01052nas a2200133   4500008004100000245005200041210005200093300001200145490000800157520061700165100001700782700001900799856010000818       2001                        eng d00aReconstruction of discrete sets with absorption0 aReconstruction of discrete sets with absorption  a171-1940 v3393 a<p>The uniqueness problem is considered when binary matrices are to be reconstructed from their absorbed row and column sums. Let the absorption coefficient n be selected such that en = (1+5^0.5)/2. Then it is proved that if a binary matrix is non-uniquely determined, then it contains a special pattern of 0s and 1s called composition of alternatively corner-connected components. In a previous paper [Discrete Appl. Math. (submitted)] we proved that this condition is also sufficient, i.e., the existence of such a pattern in the binary matrix is necessary and sufficient for its non-uniqueness. <tt> </tt></p>1 aKuba, Attila1 aNivat, Maurice  uhttp://www.sciencedirect.com/science/article/B6V0R-44CHW26-C/2/e4cd2b3dc91dbb828db15e331a6230cc