Linear Recurrences in the Degree Sequences of Monomial Mappings

TL;DR

This paper explores how the eigenvalues of an integer matrix influence the presence of linear recurrence relations in the degree sequences of associated monomial maps, revealing a fundamental link between algebraic properties and dynamical degrees.

Contribution

It establishes a novel connection between eigenvalues of matrices and linear recurrence relations in degree sequences of monomial mappings.

Findings

Eigenvalues determine the existence of linear recurrences in degree sequences.

The degree sequence's behavior is directly linked to the spectral properties of the matrix.

The results provide a new perspective on the algebraic dynamics of monomial maps.

Abstract

Let $A$ be an integer matrix, and let $f_A$ be the associated monomial map. We give a connection between the eigenvalues of $A$ and existence of a linear recurrence relation in the sequence of degrees.