On a characterization of symmetric balanced incomplete block designs

• Autorzy: R.N. Mohan , Sanpei Kageyama , M.M. Nair
• Języki publikacji: EN

Abstrakty

EN

All the symmetric balanced incomplete block (SBIB) designs have been characterized and a new generalized expression on parameters of SBIB designs has been obtained. The parameter b has been formulated in a different way which is denoted by bi, i = 1, 2, 3, associating with the types of the SBIB design Di. The parameters of all the designs obtained through this representation have been tabulated while corresponding them with the suitable formulae for the number ofblocks bi and the expression Si for the convenience of practical users for constructional methods of certain designs, which is the main theme of this paper.

Słowa kluczowe

EN

symmetric balanced incomplete block (SBIB) design

Kategorie tematyczne

• 05B05: Block designs

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2004
• Tom: 24
• Numer: 1
• Strony: 41-58

Daty

wydano

2004

otrzymano

2003-09-15

Twórcy

autor

R.N. Mohan

• P.G. Department of Mathematics, Sir C.R.R. College, Eluru-534007, India

autor

Sanpei Kageyama

• Hiroshima University, Higashi-Hiroshima 739-8524, Japan

autor

M.M. Nair

• Sarathi Institute of Engineering and Technology, Nuzvid-521201, India

Bibliografia

• [1] S. Chowla and H.J. Ryser, Combinatorial problems, Can. J. Math. 2 (1950), 93-99.
• [2] R.J. Collins, Constructing BIB designs with computer, Ars Combin. 2 (1976), 285-303.
• [3] J.D. Fanning, A family of symmetric designs, Discrete Math. 146 (1995), 307-312.
• [4] Q.M. Hussain, Symmetrical incomplete block designs with l = 2,k = 8 or 9, Bull. Calcutta Math. Soc. 37 (1945), 115-123.
• [5] Y.J. Ionin, A technique for constructing symmetric designs, Designs, Codes and Cryptography 14 (1998), 147-158.
• [6] Y.J. Ionin, Building symmetric designs with building sets, Designs, Codes and Cryptography 17 (1999), 159-175.
• [7] S. Kageyama, Note on Takeuchi's table of difference sets generating balanced incomplete block designs, Int. Stat. Rev. 40, (1972), 275-276.
• [8] S. Kageyama and R.N. Mohan, On m-resolvable BIB designs, Discrete Math. 45 (1983), 113-121.
• [9] R. Mathon and A. Rosa, 2-(v, k, l) designs of small order, The CRC Handbook of Combinatorial Designs (ed. Colbourn, C. J. and Dinitz, J. H.). CRC Press, New York, (1996), 3-41.
• [10] R.N. Mohan, A note on the construction of certain BIB designs, Discrete Math. 29 (1980), 209-211.
• [11] R.N. Mohan, On an Mn-matrix, Informes de Matematica (IMPA-Preprint), Series B-104, Junho/96, Instituto de Matematica Pura E Aplicada, Rio de Janeiro, Brazil 1996.
• [12] R.N. Mohan, A new series of affine m-resolvable (d+1)-associate class PBIB designs, Indian J. Pure and Appl. Math. 30 (1999), 106-111.
• [13] D. Raghavarao, Constructions and Combinatorial Problems in Design of Experiments, Wiley, New York 1971.
• [14] S.S. Shrikhande, The impossibility of certain symmetrical balanced incomplete designs, Ann. Math. Statist. 21 (1950), 106-111.
• [15] S.S. Shrikhande and N.K. Singh, On a method of constructing symmetrical balanced incomplete block designs, Sankhy¯a A24 (1962), 25-32.
• [16] S.S. Shrikhande and D. Raghavarao, A method of construction of incomplete block designs, Sankhy¯a A25 (1963), 399-402.
• [17] G. Szekers, A new class of symmetrical block designs, J. Combin. Theory 6 (1969), 219-221.
• [18] K. Takeuchi, A table of difference sets generating balanced incomplete block designs, Rev. Inst. Internat. Statist. 30 (1962), 361-366.
• [19] N.H. Zaidi, Symmetrical balanced incomplete block designs with l = 2 and k = 9, Bull. Calcutta Math. Soc. 55 (1963), 163-167.

Identyfikatory

DOI

10.7151/dmps.1045