Geodesic
About the minimal primitive matrices
Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 7-9

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A quadratic Boolean matrix $A$ is called a primitive matrix if some its degree does not contain 0's. A primitive matrix is called a minimal primitive matrix if it becomes non-primitive matrix after replacing any one 1 in it by 0. The height of a primitive matrix is defined as the least Hamming's distance between it and a minimal primitive matrix. In the paper, properties of minimal primitive matrices are studied. The amount of minimal primitive matrices of order $n$ is estimated. An algorithm for estimating the height of a primitive matrix is proposed.
Mots-clés : primitive matrix, antichain
Keywords: lattice, computational complexity of the algorithm. 
@article{PDMA_2014_7_a0,
     author = {R. I. Bar-Gnar and V. M. Fomichev},
     title = {About the minimal primitive matrices},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {7--9},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2014_7_a0/}
}
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R. I. Bar-Gnar; V. M. Fomichev. About the minimal primitive matrices. Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 7-9. http://geodesic.mathdoc.fr/item/PDMA_2014_7_a0/