# Characteristic Parameters and Special Trapezoidal Words

## TL;DR

This paper investigates the properties of trapezoidal words, focusing on their characteristic parameters and classifications, including their prefixes, symmetry, and special types, extending previous work on Sturmian words.

## Contribution

It provides new characterizations of right special and strictly bispecial trapezoidal words, expanding understanding of their structure and parameters.

## Key findings

- Characterization of right special trapezoidal words
- Identification of strictly bispecial trapezoidal words
- Analysis of prefixes' symmetry and periodicity

## Abstract

Following earlier work by Aldo de Luca and others, we study trapezoidal words and their prefixes, with respect to their characteristic parameters $K$ and $R$ (length of shortest unrepeated suffix, and shortest length without right special factors, respectively), as well as their symmetric versions $H$ and $L$. We consider the distinction between closed (i.e., periodic-like) and open prefixes, and between Sturmian and non-Sturmian ones. Our main results characterize right special and strictly bispecial trapezoidal words, as done by de Luca and Mignosi for Sturmian words.