A note on Kostka numbers

Abstract

We give an elementary proof of a well-known result on Kostka numbers, following a question from Mark Wildon on MathOverflow. Namely, we show that given partitions $\lambda,\mu,\nu$ of $n$ with $\mu\trianglerighteq\nu$, we have $K_{\lambda\nu}\geqslant K_{\lambda\mu}$.