The MacMahon q-Catalan is convex
Abstract
Let n≥2 be an integer. In this paper, we study the convexity of the so-called MacMahon's q-Catalan polynomials Cn(q)=1[n+1]q[ 2n n ]q as functions of q. Along the way, several intermediate results on inequalities are presented including a commentary on the convexity of the generation function for the integer partitions.
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