A SHORT PROOF OF THE RANK FORMULA FOR INCLUSION MATRICES

We present a new proof of the well-known formula for the rank of the inclusion matrix by constructing a k𝒮n-module spanned by the columns of this matrix and calculating its dimension. This gives a representation theoretic interpretation of this formula as the sum of dimensions of Specht modules.

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Publication Details

Journal
Rocky Mountain Journal of Mathematics
Published
2024-09-26
DOI
https://doi.org/10.1216/rmj.2024.54.1359
Citations
1
Primary Topic
Graph theory and applications
Type
article
Field-Weighted Citation Impact
1.01
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article

A SHORT PROOF OF THE RANK FORMULA FOR INCLUSION MATRICES

Liam Jolliffe
1 citations
Rocky Mountain Journal of Mathematics
Graph theory and applications
1.01
article

A SHORT PROOF OF THE RANK FORMULA FOR INCLUSION MATRICES

Liam Jolliffe
article en
1 citations

Abstract

We present a new proof of the well-known formula for the rank of the inclusion matrix by constructing a k𝒮n-module spanned by the columns of this matrix and calculating its dimension. This gives a representation theoretic interpretation of this formula as the sum of dimensions of Specht modules.

Rocky Mountain Journal of MathematicsVol. 54(5)
Reduced inequalities
Openalex Percentile: Top 24%
Graph theory and applications
1.01
DOISourceOpenAlex
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A SHORT PROOF OF THE RANK FORMULA FOR INCLUSION MATRICES — Liam Jolliffe · Rocky Mountain Journal of Mathematics (2024) | TGRS Research Map | TGRS