A Short Proof of the Rank Formula for Inclusion Matrices using the Representation Theory of the Symmetric Group

2020/09/11 by Liam Jolliffe, Jolliffe, Liam · 1 citation
Computer Science · Engineering · Mathematics · #05B20 #20C30 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2009.05202

openalex publication_date 2020/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new proof of the well known formula for the rank of the inclusion matrix by constructing a kS_n-module spanned by the columns of this matrix and calculating its dimension.

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• Total trades, intersection matrices and Specht modules

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