Abstract
It is shown that if there is a Room design of sidev 1 and a Room design of sidev 2 containing a subdesign of sidev 3, then there exists a design of side v1 (v2 — v3)+v3, provided thats = v 2 — v3 ≠ 6. Further, ifs ≠ 0, each of the 3 initial designs is isomorphic to a subdesign of the resultant design. It is also shown that there exist Room designs of sidev for all Fermat primesv > 65537.
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References
Mullin, R. C. andNemeth, E.,An Existence Theorem for Room Squares, Canad. Math. Bull.12, 493–497 (1969).
Stanton, R. G. andMullin, R. C.,Construction of Room Squares, Ann. Math. Statist.39, 1540–1548 (1968).
Stanton, R. G. andHorton, J. D.,A Multiplication Theorem for Room Squares, J. Combinatorial Theory (to appear).
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Horton, J.D., Mullin, R.C. & Stanton, R.G. A recursive construction for Room designs. Aeq. Math. 6, 39–45 (1971). https://doi.org/10.1007/BF01833236
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DOI: https://doi.org/10.1007/BF01833236