On a characterization of symmetric balanced incomplete block designs

R.N. Mohan; Sanpei Kageyama; M.M. Nair

Discussiones Mathematicae Probability and Statistics (2004)

  • Volume: 24, Issue: 1, page 41-58
  • ISSN: 1509-9423

Abstract

top
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.

How to cite

top

R.N. Mohan, Sanpei Kageyama, and M.M. Nair. "On a characterization of symmetric balanced incomplete block designs." Discussiones Mathematicae Probability and Statistics 24.1 (2004): 41-58. <http://eudml.org/doc/287752>.

@article{R2004,
abstract = {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.},
author = {R.N. Mohan, Sanpei Kageyama, M.M. Nair},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {symmetric balanced incomplete block (SBIB) design; symmetric balanced incomplete block design; affine -resolvable balanced incomplete block design},
language = {eng},
number = {1},
pages = {41-58},
title = {On a characterization of symmetric balanced incomplete block designs},
url = {http://eudml.org/doc/287752},
volume = {24},
year = {2004},
}

TY - JOUR
AU - R.N. Mohan
AU - Sanpei Kageyama
AU - M.M. Nair
TI - On a characterization of symmetric balanced incomplete block designs
JO - Discussiones Mathematicae Probability and Statistics
PY - 2004
VL - 24
IS - 1
SP - 41
EP - 58
AB - 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.
LA - eng
KW - symmetric balanced incomplete block (SBIB) design; symmetric balanced incomplete block design; affine -resolvable balanced incomplete block design
UR - http://eudml.org/doc/287752
ER -

References

top
  1. [1] S. Chowla and H.J. Ryser, Combinatorial problems, Can. J. Math. 2 (1950), 93-99. Zbl0037.00603
  2. [2] R.J. Collins, Constructing BIB designs with computer, Ars Combin. 2 (1976), 285-303. 
  3. [3] J.D. Fanning, A family of symmetric designs, Discrete Math. 146 (1995), 307-312. Zbl0838.05012
  4. [4] Q.M. Hussain, Symmetrical incomplete block designs with l = 2,k = 8 or 9, Bull. Calcutta Math. Soc. 37 (1945), 115-123. Zbl0060.31408
  5. [5] Y.J. Ionin, A technique for constructing symmetric designs, Designs, Codes and Cryptography 14 (1998), 147-158. Zbl0906.05006
  6. [6] Y.J. Ionin, Building symmetric designs with building sets, Designs, Codes and Cryptography 17 (1999), 159-175. Zbl0935.05008
  7. [7] S. Kageyama, Note on Takeuchi's table of difference sets generating balanced incomplete block designs, Int. Stat. Rev. 40, (1972), 275-276. Zbl0251.05017
  8. [8] S. Kageyama and R.N. Mohan, On m-resolvable BIB designs, Discrete Math. 45 (1983), 113-121. Zbl0512.05006
  9. [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. Zbl0845.05008
  10. [10] R.N. Mohan, A note on the construction of certain BIB designs, Discrete Math. 29 (1980), 209-211. Zbl0449.05005
  11. [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. [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. [13] D. Raghavarao, Constructions and Combinatorial Problems in Design of Experiments, Wiley, New York 1971. 
  14. [14] S.S. Shrikhande, The impossibility of certain symmetrical balanced incomplete designs, Ann. Math. Statist. 21 (1950), 106-111. Zbl0040.36203
  15. [15] S.S. Shrikhande and N.K. Singh, On a method of constructing symmetrical balanced incomplete block designs, Sankhy¯a A24 (1962), 25-32. Zbl0105.33601
  16. [16] S.S. Shrikhande and D. Raghavarao, A method of construction of incomplete block designs, Sankhy¯a A25 (1963), 399-402. Zbl0126.35601
  17. [17] G. Szekers, A new class of symmetrical block designs, J. Combin. Theory 6 (1969), 219-221. 
  18. [18] K. Takeuchi, A table of difference sets generating balanced incomplete block designs, Rev. Inst. Internat. Statist. 30 (1962), 361-366. Zbl0109.12204
  19. [19] N.H. Zaidi, Symmetrical balanced incomplete block designs with l = 2 and k = 9, Bull. Calcutta Math. Soc. 55 (1963), 163-167. Zbl0137.13204

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.