Tableau Cycling and Catalan Numbers

We develop two combinatorial proofs of the fact that certain Young tableaux are counted by the Catalan numbers. The setting is a larger class of tableaux where labels increase along rows without attention to whether labels increase down columns. We define a new operation called tableau cycling. It is used to duplicate the reflection argument attributed to Andr´e in the tableaux setting, and also to prove a tableaux analog of the Chung-Feller theorem.