Factorization of homotopies of nanophrases

Abstract

AbstractHomotopy on nanophrases is an equivalence relation defined using some data called a homotopy data triple. We define a product on homotopy data triples. We show that any homotopy data triple can be factorized into a product of prime homotopy data triples and this factorization is unique up to isomorphism and order. For any homotopy given by a composite homotopy data triple we define a complete invariant of nanophrases. This invariant is used to show that equivalence of nanophrases under such a homotopy can be calculated just by using the homotopies given by its prime factors.