Seminar

# Hook-lengths of random cells in random partitions

#### Arvind Ayyer - Indian Institute of Science

For an integer $t \geq 2$, the t-core of a partition $\lambda$ is another partition obtained by removing as many rim-hooks of size t as possible from the Young diagram of $\lambda$. For an integer n, we consider the size of the t-core of a uniformly random partition of n. We determine the full distribution of this random variable as n tends to infinity. In particular, we prove that the expectation grows like $\sqrt{n}$. We use this result to show that the probability that t divides the hook length of a uniformly random cell in a uniformly random partition of n approaches 1/t as n tends to infinity. This is joint work with Shubham Sinha (UCSD).
Organizers
Sara Billey
University of Washington
Petter Brändén
KTH Royal Institute of Technology
Sylvie Corteel
Université Paris Diderot, Paris 7
Svante Linusson
KTH Royal Institute of Technology

# ProgramContact

Svante Linusson

linusson@math.kth.se

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