Till innehåll på sidan

# Arvind Ayyer: Hook-lengths of random cells in random partitions

Tid: Ti 2020-01-28 kl 14.30 - 15.20

Föreläsare: Arvind Ayyer, Indian Institute of Science

### Abstract

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).

Innehållsansvarig:webmaster@math.kth.se
Tillhör: Institutionen för matematik