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 $\mu ⊵\nu$, we have $K_{\lambda \nu }⩾K_{\lambda \mu }$.

No originality is claimed, and no (further) publication is intended. I have been asked to post this note to arXiv so that it can be cited