Aritram Dhar

Affiliation: University of Florida

Title Of Talk: On Glaisher's Partition Theorem

Abstract: 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 divisible by $m$. The $m=2$ case is Euler's famous partition theorem. Recently, Andrews, Kumar, and Yee gave two new partition functions $C(n)$ and $D(n)$ related to Euler's theorem. Lin and Zhang extended their result to Glaisher's theorem by generalizing $C(n)$. In this talk, we generalize $D(n)$, prove an analogous partition identity for the $m=3$ case, and show that the general case is an example of an almost partition identity. We also provide a new series equal to Glaisher's product both in the finite and infinite cases. This is joint work with George E. Andrews.

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