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Abstract
A square real matrix Ais called convertible if there is a matrix  obtained from Aby affixing ± sings to entries of Aso that per A=detÂ. A convertible (0,1)-matrix with total support is called maximal convertible if it is fully indecomposable and no matrix obtained from Aby replacing a 0 with a 1 is convertible. In this paper, the existence of maximal convetible matrices with exactly r1's for each integer rwith 4n−4≤r≤(n 2+3 n −2)/2 is proved.