Reconstruction of discrete sets with absorption

The uniqueness problem is considered when binary matrices are to be reconst ructed from their absorbed row and column sums. Let the absorption coeffici ent A be selected such that e(mu) = (1 + root5)/2. Then it is proved that i f a binary matrix is non-uniquely determined, then it contains a special pa ttern of 0s and 1s called composition of alternatively corner-connected com ponents. In a previous paper [Discrete Appl. Math. (submitted)] we proved t hat this condition is also sufficient, i.e., the existence of such a patter n in the binary matrix is necessary and sufficient for its non-uniqueness. (C) 2001 Elsevier Science Inc. All rights reserved.