Palindromic Saturation

TL;DR

This paper proves that two different definitions of infinite words with the maximum number of palindromes are equivalent, using properties of return words and graph theory, confirming a previous result.

Contribution

It establishes the equivalence of two definitions of palindromic saturation in infinite words, providing a new proof of a known result.

Findings

The two definitions of palindromic saturation coincide.

A new proof of the equivalence using return words and graph theory.

Confirmation of the result announced in prior work.

Abstract

We consider two {seemingly} different definitions of infinite words which contain {the} utmost number of palindromes. We show that these two definitions coincide. {The keynote of the proof is a meticulous inspection of properties of complete return words and the application of some basic graph theory.} In fact, we provide another proof of the result announced in \cite{Zamboni}.