Further results on biases in integer partitions
Bull. Korean Math. Soc.
Published online August 31, 2021
Shane Chern
Penn State University
Abstract : 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 expansion.
Keywords : integer partition, bias, generating function
MSC numbers : 05A17, 11P81
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