Séminaire Lotharingien de Combinatoire, B39d (1997), 8pp.

Dominique Foata and Guo-Niu Han

Inverses of Words

Abstract. The inverse of a permutation is one of the basic operations in the symmetric group. In this paper we propose an extension of this operation to words (with repetitions) by constructing an explicit one-to-one transformation on words. We also show that there exists another transformation having one more property that would be the definitive bijection for deriving the inverse of a word. The open problem is to imagine its construction.

Received: January 30, 1998; Accepted: February 13, 1998.

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Correction

The only change brought to the old version is the correction of the data in the example at the end of section 3. Only one sentence was modified. The correction was made by Alex Burnstein (Philadelphia) on May 4, 1998.