Application d'une propri�t� combinatoire des parties d'un ensemble aux groupes et aux relations

Pouzet, Maurice

doi:10.1007/bf01215230

Cited by 81 publications

(53 citation statements)

References 7 publications

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“…Several other authors, including Cameron [4], Mnukhin [13], and Pouzet [14] have looked at such reconstruction problems. Indeed, from one point of view every reconstruction problem concerns the action of a group on the collection of combinatorial objects being reconstructed, and on their subobjects.…”

Section: The Approach For General Nmentioning

confidence: 99%

Reconstructing Subsets of Zn

Radcliffe

Scott

1998

Journal of Combinatorial Theory, Series A

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Section: The Approach For General Nmentioning

confidence: 99%

Reconstructing Subsets of Zn

Radcliffe

Scott

1998

Journal of Combinatorial Theory, Series A

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“…Lemma 2 [9]. Let P and P$ be posets, if P and P$ are [q]-hypomorphic, where 1 q |V(P)| &1, then for p=1, ..., min(q, |V(P)| &q), P and P$ are [ p]-hypomorphic.…”

Section: Preliminariesmentioning

confidence: 97%

Reconstruction of Posets with the Same Comparability Graph

Ille¹,

Rampon²

1998

Journal of Combinatorial Theory, Series B

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“…Rosenberg a alors demandé si toutes les relations binaires finies, non (≤5)-reconstructibles,étaient obtenues par le même procédé? Voici nos résultats (pour les définitions, voir Section 2): THÉORÈME Dans [9], Lopez aétendu son résultat [8], au cas des multirelationsà composantes binaires, répondant ainsià une question de Pouzet [11]. Suiteà ce dernier résultat, nousétendons, dans la Section 4, le Corollaire 2 aux multirelations: THÉORÈME 3.…”

Section: X Yéléments Distincts De E R(x X) = R(y Y) Et R(x Y) = unclassified

La 5-reconstructibilité et L’indécomposabilité Des Relations Binaires

Boudabbous¹

2002

European Journal of Combinatorics

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A binary relation is (≤k)-reconstructible, if it is determined up to isomorphism by its restriction to subsets of at most k elements. In [8], Lopez has shown that finite binary relations are (≤6)-reconstructible. To prove that the value 6 of its result, is optimal, Lopez [3], associates to all finite binary relation, an infinity of finite extensions, that are not (≤5)-reconstructible. These extensions are obtained from the relations given, by creation of intervals. Rosenberg has then asked if all finite binary relations, not (≤5)-reconstructible, were obtained by the same process. In this paper, we give an affirmative answer to the question, by characterizing finite binary relations that are not (≤5)-reconstructible. We deduce the 5-reconstructibility of finite indecomposable binary relations, of at least 9 elements. We extend then this last result to the binary multirelations.

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Application d'une propri�t� combinatoire des parties d'un ensemble aux groupes et aux relations

Cited by 81 publications

References 7 publications

Reconstructing Subsets of Zn

Reconstructing Subsets of Zn

Reconstruction of Posets with the Same Comparability Graph

La 5-reconstructibilité et L’indécomposabilité Des Relations Binaires

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