Schmidt type partitions and Partition Analysis

When/Where:

January 18, 2022, 1:55 — 2:45 pm at LIT 368.

Abstract:

In 1999, Frank Schmidt noted that the number of partitions of integers with distinct parts in which the first, third, fifth, etc., summands add to n is equal to p(n), the number of partitions of n. In this talk, we shall provide a context for this result via MacMahon’s Partition Analysis which leads directly to many other theorems of this nature, and which can be viewed as a continuation of our work on elongated partition diamonds. We find that generating functions which are infinite products built by the Dedekind eta function lead to interesting arithmetic theorems and conjectures for the related partition functions.

This is joint work with my PhD student Peter Paule.