Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  consider infinite words that arise as fixed points of primitive substitutions on a finite alphabet and finite colorings of their factors. Any such infinite word exhibits a “hierarchal structure” that will allow us to define, under the additional condition of strong recognizability  , certain remarkable finite colorings of its factors. In particular  generalize two combinatorial results by Justin and Pirillo concerning arbitrarily large monochromatic kk-pors occurring in infinite words; in view of a recent paper by de Luca, Pribavkina and Zamboni,  will give new examples of classes of infinite words uu and finite colorings that do not allow infinite monochromatic factorizations u=u1u2u3…u=u1u2u3….
['Andre Bernardino', 'Manuel Silva', 'Rui Pacheco']
I am writing a research paper on a idea Coloring Factors of Substitutive Infinite Words
[{"from": "human", "value": "I am writing a research paper on a idea Coloring Factors of Substitutive Infinite Words"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  consider infinite words that arise as fixed points of primitive substitutions on a finite alphabet and finite colorings of their factors. Any such infinite word exhibits a \u201chierarchal structure\u201d that will allow us to define, under the additional condition of strong recognizability \u00a0, certain remarkable finite colorings of its factors. In particular  generalize two combinatorial results by Justin and Pirillo concerning arbitrarily large monochromatic kk-pors occurring in infinite words; in view of a recent paper by de Luca, Pribavkina and Zamboni,  will give new examples of classes of infinite words uu and finite colorings that do not allow infinite monochromatic factorizations u=u1u2u3\u2026u=u1u2u3\u2026."}]