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ON $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\gamma $-VECTORS AND THE DERIVATIVES OF THE TANGENT AND SECANT FUNCTIONS

Part of: Combinatorics

Published online by Cambridge University Press:  10 April 2014

SHI-MEI MA
SHI-MEI MA*
Affiliation:
School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Hebei 066004, PR China email shimeimapapers@gmail.com
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Abstract

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In this paper, we show that the $\gamma $-vectors of Coxeter complexes (of types A and B) and associahedrons (of types A and B) can be obtained by using derivative polynomials of the tangent and secant functions. We provide a unified grammatical approach to generate these $\gamma $-vectors and the coefficient arrays of Narayana polynomials, Legendre polynomials and Chebyshev polynomials of both kinds.

Keywords

derivative polynomialsContext-free grammarsNarayana polynomialsLegendre polynomials

MSC classification

Secondary: 05A05: Permutations, words, matrices 05A15: Exact enumeration problems, generating functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 2 , October 2014 , pp. 177 - 185
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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