A Symmetry Property of Christoffel Words

TL;DR

This paper introduces a new symmetry property for Christoffel words, inspired by trapezoidal words, and demonstrates that this symmetry uniquely characterizes Christoffel words, enriching their theoretical understanding.

Contribution

The paper presents a novel bivariate symmetry property that characterizes Christoffel words, expanding the theoretical framework of combinatorics on words.

Findings

Symmetry property characterizes Christoffel words

Establishment of a bivariate symmetry variant

Connections to trapezoidal words

Abstract

Motivated by the theory of trapezoidal words, whose sequences of cardinality of factors by length are symmetric, we introduce a bivariate variant of this symmetry. We show that this symmetry characterizes Christoffel words, and establish other related results.