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Séminaire Lotharingien de Combinatoire, 39d, 1997, 8 pages

# 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.

foata@math.u-strasbg.fr, guoniu@math.u-strasbg.fr

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