Geodesic
On Boolean matrices with full factor rank
Sbornik. Mathematics, Tome 204 (2013) no. 11, pp. 1691-1699

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It is demonstrated that every $(0,1)$-matrix of size $n\times m$ having Boolean rank $n$ contains a column with at least $\sqrt{n}/2-1$ zero entries. This bound is shown to be asymptotically optimal. As a corollary, it is established that the size of a full-rank Boolean matrix is bounded from above by a function of its tropical and determinantal ranks. Bibliography: 16 titles.
Keywords: Boolean rank, isolation number.
Mots-clés : $(0,1)$-matrices 
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     author = {Ya. N. Shitov},
     title = {On {Boolean} matrices with full factor rank},
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Ya. N. Shitov. On Boolean matrices with full factor rank. Sbornik. Mathematics, Tome 204 (2013) no. 11, pp. 1691-1699. http://geodesic.mathdoc.fr/item/SM_2013_204_11_a7/