Alexander Lazar: q-Enumeration of Barely Set-Valued Tableaux and P-Partitions

Abstract: Set-valued tableaux are a generalization of Young tableaux in which the entries of the cells are allowed to be nonempty sets of positive integers. They have a rich combinatorial structure and arise naturally in algebraic geometry. The problem of counting standard set-valued tableaux is difficult in general, but in certain special cases there are product formulas for this count which generalize the hook-length formula for standard Young tableaux.

This talk will focus on the case of "barely set-valued" tableaux: set-valued tableaux in which all but one cell are filled with single elements and the remaining cell has exactly two entries. I will discuss joint work with Sam Hopkins and Svante Linusson in which we give a q-analog of Chan et al.'s formula for the number of barely set-valued tableaux for the rectangular shape a x b. The proofs of our results rely on a new family of probability distributions on posets which we think may be of further interest.

Zoom meeting ID: 654 5562 3260

Zoom link: https://kth-se.zoom.us/j/65455623260