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A new proof of the Doyen-Wilson theorem

Published online by Cambridge University Press:  09 April 2009

D. R. Stinson
Affiliation:
Department of Computer Science, University of Manitoba, Winnipeg Manitoba R3T 2N2, Canada
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Abstract

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We describe several recursive constructions for designs which use designs with “holes”. As an application, we give a short new proof of the Doyen-Wilson Theorem.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Assaf, A. M. and Hartman, A., ‘ Resolvable group divisible designs with block size 3’, Ann. Discrete. Math., to appear.Google Scholar
[2]Brouwer, A. E., ‘Optimal packings of K4's into a Kn’, J. Combin. Theory Ser. A 26 (1979), 278297.CrossRefGoogle Scholar
[3]Doyen, J. and Wilson, R. M., ‘Embeddings of Steiner triple systems’, Discrete Math. 5 (1973), 229239.CrossRefGoogle Scholar
[4]Horton, J. D., Mullin, R. C., and Stanton, R. G., ‘Minimal coverings of pairs by quadruples’, Proc. 2nd Louisiana Conf. on Combinatorics, Graph Theory and Computing, Baton Rouge, La. (1971), 495516.Google Scholar
[5]Kalbfleisch, J. G., Mullin, R. C., and Stanton, R. G., ‘ Covering and packing designs ’, Proc. 2nd Chapel Hill Conf. on Combinatorial Math. (1970), 428456.Google Scholar
[6]Mendelsohn, E. and Hao, S., ‘A construction of resolvable group divisible designs with block size three’, Ars Combin. 24 (1987), 3943.Google Scholar
[7]Mendelsohn, E. and Rosa, A., ‘Embedding maximal packings of triples’, Congr. Numer. 40 (1983), 235247.Google Scholar
[8]Mullin, R. C., ‘A generalization of the singular direct product with application to skew Room squares’, J. Combin. Theory Ser. A. 29 (1980), 306318.CrossRefGoogle Scholar
[9]Mullin, R. C., Schellenberg, P. J., Vanstone, S. A. and Wallis, W. D., ‘On the existence of frames’, Discrete Math. 37 (1981), 79104.CrossRefGoogle Scholar
[10]Ray-Chaudhuri, D. K. and Wilson, R. M., ‘Solution of Kirkman's school-girl problem’, Amer. Math. Soc. Proc. Sympos. Pure Math. 19 (1971), 187204.CrossRefGoogle Scholar
[11]Rees, R. and Stinson, D. R., ‘On resolvable group-divisible designs with block size 3’, Ars Combin. 23 (1987), 107120.Google Scholar
[12]Rees, R. and Stinson, D. R., ‘On combinatorial designs with subdesigns’, Ann. Discrete Math., to appear.Google Scholar
[13]Stanton, R. G. and Allston, J. L., ‘A census of values for gk(1, 2; v), Ars Combin. 20 (1985), 203216.Google Scholar
[14]Stern, G., ‘Tripelsysteme mit Untersystemen’, Arch. Math. 33 (1979), 204208.CrossRefGoogle Scholar
[15]Stern, G. and Lenz, H., ‘Steiner triple systems with given subspaces; another proof of the Doyen-Wilson theorem’, Boll. Un. Mat. Ital. A 17 (1980), 109114.Google Scholar
[16]Wilson, R. M., ‘Constructions and uses of pairwise balanced designs’, Math. Centre Tracts 55 (1974), 1841.Google Scholar