  We give a counting formula for the set of rectangular increasing tableaux in
terms of generalized Narayana numbers. We define small $m$-Schr\"oder paths and
give a bijection between the set of increasing rectangular tableaux and small
$m$-Schr\"oder 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.
