zbMATH — the first resource for mathematics

Families of proper generalized neighbor designs. (English) Zbl 1110.62096
Summary: A generalized neighbor design relaxes the equality condition on the number of times two treatments occur as neighbors in the design. In this article we have constructed a new series of generalized neighbor designs with equal block sizes, a series of neighbor designs of D. H. Rees [Some designs of use in serology. Biometrics 23, 779–791 (1967)] and a series of neighbor designs with two distinct block sizes. Two more new series of $$GN_{2}$$ designs are also constructed for even number of treatments. It has been shown that quasi neighbor designs introduced by D. A. Preece [Balanced Ouchterlony neighbour designs and quasi-Rees neighbour designs. J. Comb. Math. Comb. Comput. 15, 197–219 (1994; Zbl 0806.05022)] are special cases of generalized neighbor designs with $$t=2$$. All the designs given here are binary. A new definition – partially balanced circuit design – is introduced which is a special case of generalized neighbor designs with binary blocks.

MSC:
 62K10 Statistical block designs 05B05 Combinatorial aspects of block designs
Full Text:
References:
 [1] Bailey, R.A.; Ollis, M.A.; Preece, D.A., Round dance neighbor designs from terraces, Discrete math., 266, 69-86, (2003) · Zbl 1025.05010 [2] Bermond, J.C.; Huang, C.; Sotteau, D., Balanced cycles and circuit designs: even cases, Ars combin., 5, 293-318, (1978) · Zbl 0434.05020 [3] Chaure, K.; Misra, B.L., On construction of generalized neighbor designs, Sankhya, 58, B, pt 2, 245-253, (1996) · Zbl 0874.62085 [4] Das, A.D.; Saha, G.M., On construction of neighbor designs, Calcutta statist. assoc. bull., 25, 151-164, (1976) · Zbl 0382.62062 [5] Hwang, F.K., Constructions for some classes of neighbor designs, Ann. statist., 1, 4, 786-790, (1973) · Zbl 0262.62038 [6] Hwang, F.K.; Lin, S., Neighbor designs, J. combin. theory A, 23, 302-313, (1977) · Zbl 0405.05017 [7] Kageyama, S., A note on designs in serology, J. Japan statist. soc., 9, 37-40, (1979) [8] Lawless, J.F., A note on certain types of BIBD’s balanced for residual effects, Ann. math. statist., 42, 1439-1441, (1971) · Zbl 0237.05006 [9] Misra, B.L.; Bhagwandas; Nutan, Families of neighbor designs and their analysis, Commun. statist. simul. comput., 20, 2 and 3, 427-436, (1991) · Zbl 0850.62613 [10] Preece, D.A., Balanced ouchterlony neighbor designs, J. combin. math. combin. comput., 15, 197-219, (1994) · Zbl 0806.05022 [11] Rees, D.H., Some designs of use in serology, Biometrics, 23, 779-791, (1967) [12] Rosa, A.; Huang, C., Another class of balanced graph designs: balanced circuit designs, Discrete math., 12, 269-293, (1975) · Zbl 0306.05013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.