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(≤k)-reconstructible binary relations

Abstract : Abstract A relation R is ( ≤ k ) -reconstructible ( k a positive integer) if it is isomorphic with any relation S on the same vertex set with the property that the relations induced by R and S on any set of at most k vertices are isomorphic; it is ( ≤ k ) -self dual if every restriction to at most k vertices is self dual, i.e.  isomorphic to its dual relation (the relation obtained by reversing its arcs). In particular, relying on the description of ( ≤ k ) -self dual binary relations, we characterize, for each k ≥ 4 , all ( ≤ k ) -reconstructible binary relations: A binary relation is ( ≤ k ) -reconstructible if and only if its modules that are chains are finite and its ( ≤ k ) -self dual modules are self dual.
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Contributor : Nicolas Alarcon <>
Submitted on : Monday, August 24, 2015 - 2:27:51 PM
Last modification on : Monday, September 2, 2019 - 9:42:16 AM




Youssef Boudabbous, Christian Delhommé. (≤k)-reconstructible binary relations. European Journal of Combinatorics, Elsevier, 2013, 37, pp.43 - 67. ⟨10.1016/j.ejc.2013.07.010⟩. ⟨hal-01186137⟩



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