CDMTCS Research Report Series Generalisations of Disjunctive Sequences

The present paper proposes a generalisation of the notion of disjunctive (or rich) sequence, that is, of an infinite sequence of letters having each finite sequence as a subword. Our aim is to give a reasonable notion of disjunc-tiveness relative to a given set of sequences F. We show that a definition like " every subword which occurs at infinitely many different positions in sequences in F has to occur infinitely often in the sequence " fulfils properties similar to the original unrelativised notion of disjunctiveness. Finally, we investigate our concept of generalised disjunctiveness in spaces of Cantor expansions of reals.