Arithmetic progressions and its applications to $(m,q)$-isometries: a survey

TL;DR

This survey explores higher-order arithmetic progressions and their applications to $(m,q)$-isometries, providing a comprehensive overview of polynomial sequences and their role in this mathematical context.

Contribution

It compiles and discusses key results on polynomial sequences and introduces their applications to $(m,q)$-isometric maps, highlighting recent developments.

Findings

Summarizes properties of higher-order arithmetic progressions

Connects polynomial sequences to $(m,q)$-isometries

Provides a comprehensive overview of related results

Abstract

In this paper we collect some results about arithmetic progressions of higher order, also called polynomial sequences. Those results are applied to $(m,q)$-isometric maps.