Normalization of ternary generalized pseudostandard words

TL;DR

This paper introduces an algorithm for normalizing directive bi-sequences over a ternary alphabet in generalized pseudostandard words, extending previous binary alphabet methods, with implementation and testing in Python.

Contribution

It presents the first algorithm for normalizing ternary directive bi-sequences in generalized pseudostandard words, with a publicly available Python implementation.

Findings

Algorithm successfully normalizes ternary directive bi-sequences.

Implementation is tested and publicly available.

Extends binary normalization methods to ternary alphabet.

Abstract

This paper focuses on generalized pseudostandard words, defined by de Luca and De Luca in 2006. In every step of the construction, the involutory antimorphism to be applied for the pseudopalindromic closure changes and is given by a so called directive bi-sequence. The concept of a normalized form of directive bi-sequences was introduced by Blondin-Mass\'e et al. in 2013 and an algorithm for finding the normalized directive bi-sequence over a binary alphabet was provided. In this paper, we present an algorithm to find the normalized form of any directive bi-sequence over a ternary alphabet. Moreover, the algorithm was implemented in Python language and carefully tested, and is now publicly available in a module for working with ternary generalized pseudostandard words.