Geodesic
Inverses of Words
Séminaire lotharingien de combinatoire, Tome 39 (1997) 
Dominique Foata; Guo-Niu Han. Inverses of Words. Séminaire lotharingien de combinatoire, Tome 39 (1997). http://geodesic.mathdoc.fr/item/SLC_1997_39_a3/
@article{SLC_1997_39_a3,
     author = {Dominique Foata and Guo-Niu Han},
     title = {Inverses of {Words}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {1997},
     volume = {39},
     url = {http://geodesic.mathdoc.fr/item/SLC_1997_39_a3/}
}
TY  - JOUR
AU  - Dominique Foata
AU  - Guo-Niu Han
TI  - Inverses of Words
JO  - Séminaire lotharingien de combinatoire
PY  - 1997
VL  - 39
UR  - http://geodesic.mathdoc.fr/item/SLC_1997_39_a3/
ID  - SLC_1997_39_a3
ER  - 
%0 Journal Article
%A Dominique Foata
%A Guo-Niu Han
%T Inverses of Words
%J Séminaire lotharingien de combinatoire
%D 1997
%V 39
%U http://geodesic.mathdoc.fr/item/SLC_1997_39_a3/
%F SLC_1997_39_a3

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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.

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.