A q-rious positivity

Warnaar, S. Ole and Zudilin, W. (2011) A q-rious positivity. Aequationes Mathematicae, 81 1-2: 177-183. doi:10.1007/s00010-010-0055-9

Author Warnaar, S. Ole
Zudilin, W.
Title A q-rious positivity
Formatted title
A q-rious positivity
Journal name Aequationes Mathematicae   Check publisher's open access policy
ISSN 0001-9054
Publication date 2011-03
Year available 2010
Sub-type Article (original research)
DOI 10.1007/s00010-010-0055-9
Volume 81
Issue 1-2
Start page 177
End page 183
Total pages 7
Place of publication Basel, Switzerland
Publisher Birkhaeuser Verlag AG
Collection year 2011
Language eng
Formatted abstract
The q-binomial coefficients [n m] = ∏mi=1(1-qn-m+i)/(1-qi)for integers 0 ≤ mn, 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.
© 2010 Springer Basel AG.
Keyword Binomial coefficients
q-binomial coefficients
Gaussian polynomials
Factorial ratios
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online October 30, 2010.

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
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Citation counts: TR Web of Science Citation Count  Cited 7 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 6 times in Scopus Article | Citations
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Created: Sun, 20 Mar 2011, 00:13:34 EST