New results on q-positivity
نویسندگان
چکیده
منابع مشابه
A q-RIOUS POSITIVITY
The q-binomial coefficients [ n m ] = ∏m i=1(1 − qn−m+i)/(1 − q), 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-facto...
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Abstract. Several new transformations for q-binomial coefficients are found, which have the special feature that the kernel is a polynomial with nonnegative coefficients. By studying the group-like properties of these positivity preserving transformations, as well as their connection with the Bailey lemma, many new summation and transformation formulas for basic hypergeometric series are found....
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ژورنال
عنوان ژورنال: Positivity
سال: 2012
ISSN: 1385-1292,1572-9281
DOI: 10.1007/s11117-012-0191-7