Generalized Chacon polynomial constructions

TL;DR

This paper generalizes Chacon's classical automorphism, providing a new family of polynomials with recurrence relations, and investigates its key properties such as palindromic structure and degree sequence.

Contribution

It introduces a generalized construction of Chacon automorphisms and derives their polynomial representations, extending understanding of their algebraic properties.

Findings

Polynomial family with recurrence relations

Palindromic property of the polynomials

Sequence of degrees characterized

Abstract

We define a generalization of Chacon's classical automorphism and answer the question of whether its important properties remain. We calculate the family of polynimials representing the automorphism, given in recurrence formulae, and infer its basic characterictics, namely the palindromic property and the sequence of degrees.