- Title
- A q-rious positivity
- Creator
- Warnaar, S. Ole; Zudilin, W.
- Relation
- Aequationes Mathematicae Vol. 81, p. 177-183
- Publisher Link
- http://dx.doi.org/10.1007/s00010-010-0055-9
- Publisher
- Birkhaeuser Verlag AG
- Resource Type
- journal article
- Date
- 2011
- Description
- The q-binomial coefficients [nm] = ᴨmi=1(1-qn-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 [nm]. 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.
- Subject
- binomial coefficients; q-binomial coefficients; Gaussian polynomials; factorial ratios; basic hypergeometric series; cyclotomic polynomials; positivity
- Identifier
- http://hdl.handle.net/1959.13/934813
- Identifier
- uon:11911
- Identifier
- ISSN:0001-9054
- Rights
- The final publication is available at www.springerlink.com
- Language
- eng
- Full Text
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