Geodesic
On the Block Structure of Quartic Designs
Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 377-389

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

Raghavarao and Chandrasekhararao [3] introduced a family of PBIB designs having three associate classes known as cubic designs. In this paper a detailed analysis of the case of PBIB designs having four associate classes, which are called quartic designs, is given. Results are obtained pertaining to construction and existence of quartic designs. Moreover, using methods similar to those used by Shah [5], [6], [7], the block structure of certain quartic designs is studied. 
O'Shaughnessy, C. D. On the Block Structure of Quartic Designs. Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 377-389. doi: 10.4153/CMB-1971-068-3
@article{10_4153_CMB_1971_068_3,
     author = {O'Shaughnessy, C. D.},
     title = {On the {Block} {Structure} of {Quartic} {Designs}},
     journal = {Canadian mathematical bulletin},
     pages = {377--389},
     year = {1971},
     volume = {14},
     number = {3},
     doi = {10.4153/CMB-1971-068-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-068-3/}
}
TY  - JOUR
AU  - O'Shaughnessy, C. D.
TI  - On the Block Structure of Quartic Designs
JO  - Canadian mathematical bulletin
PY  - 1971
SP  - 377
EP  - 389
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-068-3/
DO  - 10.4153/CMB-1971-068-3
ID  - 10_4153_CMB_1971_068_3
ER  - 
%0 Journal Article
%A O'Shaughnessy, C. D.
%T On the Block Structure of Quartic Designs
%J Canadian mathematical bulletin
%D 1971
%P 377-389
%V 14
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-068-3/
%R 10.4153/CMB-1971-068-3
%F 10_4153_CMB_1971_068_3

[1] 1. Connor, W. S. and Clatworthy, W. H., Some theorems for partially balanced designs, Ann. Math. Statist. 25 (1954), 100-112. Google Scholar

[2] 2. Ogawa, Junjiro, A necessary condition for the existence of regular and symmetrical experimental designs of triangular type, with partially balanced incomplete blocks, Ann. Math. Statist. 30 (1959), 1063-1071. Google Scholar

[3] 3. Raghavarao, D. and Chandrasekhararao, K., Cubic designs, Ann. Math. Statist. 35 (1964), 389-397. Google Scholar

[4] 4. Shah, B. V., A generalization of partially balanced incomplete block designs, Ann. Math. Statist. 30 (1959), 1041-1050. Google Scholar

[5] 5. Shah, S. M., An upper bound for the number of disjoint blocks in certain PBIB designs, Ann. Math. Statist. 35 (1964), 398-407. Google Scholar

6.Shah, S. M., Bounds for the number of common treatments between any two blocks of certain PBIB designs, Ann. Math. Statist. 36 (1965), 337-342. Google Scholar

[7] 7. Shah, S. M., On the block structure of certain partially balanced incomplete block designs, Ann. Math. Statist. 37 (1966), 1016-1020. Google Scholar

[8] 8. Shrikhande, S. S. and Jain, N. C., The non-existence of some partially balanced incomplete block designs with Latin square type association scheme, Sankhyā Ser. A, 24 (1966), 259-268. Google Scholar

[9] 9. Shrikhande, S. S., Raghavarao, D., and Tharthare, S. K., Non-existence of some unsymmetrical partially balanced incomplete block designs, Canad. J. Math. 15 (1963), 686-701. Google Scholar

Cité par Sources :