Séminaire Lotharingien de Combinatoire, B22l (1989), 4 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1990, 414/S-22, p. 133-136.]

Giuseppe Pirillo

Su alcune recenti generalizzazioni del teorema di Shirshov

Abstract. A well-known theorem of Shirshov says that every sufficiently long word in a finite alphabet contains either a factor which is 'n-divided' or a factor which is a pth power.

Using the properties of Lyndon words, Reutenauer presented a very elegant proof of this theorem, which, by analogous techniques, Varricchio extended to words that are infinite on the right.

The aim of this work is to give a brief outline of an extension of the theorem of Shirshov to bi-infinite words.


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