Induced orders in free monoids of words

TL;DR

This paper introduces a family of partial orders in free monoids of words, extending previous concepts like chronological and morphological orders, and demonstrates their natural behavior under alphabet homomorphisms.

Contribution

It generalizes existing orders in free monoids to broader classes induced from alphabet partial orders, providing a unified framework.

Findings

Induced orders extend chronological and morphological orders.

The orders are compatible with alphabet homomorphisms.

The framework unifies various partial orders in word monoids.

Abstract

A family of partial orders in the free monoid of words, induced from a partial order in alphabet, is presented. The induced orders generalize the chronological posets that have been defined for the two-letter alphabet only, and the morphological order. We show that the induced orders are natural with respect to alphabet homomorphisms.