On the Combinatorics of Palindromes and Antipalindromes

TL;DR

This paper explores the combinatorial properties and enumeration of palindromes and antipalindromes, including their conjugates, pairs, and rich words, providing new insights into their structural characteristics.

Contribution

It introduces new results on the structure and enumeration of palindromes and antipalindromes, extending existing combinatorial frameworks.

Findings

Characterization of conjugates of palindromes

Enumeration formulas for palindromic pairs

Structural analysis of rich words and antipalindromes

Abstract

We prove a number of results on the structure and enumeration of palindromes and antipalindromes. In particular, we study conjugates of palindromes, palindromic pairs, rich words, and the counterparts of these notions for antipalindromes.