Geodesic
About primitive systems of natural numbers
Prikladnaâ diskretnaâ matematika, no. 2 (2012), pp. 5-14

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The set structure of primitive systems of natural numbers is described, and the main properties of such systems are installed. An algorithm for enumerating primitive systems of numbers not exceeding a given number $m$ is constructed using the concepts of deadlockness and $k$-minimalities of primitive systems. Also, some algorithms are offered for determining the primitiveness index of a finite directed graph by means of depth-first search and the exponentiation of the vertex adjacency matrix. Computational complexity of the algorithms is estimated.
Keywords: primitive system of natural numbers, primitive graph, exponent
Mots-clés : primitive matrix, subexponent. 
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     author = {S. N. Kjazhin and V. M. Fomichev},
     title = {About primitive systems of natural numbers},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {5--14},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2012_2_a0/}
}
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S. N. Kjazhin; V. M. Fomichev. About primitive systems of natural numbers. Prikladnaâ diskretnaâ matematika, no. 2 (2012), pp. 5-14. http://geodesic.mathdoc.fr/item/PDM_2012_2_a0/