Strict Partitions of Maximal Projective Degree

TL;DR

This paper computes and analyzes strict partitions with maximal projective degree for all n < 221, revealing patterns and supporting a conjecture on their limiting shape.

Contribution

It extends previous computations of maximal projective degree strict partitions to larger n and observes their close proximity, supporting a conjecture on their limiting shape.

Findings

Maximal projective degree partitions for n < 101 and n < 221 identified.

Partitions with maximal degree tend to be close to each other for successive n.

Results support a conjecture on the limiting shape of these partitions.

Abstract

The projective degrees of strict partitions of n were computed for all n < 101 and the partitions with maximal projective degree were found for each n. It was observed that maximizing partitions for successive values of n "lie close to each other" in a certain sense. Conjecturing that this holds for larger values of n, the partitions of maximal degree were computed for all n < 221. The results are consistent with a recent conjecture on the limiting shape of the strict partition of maximal projective degree.