Some Constructions of Nearly µ-Resolvable Designs

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

¹School of Statistics, DAVV, Indore, India

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

This 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.