Pacific Journal of Mathematics

Strongly regular graphs, partial geometries and partially balanced designs.

R. C. Bose

Article information

Source
Pacific J. Math., Volume 13, Number 2 (1963), 389-419.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103035734

Mathematical Reviews number (MathSciNet)
MR0157909

Zentralblatt MATH identifier
0118.33903

Subjects
Primary: 05.27
Secondary: 50.30

Citation

Bose, R. C. Strongly regular graphs, partial geometries and partially balanced designs. Pacific J. Math. 13 (1963), no. 2, 389--419. https://projecteuclid.org/euclid.pjm/1103035734


Export citation

References

  • [1] R. C. Bose and W. H. Clatworthy, Some classes of partially balanced designs, Ann.. Math. Stat., 26 (1955), 212-232.
  • [2] R. C. Bose and D. M. Mesner, On linear associative algebras corresponding to associ- ation schemes of partially balanced designs, Ann. Math. Stat., 3O (1959), 21-38.
  • [3] R. C. Bose and K. R. Nair, Partially balanced incomplete block designs, Sankhya, 4 (1939), 337-372.
  • [4] R. C. Bose and T. Shimamoto, Classification and analysis of partially balanced in- complete block designs, with two associate classes, J. Amer. Stat. Assn., 47 (1952), 151- 184.
  • [5] R. H. Bruck, Finite nets II.Uniqueness and imbedding,Pacific J. Math., 13 (1963), 421-457.
  • [6] Chang Li-chien, The uniqueness and non-uniqueness of the triangularassociation schemes, Science Record, Math., New Ser., 3 (1959), 604-613.
  • [7] Chang Li-chien, Association schemes of partially balanced designs with parameters v = 28, m = 12, m = 15 and p2n = 4. Science Record, Math., New Ser. 4 (1960), 12-18.
  • [8] W. H. Clatworthy, A geometrical configuration wich is a partially balanced incom- plete block design, Proc. Amer. Math. Soc, 5 (1954), 47-55.
  • [9] W. S. Connor, The uniqueness of the triangular association scheme, Ann. Math. Stat.r 29 (1958), 262-266.
  • [10] W. S. Connor, On the structure of balanced incomplete block designs,^.Ann. Math. Stat., 23 (1952), 57-71.
  • [11] W. S. Connor and W. H. Clatworthy, Some theorems for partially balanced designs, 25 (1954), 100-112.
  • [12] Marsnall Hall and W. S. Connor, An embedding theorem for balanced incomplete block designs, Can. J. Math., 6 (1953), 35-41.
  • [13] A. J. Hoffman, On the uniqueness of the triangular association scheme, Ann. Math. Stat., 31 (1960), 492-497.
  • [14] A. J. Hoffman,On the exceptional case in a characterization of the arcs of a complete graph, IBM J., 4 (1960), 487-496.
  • [15] D. M. Mesner, An investigation of certain combinatorial properties of partially balanced incomplete block experimental designs and association schemes, with a detailed study of designs of Latin square and related types, unpublished doctoral thesis, Michigan State University, 1956.
  • [16] E. J. F. Primrose, Quadratics in finite geometries, Proc. Camb. Phil. Soc. 47 (1951),. 299-304.
  • [17] D. K. Ray-Chaudhuri, Some results on quadrics in finite protective geometry, Can. J. Math., 14 (1962), 129-138.
  • [18] D. K. Ray-Chaudhuri, Application of the geometry of quadrics for constructing PBIB designs,. Ann. Math. Stat., 33 (1962), 1175-1186.
  • [19] S. S. Shrikhande, The uniqueness of the Li 'association scheme Ann. Math. Stat., 30 (1959), 781-798.
  • [20] S. S. Shrikhande, A note on mutuallyorthogonal Latinsquares, Sankhya, 23 (1961), 115-116.
  • [21] S. S. Shrikhande, On a characterization of the triangular association scheme, Ann. Math. Stat., 30 (1959), 39-47.
  • [22] S. S. Shrikhande, Relations between certain incomplete block designs, Contributions to prob- ability and statistics, Essays in honor of Harold Hotelling, Stanford U. Press (I960), 388-395.
  • [23] S. S. Shrikhande, On the dual of some balanced incomplete block designs, Biometrics, 8 (1952), 66-72.
  • [24] F. Yates, Lattice squares, J. Ag. So., 30 (1940), 672-687.