1 research outputs found
On Bergeron's positivity problem for -binomial coefficients
F. Bergeron recently asked the intriguing question whether has nonnegative coefficients as a polynomial in ,
whenever are positive integers, is the smallest, and . We
conjecture that, in fact, this polynomial is also always unimodal, and
combinatorially show our conjecture for and any . The main
ingredient will be a novel (and rather technical) application of Zeilberger's
KOH theorem.Comment: Final version. To appear in the Electronic J. Combinatoric