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 (9)

• Simultaneous core partitions: parameterizations and sums
• Theorems, Problems and Conjectures
• 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
• Explicit Expressions for the Variance and Higher Moments of the Size of a Simultaneous Core Partition and its Limiting Distribution
• Simultaneous cores with restrictions and a question of Zaleski and Zeilberger
• Explicit expressions for the moments of the size of an (n, dn-1)-core partition with distinct parts
• On the Intriguing Problem of Counting (n+1,n+2)-Core Partitions into Odd Parts
• Spectral Analysis of Word Statistics

Cited by in corpus (1)

• Spectral Analysis of Word Statistics