Bulletin of the
Korean Mathematical Society BKMS

Let $p_{a,b,m}(n)$ be the number of integer partitions of $n$ with more parts congruent to $a$ modulo $m$ than parts congruent to $b$ modulo $m$. We prove that $p_{a,b,m}(n)\ge p_{b,a,m}(n)$ whenever $1\le a<b\le m$. We also propose some conjectures concerning series with nonnegative coefficients in their expansions.

Keywords: Integer partition, bias, generating function, nonnegativity

MSC numbers: Primary 05A17, 11P81