Apr 27 2021

Combinatorics and Probability Seminar: Sorting probability for Young diagrams, by Swee Hong Chan

April 27, 2021

3:00 PM - 3:50 PM

Location

Zoom

Address

Chicago, IL

Swee Hong Chan (UCLA): Sorting probability for Young diagrams

Can you always find two elements x,y of a partially ordered set, such that, the probability that x is ordered before y when the poset is ordered randomly, is between 1/3 and 2/3? This is the celebrated 1/3-2/3 Conjecture, which has been called "one of the most intriguing problems in the combinatorial theory of posets". We will explore this conjecture for posets that arise from (skew-shaped) Young diagrams, where total orderings of these posets correspond to standard Young tableaux. We will show that that these probabilities are arbitrarily close to 1/2, by using random walk estimates and the state-of-the-art hook-length formulas of Naruse. This is a joint work with Igor Pak and Greta Panova. This talk is aimed at a general audience.

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Contact

Will Perkins

Date posted

Apr 21, 2021

Date updated

Apr 21, 2021

Speakers

Swee Hong Chan | (UCLA)