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

Plats: Institut Mittag-Leffler, Seminar Hall Kuskvillan

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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Senast ändrad: 2020-01-22