On the permutation capacity of digraphs

TL;DR

This paper extends the concept of permutation capacity from finite to infinite directed graphs, exploring combinatorial properties and posing new open problems in the intersection of graph theory and information theory.

Contribution

It generalizes permutation capacity to infinite digraphs and introduces new open problems, expanding the theoretical framework of graph-different permutations.

Findings

Extended permutation capacity results to infinite digraphs

Connected permutation capacity with zero-error information theory

Posed new open problems in the field

Abstract

We extend several results of the third author and C. Malvenuto on graph-different permutations to the case of directed graphs and introduce new open problems. Permutation capacity is a natural extension of Sperner capacity from finite directed graphs to infinite digraphs. Our subject is combinatorial in nature, but can be equally regarded as zero-error information theory.