A Short Proof of the Rank Formula for Inclusion Matrices using the Representation Theory of the Symmetric Group
Liam Jolliffe·2020-09-11·via math.CO updates on arXiv.org
We present a new proof of the well known formula for the rank of the inclusion matrix by constructing a $k\mathcal{S}_n$-module spanned by the columns of this matrix and calculating its dimension.