The duality between the anti-exchange closure operators and the path independent choice operators on a finite
set
Résumé.
Ce papier montre que la correspondance entre les fermetures anti-échanges et les fonctions de choix
chemin-indépendantes, découverte par Koshevoy (1999) et Johnson et Dean (1998), est en faite une
dualité entre deux demi-treillis. Cette dualité permet d'obtenir tous les (et notamment de
nouveaux) résultats sur les fermetures anti-échanges (et inversement).
Abstract.
In this paper, we show that the correspondence discovered by Koshevoy (1999) and, Johnson and Dean (1998) between
anti-exchange closure operators and path independent choice operators is a duality between two semilattices of
such operators. Then we use this duality to obtain old and new results concerning the "ordinal" representations
of choice functions from the theory of anti-exchange closure operators.
AMS Classification :
90A08, 06D00.
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