Matrix divisibility sequences
Gunther Cornelissen, Jonathan Reynolds
TL;DR
This paper reveals that many divisibility sequences can be understood as determinants of matrix sequences derived from Jacobian matrices of group maps on affine spaces, providing a unifying algebraic framework.
Contribution
It introduces a novel perspective linking divisibility sequences to matrix determinants from Jacobian matrices, expanding the understanding of their algebraic structure.
Findings
Many divisibility sequences are determinants of matrix sequences.
Matrix divisibility sequences originate from Jacobian matrices of group maps.
Provides a unifying algebraic framework for divisibility sequences.
Abstract
We show that many existing divisibility sequences can be seen as sequences of determinants of matrix divisibility sequences, which arise naturally as Jacobian matrices associated to groups of maps on affine spaces.
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