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Cyclic Incidence Matrices

Published online by Cambridge University Press:  20 November 2018

Marshall Hall  and
H. J. Ryser
Marshall Hall
Affiliation:
Ohio State University
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 495 - 502
Copyright
Copyright © Canadian Mathematical Society 1951

References

1. Bruck, R. H. and Ryser, H. J., The nonexistence of certain finite projective planes, Can. J. Math., vol. 1 (1949), 88–93.Google Scholar
2. Chowla, S., On difference sets, Proc. Nat. Acad. Sci., vol. 35 (1949), 92–94.Google Scholar
3. Chowla, S. and Ryser, H. J., Combinatorial problems, Can. J. Math., vol. 2 (1950), 93–99.Google Scholar
4. J., Marshall Hall, Cyclic projective planes, Duke Math. J., vol. 14 (1947), 1079–1090.Google Scholar
5. Mann, H. B., Analysis and Design of Experiments (New York, 1949).Google Scholar
6. Paley, R. E. A. C., On orthogonal matrices, J. Math, and Phys., vol. 12 (1933), 311–320.Google Scholar
7. Ryser, H. J., A note on a combinatorial problem, Proc. Amer. Math. Soc, vol. 1 (1950), 422–424.Google Scholar
8. Shrikhande, S. S., The impossiblity of certain symmetrical balanced incomplete block designs, Ann. Math. Statist., vol. 21 (1950), 106–111.Google Scholar
9. Singer, James, A theorem in finite projective geometry and some applications to number theory, Trans. Amer. Math. Soc, vol. 43 (1938), 377–385.Google Scholar
10. Todd, J. A., A combinatorial problem, J. Math, and Phys., vol. 12 (1933), 321–333.Google Scholar