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# Jang Soo Kim: Counting standard barely set-valued tableaux of shifted shapes

Tid: Ti 2020-01-28 kl 09.00 - 09.50

Föreläsare: Jang Soo Kim, Sungkyunkwan University, Suwon

### Abstract

A standard barely set-valued tableau of shape $$\lambda$$ is a filling of the Young diagram $$\lambda$$ with integers $$1,2,\dots,|\lambda|+1$$ such that the integers are increasing in each row and column, and every cell contains one integer except one cell that contains two integers. Counting standard barely set-valued tableaux is closely related to the coincidental down-degree expectations (CDE) of Young posets. Using $$q$$-integral techniques we give a formula for the number of standard barely set-valued tableaux of arbitrary shifted shape. We then prove a conjecture of Reiner, Tenner and Yong on the CDE property of shifted shape $$(n,n-2,\dots,n-2k)$$. This is joint work with Michael Schlosser and Meesue Yoo.

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Tillhör: Institutionen för matematik