Quasideterminants and q-commuting minors
Aaron Lauve
TL;DR
This paper introduces two novel proofs demonstrating the q-commuting property of specific quantum minors in an n x n q-generic matrix, utilizing quasideterminants and graph path methods.
Contribution
It provides new proofs of q-commuting properties of quantum minors using elementary quasideterminantal arithmetic and graph path techniques.
Findings
Proves q-commuting property using quasideterminants
Provides an alternative proof via directed graph paths
Enhances understanding of quantum minors' algebraic relations
Abstract
We present two new proofs of the the important q-commuting property holding among certain pairs of quantum minors of an n x n q-generic matrix. The first uses elementary quasideterminantal arithmetic; the second involves paths in an edge-weighted directed graph.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Topics in Algebra