The minimal non-image-reconstructible relations Original Research Article

Given a finite set E, a relation with base image is a mapping image such that for all image. The restriction of R to a subset X of E is R considered as a mapping from image into image. Given an integer image and a relation R with base E, we call image-reconstruction of R every relation with the same base, any restriction of which to a subset X of E with up to k elements is isomorphic to the restriction of R to X. The relation R is image-reconstructible when each image-reconstruction of R is isomorphic to R. In this work, the structure of the non-image-reconstructible relations is studied for all image. This study leads to an introduction of the minimal non-image-reconstructible relations and to characterization of the class of such relations for all image. This class includes in particular the class of the indecomposable non-image-reconstructible relations.