New examples of determinant divisibility sequences

TL;DR

This paper explores divisibility sequences derived from matrix powers, showing that their determinants form generalized Lucas sequences, thus connecting matrix algebra with classical number sequences.

Contribution

It introduces a new class of determinant divisibility sequences from matrix powers and proves their relation to generalized Lucas sequences.

Findings

Determinant sequences from matrix powers are generalized Lucas sequences.

Matrix divisibility sequences are associated with semigroups and affine endomorphisms.

The work extends classical divisibility sequence theory to matrix algebra.

Abstract

In this paper we consider divisibility sequences obtained from square matrices. We work with of matrix divisibility sequences associated to a semigroup and arising from endomorphisms of an affine space. We prove that determinant divisibility sequences originated from powers of square matrices are generalized Lucas sequences.