Abstract
The problem of arranging object so that cetain criteria are fulfilled is of great generality in combinatorial analysis. Such an arrangement is known as an incidence system or tactical configuration. A special type of incidence system is balanced incomplete block design(BIBD). The dual of a design is defined as a new design whose treatments and blocks are correspondance with blocks and treatments of the original design, and incidence is preserved. Purpose of this study is to work on geometrical structure of some dual designs. These dual designs are members of class of the incomplete block design.
References
- BAYRAK, H. ve GÖNEN, S. (1998), Sanal Deney Düzeninde Dualite, İstatistik Konferansı, Gazi Üniv., ss 245-250.
- BAYRAK, H. ve GÖNEN, S. (2002), The Geometrical Structures of Some Dual Designs, İstatistik Günleri 2002 Sempozyumu, Hacettepe Üniversitesi.
- BOSE, R. C. (1963), Strongly Regular Graphs, Partial Geometries and Partially Balanced Designs, Pacific, J. of Maths., 13, pp 389-419.
- DRAKE, A. D. (1979), Partial Λ-Geometries and Generalized Hadamard Matrices Over Groups, Can. J. Math., Vol. 31, No:3, pp 617-627.
- HANANI, H. (1974), on Transversal Designs, Proceedings of the Advanced Study Institute on Combinatorics Breukelen, Math. Centre Tract 55, Amsterdam, pp 42-52.
- MAVRON, V. C. (2000), Frequency Squares and Affine Designs, the Electronic Journal of Combinatorics 7, R56, pp 1-6.
- RAGHAVARAO, D. (1971), Constructions and Combinatorial Problems in Design,of Experiments, Döver Publications, Inc., New York.
- STREET, A.P. and STREET, D. J. (1987), Combinatorics of Experimental Design, Oxford Univ. Press.
- SHRIKHANDE, S. S. (1952), on the Dual of Some Balanced Incomplete Block Designs, Biometrics, 8, pp 66-72.
- SHRIKHANDE, S. S. and BAHAGWANDAS, (1956), Dual of Incomplete Block Designs J. Indian Stat. Assn., 3, pp 30-37.
Abstract
Nesnelerin belirli kriterler altında düzenlenmesi problemi kombinatöriyel analizde önemli bir yer tutar. Böyle bir düzenleme isabet yapısı yada konfigürasyon olarak bilinir. İsabet yapılarının özel bir tipi tamamlanmamış blok düzenleridir. Bir düzenin duali işlemleri ve blokları sırasıyla orijinal düzenin bloklarına ve işlemlerine karşılık gelen yeni bir düzendir. Bu çalışmanın amacı bazı dual düzenlerin geometrik yapılarını incelemektedir. Bu dual düzenler tamamlanmamış blok düzenler sınıfındadır.
References
- BAYRAK, H. ve GÖNEN, S. (1998), Sanal Deney Düzeninde Dualite, İstatistik Konferansı, Gazi Üniv., ss 245-250.
- BAYRAK, H. ve GÖNEN, S. (2002), The Geometrical Structures of Some Dual Designs, İstatistik Günleri 2002 Sempozyumu, Hacettepe Üniversitesi.
- BOSE, R. C. (1963), Strongly Regular Graphs, Partial Geometries and Partially Balanced Designs, Pacific, J. of Maths., 13, pp 389-419.
- DRAKE, A. D. (1979), Partial Λ-Geometries and Generalized Hadamard Matrices Over Groups, Can. J. Math., Vol. 31, No:3, pp 617-627.
- HANANI, H. (1974), on Transversal Designs, Proceedings of the Advanced Study Institute on Combinatorics Breukelen, Math. Centre Tract 55, Amsterdam, pp 42-52.
- MAVRON, V. C. (2000), Frequency Squares and Affine Designs, the Electronic Journal of Combinatorics 7, R56, pp 1-6.
- RAGHAVARAO, D. (1971), Constructions and Combinatorial Problems in Design,of Experiments, Döver Publications, Inc., New York.
- STREET, A.P. and STREET, D. J. (1987), Combinatorics of Experimental Design, Oxford Univ. Press.
- SHRIKHANDE, S. S. (1952), on the Dual of Some Balanced Incomplete Block Designs, Biometrics, 8, pp 66-72.
- SHRIKHANDE, S. S. and BAHAGWANDAS, (1956), Dual of Incomplete Block Designs J. Indian Stat. Assn., 3, pp 30-37.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Statistics |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | April 15, 2003 |
| Published in Issue | Year 2003 Volume: 2 Issue: 1 |
