
TL;DR
This paper characterizes all commuting upper triangular binary morphisms, which are morphisms with an upper triangular matrix structure, from the free monoid into itself.
Contribution
It provides a complete characterization of all pairs of upper triangular binary morphisms that commute.
Findings
Identifies conditions under which two upper triangular binary morphisms commute.
Provides a classification of all such morphisms based on their matrix structure.
Abstract
A morphism from the free monoid into itself is called upper triangular if the matrix of is upper triangular. We characterize all upper triangular binary morphisms and such that .
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