Sizes of Simultaneous Core Partitions

Abstract

There is a well-studied correspondence by Jaclyn Anderson between partitions that avoid hooks of length s or t and certain binary strings of length s+t. Using this map, we prove that the total size of a random partition of this kind converges in law to Watson's U^2 distribution, as conjectured by Doron Zeilberger.

References in corpus (3)

• Armstrong's Conjecture for $(k,mk+1)$-Core Partitions
• Explicit expressions for the moments of the size of an (s,s+1)-core partition with distinct parts
• Spectral Analysis of Word Statistics

Cited by in corpus (1)

• Spectral Analysis of Word Statistics