  Standard set-valued Young tableaux are a generalization of standard Young
tableaux in which cells may contain more than one integer, with the added
conditions that every integer at position $(i,j)$ must be smaller than every
integer at positions $(i,j+1)$ and $(i+1,j)$. This paper explores the
combinatorics of standard set-valued Young tableaux with two-rows, and how
those tableaux may be used to provide new combinatorial interpretations of
generalized Catalan numbers. New combinatorial interpretations are provided for
the two-parameter Fuss-Catalan numbers (Raney numbers), the rational Catalan
numbers, and the solution to the so-called "generalized tennis ball problem".
Methodologies are then introduced for the enumeration of standard set-valued
Young tableaux, prompting explicit formulas for the general two-row case. The
paper closes by drawing a bijection between arbitrary classes of two-row
standard set-valued Young tableaux and collections of two-dimensional lattice
paths that lie weakly below a unique maximal path.
