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RECONSTRUCTION OF BINARY RELATIONS FROM THEIR RESTRICTIONS OF CARDINALITY 2, 3, 4 and (n ‐ 1) II

Gérard Lopez, Claire Rauzy

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Abstract

Abstract We shall prove here that any binary relation on a base E with cardinality n > 6 is reconstructible from its restrictions of cardinality 2, 3, 4 and (n ‐ 1). This proof needs results of part I of this paper where we characterize any pair of relations R, R' which are 2‐, 3‐ and 4‐hypomorphic. As a corollary we obtain that any binary relation is (n ‐ 4)‐reconstructible (when n > 9).

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Abstract We shall prove here that any binary relation on a base E with cardinality n > 6 is reconstructible from its restrictions of cardinality 2, 3, 4 and (n ‐ 1). This proof needs results of part I of this paper where we characterize any pair of relations R, R' which are 2‐, 3‐ and 4‐hypomorphic. As a corollary we obtain that any binary relation is (n ‐ 4)‐reconstructible (when n > 9).

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Available abstract

Abstract We shall prove here that any binary relation on a base E with cardinality n > 6 is reconstructible from its restrictions of cardinality 2, 3, 4 and (n ‐ 1). This proof needs results of part I of this paper where we characterize any pair of relations R, R' which are 2‐, 3‐ and 4‐hypomorphic. As a corollary we obtain that any binary relation is (n ‐ 4)‐reconstructible (when n > 9).

Key concepts: Cardinality (data modeling), Mathematics, Corollary, Binary relation, Binary number, Relation (database), Combinatorics, Base (topology)

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