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Cyclic Incidence Matrices

  • Marshall Hall (a1) and H. J. Ryser

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Let it be required to arrange v elements into v sets such that each set contains exactly k distinct elements and such that each pair of sets has exactly λ elements in common (0 < λ < k < v). This problem we refer to as the v, k,λ combinatorial problem.

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References

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1. Bruck, R. H. and Ryser, H. J., The nonexistence of certain finite projective planes, Can. J. Math., vol. 1 (1949), 8893.
2. Chowla, S., On difference sets, Proc. Nat. Acad. Sci., vol. 35 (1949), 9294.
3. Chowla, S. and Ryser, H. J., Combinatorial problems, Can. J. Math., vol. 2 (1950), 9399.
4. J., Marshall Hall, Cyclic projective planes, Duke Math. J., vol. 14 (1947), 10791090.
5. Mann, H. B., Analysis and Design of Experiments (New York, 1949).
6. Paley, R. E. A. C., On orthogonal matrices, J. Math, and Phys., vol. 12 (1933), 311320.
7. Ryser, H. J., A note on a combinatorial problem, Proc. Amer. Math. Soc, vol. 1 (1950), 422424.
8. Shrikhande, S. S., The impossiblity of certain symmetrical balanced incomplete block designs, Ann. Math. Statist., vol. 21 (1950), 106111.
9. Singer, James, A theorem in finite projective geometry and some applications to number theory, Trans. Amer. Math. Soc, vol. 43 (1938), 377385.
10. Todd, J. A., A combinatorial problem, J. Math, and Phys., vol. 12 (1933), 321333.
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