COMBINATORIAL PROPERTIES OF UNIFORMLY RECURRENT WORDS AND AN APPLICATION TO SEMIGROUPS

Abstract

We prove some combinatorial properties of uniformly recurrent infinite words which can be expressed in terms of bi-ideal and n-divided sequences. A consequence of these results is an improvement of a theorem of Shirshov [13] and a new finiteness condition for finitely generated semigroups which generalizes both a theorem of Restivo and Reutenauer [12] and a theorem of de Luca and Restivo [4].