CARACTERISATION DES RELATIONS BINAIRES FINIES D-DEMI-RECONSTRUCTIBLES

DAMMAK, JAMEL

doi:10.4067/S0716-09172003000100003

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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.22 n.1 Antofagasta mayo 2003

http://dx.doi.org/10.4067/S0716-09172003000100003

Proyecciones
Vol. 22, N o 1, pp. 31-62, May 2003.
Universidad Católica del Norte
Antofagasta - Chile

CARACTERISATION DES RELATIONS
BINAIRES FINIES
D-DEMI-RECONSTRUCTIBLES

JAMEL DAMMAK
Université Claude Bernard Lyon 1, France

Abstract

Given a binary relation R of basis E, we define its dual R*by
R* (x, y) = R(y, x). A relation R is self-dual if it is isomorphic to R*.
A binary relation R' is hemimorphic to R, if it is isomorphic to R or
to R*. A binary relation R is d-half-reconstructible if it is determined
by its restrictions of cardinality d, up to hemimorphism. In this paper
we characterize the finite binary relations d-half-reconstructibile for
every d Îí7, 8, 9, 10, 11ý.

MSC : 03C60; 04A05; 05C20; 05C38; 05C40.

Key Words : Relation de différence, Relation binaire, Graphe, Hypomorphe,
Hémimorphe, Reconstruction.

References

[1] J. DAMMAK : La dualité dans la demi-reconstruction des relations binaires finies, CRAS, Série I 327 (1998), p. 861-864.

[2] R. FRAÏSSÉ : Lintervalle en théorie des relations, in orders, descriptions and roles, M. Pouzet et D. Richardéd. North-Holland, 1984, p. 313-342.

[3] C. GNANVO et P.ILLE : La reconstruction des tournois. C. R. Acad. Sci. Paris, t. 306, série I, (1988), p. 577-580.

[4] J. G. HAGENDORF et G. LOPEZ : La demi-reconstructibilité des relations binaires dau moins 13 éléments. C. R. Acad. Sci. Paris, série I, 317 (1993), P. 7-12.

[5] G. LOPEZ : Lindéformabilité des relations et multirelations binaires. Zeitschrift. Math. Logik Grundlagen Math. 24 (1978), p. 303-317.

[6] G. LOPEZ et C. RAUZY : Reconstruction of binary relations from their restrictions of cardinality 2,3,4 and (n-1), I. Zeitschr. f. Math. Logik und Grundlagen d. Math. Bd. 38, S. 27-37 (1992).

[7] G. LOPEZ et C. RAUZY : Reconstruction of binary relations from their restrictions of cardinality 2,3,4 and (n-1), II. Zeitschr. f. Math. Logik und Grundlagen d. Math. Bd 38, S. 157-168 (1992).

[8] M. POUZET : Application dune propriété combinatoire des parties dun ensemble aux groupes et aux relations. Math. Zeitschr. 150 (1976), p. 117-134.

Received : December 2002.

J. Dammak

Département de Mathématiques
Faculté des Sciences de Sfax
B.P. 802, 3018 Sfax
Tunisie
Fax 216 74 274437
e-mail : jdammak@yahoo.fr