<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Attila Kuba</style></author><author><style face="normal" font="default" size="100%">Maurice Nivat</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Reconstruction of discrete sets with absorption</style></title><secondary-title><style face="normal" font="default" size="100%">Linear Algebra and its Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2001</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.sciencedirect.com/science/article/B6V0R-44CHW26-C/2/e4cd2b3dc91dbb828db15e331a6230cc</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">339</style></volume><pages><style face="normal" font="default" size="100%">171-194</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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. &lt;tt&gt; &lt;/tt&gt;&lt;/p&gt;</style></abstract></record></records></xml>