Seminar

# Hook-lengths of random cells in random partitions

#### Algebraic and Enumerative Combinatorics

#### 28 January 14:30 - 15:20

#### 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