Monoid factorisation

In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the subsets. The Chen–Fox–Lyndon theorem states that the Lyndon words furnish a factorisation. The Schützenberger theorem relates the definition in terms of a multiplicative property to an additive property. Let A* be the free monoid on an alphabet A. Let Xi be a sequence of subsets of A* indexed by a totally ordered index set I. A factorisation of a word w in A* is an expression

Monoid factorisation

In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the subsets. The Chen–Fox–Lyndon theorem states that the Lyndon words furnish a factorisation. The Schützenberger theorem relates the definition in terms of a multiplicative property to an additive property. Let A* be the free monoid on an alphabet A. Let Xi be a sequence of subsets of A* indexed by a totally ordered index set I. A factorisation of a word w in A* is an expression