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American Journal of Applied Mathematics and Statistics. 2018, 6(2), 36-43
DOI: 10.12691/AJAMS-6-2-1
Original Research

Some Constructions of Nearly µ-Resolvable Designs

Banerjee S.1, Awad R.1 and Agrawal B.1,

1School of Statistics, DAVV, Indore, India

Pub. Date: April 18, 2018

Cite this paper

Banerjee S., Awad R. and Agrawal B.. Some Constructions of Nearly µ-Resolvable Designs. American Journal of Applied Mathematics and Statistics. 2018; 6(2):36-43. doi: 10.12691/AJAMS-6-2-1

Abstract

This paper deals with general construction methods of nearly µ - resolvable balanced incomplete block designs with illustration using nearly one resolvable balanced incomplete block (BIB) designs and some known group divisible (GD) designs.

Keywords

balanced incomplete block design, symmetric balanced incomplete block design, resolvable design, μ – resolvable balanced block designs, nearly μ – resolvable balanced block designs, GD design

Copyright

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]  Abel R.J.R. (1994). Forty-Three Balanced Incomplete Block Designs. Journal of Combinatorial Theory, Series A 65, 252-267.
 
[2]  Abel R.J.R. and Furino S.F. (2007). Resolvable and near resolvable designs, in: The CRC Handbook of Combinatorial Designs, (2nd edition), (C.J. Colbourn and J.H. Dinitz, eds.), CRC Press, Boca Raton FL, U.S.A., 87-94.
 
[3]  Bose, R. C. (1942). A note on resolvability of balanced incomplete block designs. Sankhya, 6, 105-110.
 
[4]  Bose, R. C. and Nair, K. R. (1939). Partially balanced block designs. Sankhya, 4, 337-372.
 
[5]  Bose R.C., Shimamoto T. (1952). Classification and analysis of partially balanced incomplete block designs with two associate classes, Journal of the American Statistical Association, 47, 151-184.
 
[6]  Clatworthy, W. H. (1973). Tables of two-associate class partially balanced designs. NBS Applied Mathematics, Series 63.
 
[7]  Dey, A. (1986). Theory of block designs. Wiley Eastern Limited, New Delhi.
 
[8]  Haanpaa H. and Kaski P. (2005). The near resolvable 2-(13,4,3) designs and thirteen-player whist tournaments. Des. Codes Cryptogr. 35, 271-285.
 
[9]  Hall, M. Jr. (1986). Combinatorial Theory. John Wiley, New York.
 
[10]  Kageyama, S. and Mohan, R. N. (1984). Dualizing with respect to s-tuples. Proc. Japan Acad. Ser. A 60, 266-268.
 
[11]  Kageyama, S., Majumdar, A. And Pal, S. (2001). A new series of μ-resolvable BIB designs. Bull. Grad. School Educ. Hiroshima Univ., Part II, No. 50, 41-45.
 
[12]  Kageyama, S., Philip, J. and Banerjee, S. (1995). Some constructions of nested BIB and 2-associate PBIB designs under restricted dualization. Bull. Fac. Sch. Educ. Hiroshima Univ., Part II, 17, 33-39.
 
[13]  Luis B. Morales, Rodolfo San Agust´ın,1 Carlos Velarde (2007). Enumeration of all (2k + 1, k, k − 1)-NRBIBDs for 3 ≤ k ≤ 13. JCMCC, 60, 81-95
 
[14]  Malcolm Greig, Harri Haanpaa and Petteri Kaski (2005). On the coexistence of conference matrices and near resolvable 2-(2k+1, k, k-1) designs. Journal of Combinatorial Theory, Series A, 113, 703-711.
 
[15]  Mohan, R. N. and Kageyama, S. (1983). A method of construction of group divisible designs. Utilitas Math., 24, 311-316.
 
[16]  Philip, J., Banerjee, S. and Kageyama, S., (1997). Constructions of nested t-associate PBIB designs under restricted dualization. Utilitas Mathematica, 51, 27-32.
 
[17]  Raghavarao, D. (1971). Constructions and Combinatorial Problems in Designs of Experiments. John Wiley, New York.
 
[18]  Shrikhande, S. S. (1952). On the dual of some balanced incomplete block designs. Biometrics, 8, 66-72.
 
[19]  Vanstone, A. (1975). A note on a construction of BIBD’s. Utilitas Math., 7, 321-322.