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On a result of bose and shrikhande

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Book cover Combinatorial Mathematics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 686))

Abstract

Necessary and sufficient conditions are given for the extendability of a regular 2-component pairwise balanced design (PB2-design) to a balanced incomplete block design. This gives an alternative non graph-theoretic proof of a result of R.C. Bose and S.S. Shrikhande, showing extendability of a PB2-design with certain parameters to a projective plane of even order q, q>6.

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References

  1. R.C. Bose and S.S. Shrikhande, Embedding the complement of an oval in a projective plane of even order, Discrete Math. 6 (1973), 305–312.

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  2. W.H. Clatworthy, Tables of two-associate class partially balanced designs, U.S. Dept. of Commerce, NBS, Washington, 1973.

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  3. W.S. Connor, The uniqueness of the triangular association scheme, Ann. Math. Stat. 29 (1958), 262–266.

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  4. R.H.F. Denniston, Some maximal arcs in finite projective planes, J. Combinatorial Theory 6 (1969), 317–319.

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  5. Elizabeth J. Morgan, Arcs in block designs, Ars Combinatoria (to appear).

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  6. D. Raghavarao, Construction and combinatorial problems in design of experiments, Wiley, New York, 1971.

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  7. S.S. Shrikhande, On a characterization of the triangular association scheme, Ann. Math. Stat. 30 (1959), 39–47.

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  8. J.A. Thas, Some results concerning {(q+1)(n−1);n}-arcs and {(q+1)(n−1)+1;n}-arcs in finite projective planes of order q, J. Combinatorial Theory (A) 19 (1975), 228–232.

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  9. Paul de Witte, The exceptional case in a theorem of Bose and Shrikhande, J. Australian Math. Soc. (to appear).

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Authors and Affiliations

  1. Department of Mathematics, University of Queensland, 4067, St. Lucia, Q., Australia

    Elizabeth J. Morgan

Authors
  1. Elizabeth J. Morgan
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D. A. Holton Jennifer Seberry

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© 1978 Springer-Verlag

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Morgan, E.J. (1978). On a result of bose and shrikhande. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062537

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  • DOI: https://doi.org/10.1007/BFb0062537

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08953-7

  • Online ISBN: 978-3-540-35702-5

  • eBook Packages: Springer Book Archive

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