Matrices of 0's and 1's with restricted permanental minors (Q1185076)

Let \(A=(a_{ij})\) be a \(n\times n\) matrix of zeros and/or ones. \(M(A)\) denotes the set of permanental minor values of \(A\). If \(i\) and \(j\) are integers such that \(a_{ij}=1\) where row \(i\) and column \(j\) each contain exactly two ones \((a_{rj}=a_{is}=1\) where \(r\neq i\) and \(s\neq j\)) and \(a_{rs}=0\), \(A\) is said to contractable by the one in position \((i,j)\). For any integer \(c>1\), all matrices \(A\), up to contractions, are determined so that \(M(A)\subseteq\{1,c\}\) and likewise so that \(M(A)\subseteq\{2,4\}\). It is shown that no \(A\) exists so that \(M(A)\subseteq\{4,5\}\). Several interesting problems are proposed.