Consider the [Young's lattice](https://en.wikipedia.org/wiki/Young%27s_lattice). *What is the number of paths starting from the origin (0) to a specific Young diagram?*


For instance, the Young diagram corresponding to the integer partition 1+1+1 has 1 path leading to it, 2+1 has 2 paths leading to it and 2+2 has 2 paths leading to it.


Is there a generating function to get this combinatorics?



Number of paths to a specific vertex in the Young's lattice
These paths are the same thing as standard Young tableaux, which are enumerated by the famous [Hook Length Formula](https://en.wikipedia.org/wiki/Hook_length_formula).


