Combinatorics Seminar 2018

Speaker: Ruoxia Du (杜若霞), East China Normal University

Date: Mon, Jun 25, 2018

Time: 15:00 - 16:00

Venue: Large Meeting Room

Title: Enumeration on row-increasing tableaux of shape $2 \times n$


In this talk I will present some recent results on counting major and amajor index of increasing and row-increasing tableaux. In 2014 O. Pechenik studied the cyclic sieving of 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 study the major and amajor index of row-increasing tableaux of shape $(2 \times n)$. The resulting polynomials are both $q$-analogues of refined large Schr\"{o}der numbers. For both results we give bijective proofs.

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