Enumeration of generalized Young tableaux with bounded height

Abstract

We consider Young tableaux strictly increasing in rows, weakly increasing in columns. We show that the number of such tableaux with entries between 1 and n, with p columns having an odd number of elements and having at most 2 k rows, it the product n p 2k+p −1 p n+2k+p p П 1⩽i⩽j⩽n⩽ 2k+i+j i+j . The proof is mainly bijective, using configurations of noncrossing paths.