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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.

The following versions are available:

**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.