UNAVOIDABLE AND ALMOST UNAVOIDABLE SETS OF WORDS

Communicated by D. Perrin A set of words over a finite alphabet is called an unavoidable set if every word of sufficiently long length must contain some word from this set as a subword. Motivated by a theorem from automata theory, we introduce the notion of an almost unavoidable set and prove certain asymptotic estimates for the size of almost unavoidable sets of uniform length