Increasing tableaux and Narayana numbers

Abstract

We give a counting formula for the set of rectangular increasing tableaux in terms of generalized Narayana numbers. We define small $m$-Schröder paths and give a bijection between the set of increasing rectangular tableaux and small $m$-Schröder paths, generalizing a result of Pechenik [3]. Using $K$-jeu de taquin promotion, which was defined by Thomas and Yong [10], we give a cyclic sieving phenomenon for the set of increasing hook tableaux.

References in corpus (1)

• A skein action of the symmetric group on noncrossing partitions

Cited by in corpus (2)

• Resonance in orbits of plane partitions and increasing tableaux
• Genomic Tableaux