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

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.

9 pages, 1 figure

References in corpus (2)

• Explicit expressions for the moments of the size of an (s,s+1)-core partition with distinct parts
• Explicit (Polynomial!) Expressions for the Expectation, Variance and Higher Moments of the Size of a (2n + 1, 2n + 3)-core partition with Distinct Parts

Cited by in corpus (3)

• Explicit expressions for the moments of the size of an (s,s+1)-core partition with distinct parts
• On the largest sizes of certain simultaneous core partitions with distinct parts
• On self-conjugate $(s,s+1,\dots ,s+k)$-core partitions