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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/934813

Title: A q-rious positivity
Author/Creator: Warnaar, S. Ole; Zudilin, W.
Description: The q-binomial coefficients [ⁿ_m] = ᴨ^m_i=1(1-q^n-m+i)/(1-qⁱ), for integers 0≤m≤n, are known to be polynomials with non-negative integer coefficients. This readily follows from the q-binomial theorem, or the many combinatorial interpretations of [ⁿ_m]. In this note we conjecture an arithmetically motivated generalisation of the non-negativity property for products of ratios of q-factorials that happen to be polynomials.
Relation: Aequationes Mathematicae Vol. 81, p. 177-183
Publisher Link: http://dx.doi.org/10.1007/s00010-010-0055-9
Date: 2011
Publisher: Birkhaeuser Verlag AG
Keyword(s): binomial coefficients; q-binomial coefficients; Gaussian polynomials; factorial ratios; basic hypergeometric series; cyclotomic polynomials; positivity
Resource Type: journal article
Rights: The final publication is available at www.springerlink.com
Identifier: http://hdl.handle.net/1959.13/934813
Identifier: ISSN:0001-9054
Language: eng

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