Reconstruction of discrete sets with absorption (Q5955131)

The uniqueness problem is considered when binary matrices are to be reconstructed from their absorbed row and column sums, with an absorption coefficient \(\mu\). It is shown that if \(\beta:= \overline e^\mu\) is \((1+\sqrt{5})/2\), and if the reconstructed matrix is not unique, then the original binary matrix necessarity contains certains configuration of \(0\)'s and \(1\)'s, namely, the composition of alternatively corner connected components.NEWLINENEWLINENEWLINEThe procedure adopted in the paper also shows that the result holds certain other values of \(\beta\), provided it satisfies certain specific relation.