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This article is cited in 1 scientific paper (total in 1 paper)
Theoretical Foundations of Applied Discrete Mathematics
Generalized Narayana polynomials and their $q$-analogues
L. N. Bondarenkoa, M. L. Sharapovab a Penza State University, Penza
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow
Abstract:
Generating polynomials of the statistics $\mathrm{rise}$, $\mathrm{des}$ and $\mathrm{inv}$ are considered on the entered $312$-avoiding GS-permutations of an order $r\geq1$. It is shown that the polynomials of the statistics $\mathrm{rise}$ and $\mathrm{des}$ are some generalizations of the known Narayana polynomials. For the generalized Narayana polynomials, the inverse generating function, an algebraic equation for the generating function and a recursion relation with multiple convolutions are obtained. For the generating polynomials of pair $\mathrm{(des,inv)}$, an analogue of the obtained recursion relation and an equation for the generating function of these polynomials are found. Their particular case leads to the corresponding $q$-analogues of generalized Narayana polynomials.
Keywords:
$312$-avoiding GS-permutations, generalized Narayana polynomials, generating function, inverse function, convolution, $q$-analogues.
Citation:
L. N. Bondarenko, M. L. Sharapova, “Generalized Narayana polynomials and their $q$-analogues”, Prikl. Diskr. Mat. Suppl., 2016, no. 9, 6–8
Linking options:
https://www.mathnet.ru/eng/pdma261 https://www.mathnet.ru/eng/pdma/y2016/i9/p6
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Abstract page: | 143 | Full-text PDF : | 90 | References: | 22 |
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