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Intersection Problem for Simple 2-fold (3n, n, 3) Group Divisible Designs

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Abstract

In this paper, we will give intersection numbers for two simple 2-fold (3n, n, 3) group divisible designs. More precisely, we will develop constructions which show that there exists two simple 2-fold (3n, n, 3) group divisible designs which intersect in precisely \({k \in \{0, 1, 2, \ldots, 2n^2\}{\setminus} \{2n^2-1, 2n^2-2, 2n^2-3, 2n^2-5\}}\) triples for \({n \geq 5}\). There are some exceptions for n = 2, 3, 4.

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References

  1. Billington E.J., Donovan D., Lefevre J., McCourt T., Lindner C.C.: The triangle intersection problem for nested Steiner triple systems. Australas. J. Comb. 51, 221–233 (2011)

    MATH  MathSciNet  Google Scholar 

  2. Chee, Y.M.: Steiner triple systems intersecting in pairwise disjoint blocks. Electron. J. Combin. 11, Research Paper 27, pp. 17 (2004)

  3. Fu C.M., Fu H.L.: The intersection problem of Latin squares. J. Comb. Inform. Syst. Sci. 15, 89–95 (1990)

    MATH  Google Scholar 

  4. Fu, H.L.: On the construction of certain types of Latin squares having prescribed intersections. Ph.D. thesis, Department of Discrete and Statistical Sciences, Auburn University, Auburn (1980)

  5. Hoffman D.G., Lindner C.C.: The flower intersection problem for Steiner triple systems. Ann. Discret. Math. 34, 243–258 (1987)

    MathSciNet  Google Scholar 

  6. Lefevre, J.; McCourt, T.A.: The disjoint m-flower intersection problem for Latin squares. Electron. J. Comb. 18, Research Paper 42, pp. 33 (2011)

  7. Lindner C.C., Rosa A.: Steiner triple systems having a prescribed number of triples in common. Can. J. Math. 27, 1166–1175 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  8. Mathon R., Street A.P.: Partitions of sets of two-fold triple systems, and their relation to some strongly regular graphs. Graphs Comb. 11, 347–366 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Sade A.: Produit direct-singulier de quasigroupes orthogonaux et anti-abéliens. Ann. Soc Sci. Bruxelles Sr. L 74, 91–99 (1960)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Physics, Centre for Discrete Mathematics and Computing, University of Queensland, Brisbane, 4072, Australia

    Fatih Demirkale & Diane Donovan

  2. Department of Mathematics and Statistics, Auburn University, Auburn, AL, 36849, USA

    C. C. Lindner

Authors
  1. Fatih Demirkale
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  2. Diane Donovan
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  3. C. C. Lindner
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Correspondence to Fatih Demirkale.

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Demirkale, F., Donovan, D. & Lindner, C.C. Intersection Problem for Simple 2-fold (3n, n, 3) Group Divisible Designs. Graphs and Combinatorics 31, 537–545 (2015). https://doi.org/10.1007/s00373-013-1397-6

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  • DOI: https://doi.org/10.1007/s00373-013-1397-6

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