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.

arXiv comment9 pages, 1 figure

References in corpus (5)

• Theorems, Problems and Conjectures
• Explicit expressions for the moments of the size of an (s,s+1)-core partition with distinct parts
• Core partitions with distinct parts
• Explicit Expressions for the Variance and Higher Moments of the Size of a Simultaneous Core Partition and its Limiting Distribution
• 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 (6)

• Explicit expressions for the moments of the size of an (s,s+1)-core partition with distinct parts
• Sizes of Simultaneous Core Partitions
• On the largest sizes of certain simultaneous core partitions with distinct parts
• On the number of simultaneous core partitions with $d$-distinct parts
• On self-conjugate $(s,s+1,\dots ,s+k)$-core partitions
• On the polynomiality and asymptotics of moments of sizes for random $(n,dn\pm 1)$-core partitions with distinct parts