Explicit expressions for the moments of the size of an (s,s+1)-core partition with distinct parts

TL;DR

This paper derives explicit formulas for the moments of the size of (s,s+1)-core partitions with distinct parts, providing evidence of their asymptotic normality through computational methods.

Contribution

It introduces formulas for the expectation, variance, and higher moments of the size of (s,s+1)-core partitions with distinct parts, using computer-assisted derivations.

Findings

Formulas for moments of the partition size are derived.

Evidence suggests the distribution of size is asymptotically normal.

Computational methods are used to support theoretical results.

Abstract

For fixed s, the size of an (s, s+1)-core partition with distinct parts can be seen as a random variable X_s. Using computer-assisted methods, we derive formulas for the expectation, variance, and higher moments of X_s. Our results give good evidence that X_s is asymptotically normal.