On Bergeron's positivity problem for q -binomial coefficients
F. Bergeron recently asked the intriguing question whether ((b+c)/b)q-((a+d)/d)q has nonnegative coefficients as a polynomial in q, whenever a, b, c, dare positive integers, a is the smallest, and ad=bc. We conjecture that, in fact, this polynomial is also always unimodal, and combinatorially show our conjecture for a≤3 and any b, c≥4. The main ingredient will be a novel (and rather technical) applicationof Zeilberger’s KOH theorem.
The Electronic Journal of Combinatorics
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On Bergeron's positivity problem for q -binomial coefficients.
The Electronic Journal of Combinatorics,
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