『组合数学』学术报告（四）
题目：Some recent results on row-increasing tableaux and lattice paths
报告人：杜若霞副教授，华东师范大学
时间：2020/6/22（周一）13:00-14:00
腾讯会议ID：385 492 653
摘要：In 2014 O. Pechenik studied increasing tableaux of shape $2\times n$, and obtained a polynomial on the major index of these tableaux, which is a $q$-analogue of refined small Schr\"{o}der numbers. We define row-increasing tableaux, and show that the major and amajor index polynomials of row-increasing tableaux of shape $(2 \times n)$are both $q$-analogues of refined large Schr\"{o}der numbers. We gave the major index polynomials of increasing tableaux and row-increasing tableaux of an arbitrary two-row shape, and the distribution of the descents of these tableaux. Moreover, cyclic sieving for row-increasing tableaux are also introduced. Inspired by these work on row-increasing polynomials, we show bijectively that the number of Standard Young Tableaux of order $n$ contained in a $(2,1)$-hook is equal to the number of humps in $n$-Motzkin paths, which answers a question posed by A. Regev in 2010.
