The minimal non-(⩽k)-reconstructible relations

In this work, the structure of the non-(⩽k)-reconstructible relations is studied for all k⩾1. This study leads to an introduction of the minimal non-(⩽k)-reconstructible relations and to characterization of the class of such relations for all k≠2. This class includes in particular the class of the indecomposable non-(⩽k)-reconstructible relations.