Br"and$mathrm{acute{e}}$n which expresses the $q$-Narayana
numbers as the specializations of Schur functions, we derive several symmetric
function identities using the Littlewood-Richardson rule for the product of
Schur functions, and obtain the strong $q$-log-convexity of the Narayana
polynomials and the strong $q$-log-concavity of the $q$-Narayana numbers. | Source: | arXiv, 0806.1561 | Services: | Forum | Review | PDF | Favorites |
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