George E. Andrews

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math.CO2026

The Partition Pairing Theorems I

George Andrews, Manosij Ghosh Dastidar

The aim of this paper is to introduce pairing theory for partitions. We begin with two statistics on integer partitions, the \emph{pairing index} and the \emph{pairing rank}. The p…

math.CO2026

On Glaisher's Partition Theorem

George E. Andrews, Aritram Dhar

Glaisher's theorem states that the number of partitions of $n$ into parts which repeat at most $m - 1$ times is equal to the number of partitions of $n$ into parts which are not divi…

math.CO2025

Extending Andrews and Newman's refinement of the crank-mex theorem

George E. Andrews, Brian Hopkins

The crank-mex theorem states that the number of integer partitions of $n$ with nonnegative crank equals the number with odd minimal excludant (mex). Andrews and M. Newman recently…

math.CO2025

On Euler's Theorem

George E. Andrews, Rahul Kumar, Ae Ja Yee

Euler's theorem asserts that $A (n) = B (n)$ where $A (n)$ is the number of partitions of $n$ into distinct parts and $B (n)$ is the number of partitions of $n$ into odd parts. In this p…