On the straightening law for minors of a matrix

TL;DR

This paper presents a simplified proof of the straightening law for minors of a matrix, utilizing a generalized Laplace expansion to clarify the underlying combinatorial structure.

Contribution

It introduces a new, straightforward proof of the straightening law, enhancing understanding of the algebraic relations among minors.

Findings

Simplified proof of the straightening law

Generalization of Laplace expansion technique

Improved conceptual clarity for minors' relations

Abstract

We give a simple new proof for the straightening law of Doubilet, Rota, and Stein using a generalization of the Laplace expansion of a determinant.