Geodesic
Asymptotics of the number of $t$-minimal coverings of a~set
Diskretnaya Matematika, Tome 5 (1993) no. 1, pp. 36-44.

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The concept of a $t$-minimal covering of a set is introduced; exact and asymptotic formulae for the number of such coverings are obtained. 
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     author = {V. N. Sachkov},
     title = {Asymptotics of the number of $t$-minimal coverings of a~set},
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V. N. Sachkov. Asymptotics of the number of $t$-minimal coverings of a~set. Diskretnaya Matematika, Tome 5 (1993) no. 1, pp. 36-44. http://geodesic.mathdoc.fr/item/DM_1993_5_1_a1/