Foundations of iterated star maps and their use in combinatorics

TL;DR

This paper develops a nonstandard analysis framework for iterated star maps, demonstrating its usefulness and flexibility in addressing problems in combinatorial number theory.

Contribution

It introduces a new nonstandard analysis framework for iterated star maps, providing foundational insights and applications in combinatorial number theory.

Findings

Framework enables new combinatorial number theory techniques

Examples illustrate the strength of nonstandard methods

Potential for broad applications in combinatorics

Abstract

We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to show the strength and flexibility of such a nonstandard technique for applications in combinatorial number theory.