Geodesic
Group Partition, Factorization and the Vector Covering Problem
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 207-214

Voir la notice de l'article provenant de la source Cambridge University Press

The covering problem. Let S i(i = 1, 2,...,n) be given sets containing mi elements respectively and let 1 be their cartesian product. The elements of S (n) will be called vectors. The vector (x1 x2,..., xn) covers (y1 y2,..., yn) if xi =yi for at least n—1 values of i. A subset M of S (n) is said to be a covering (perfect covering) of S (n) if each member of S (n) is covered by at least (exactly) one member of M. A covering M is said to be linear if the sets Si are groups Gi and M is a subgroup of G (n) = S (n) Denote by σ(n; m1 m2,..., mn) the value of min |M| when M runs through all coverings of S(n) and by σ(n; m1 m2,..., mn) the value of min |M| when the sets Si are given groups Gi and M runs through all linear coverings of G (n). 
Herzog, M.; Schönheim, J. Group Partition, Factorization and the Vector Covering Problem. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 207-214. doi: 10.4153/CMB-1972-038-x
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