# Divergent permutations

## TL;DR

This paper proves the existence of infinitely many pairwise divergent permutations of natural numbers and explores their relation to permutation capacity in infinite graphs.

## Contribution

It establishes the existence of infinitely many pairwise divergent permutations and connects this to broader questions in infinite graph theory.

## Key findings

- Existence of infinitely many pairwise divergent permutations.
- Relation between divergent permutations and infinite graph capacity.
- Foundational results for permutation theory in infinite sets.

## Abstract

Two permutations of the natural numbers diverge if the absolute value of the difference of their elements in the same position goes to infinity. We show that there exists an infinite number of pairwise divergent permutations of the naturals. We relate this result to more general questions about the permutation capacity of infinite graphs.