The product of parts or "norm" of a partition

Abstract

In this article we study the "norm" of an integer partition, which we define to be the product of the parts. This partition-theoretic statistic has appeared here and there in the literature of the last century or so, and is at the heart of current research by both authors. We survey known results and give new results related to this all-but-overlooked object, which, it turns out, plays a comparable role in partition theory to the size, length, and other standard partition statistics.