 Kostka number

The Kostka number $K_{\alpha \lambda }$ is the number of semistandard Young tableaux of shape $\alpha$ and content $\lambda$: rows are weakly increasing and columns are strictly increasing.

Kostka numbers, denoted as \( K_{n, \lambda} \), arise in combinatorial representation theory and algebraic geometry. They count the number of ways to arrange a certain type of tableau (specifically, standard Young tableaux) corresponding to partitions and is related to the representation theory of the symmetric group.