Geodesic
Maximum rank of a power of a matrix of a given pattern
Commentationes Mathematicae Universitatis Carolinae, Tome 29 (1988) no. 1, p. 195
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Classification : 05C20, 05C38, 15A03 
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Poljak, Svatopluk. Maximum rank of a power of a matrix of a given pattern. Commentationes Mathematicae Universitatis Carolinae, Tome 29 (1988) no. 1, p. 195. http://geodesic.mathdoc.fr/item/CMUC_1988_29_1_a17/