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

DOI

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
@article{10_4153_CMB_1972_038_x,
     author = {Herzog, M. and Sch\"onheim, J.},
     title = {Group {Partition,} {Factorization} and the {Vector} {Covering} {Problem}},
     journal = {Canadian mathematical bulletin},
     pages = {207--214},
     year = {1972},
     volume = {15},
     number = {2},
     doi = {10.4153/CMB-1972-038-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-038-x/}
}
TY  - JOUR
AU  - Herzog, M.
AU  - Schönheim, J.
TI  - Group Partition, Factorization and the Vector Covering Problem
JO  - Canadian mathematical bulletin
PY  - 1972
SP  - 207
EP  - 214
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-038-x/
DO  - 10.4153/CMB-1972-038-x
ID  - 10_4153_CMB_1972_038_x
ER  - 
%0 Journal Article
%A Herzog, M.
%A Schönheim, J.
%T Group Partition, Factorization and the Vector Covering Problem
%J Canadian mathematical bulletin
%D 1972
%P 207-214
%V 15
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-038-x/
%R 10.4153/CMB-1972-038-x
%F 10_4153_CMB_1972_038_x

Cité par Sources :