Abstract
A Generalized Room Square (GRS) of ordern and degreek is an\(\left( {\begin{array}{*{20}c} {n - 1} \\ {k - 1} \\ \end{array} } \right) \times \left( {\begin{array}{*{20}c} {n - 1} \\ {k - 1} \\ \end{array} } \right)\) array of which each cell is either empty or contains an unorderedk-tuple of a setS, |S|=n, such that each row and each column of the array contains each element ofS exactly once and the array contains each unorderedk-tuple exactly once. A method of generating the unordered triples on the setS=GF(q) ⋃ {∞} is given, 3 ∣ (q ∣ 1). This method is used to construct GRS's of appropriate ordern and degree 3, for alln<50.
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Wallis, W. D., Street, Anne Penfold andWallis, Jennifer Seberry,Combinatorics: Room squares, sum-free sets, Hadamard matrices. Lecture Notes in Mathematics 292. Springer-Verlag, Berlin, 1972.
Stiffler, J. J. andBlake, I. F.,An infinite class of generalized room squares. Discrete Math.12 (1975), 159–163.
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Blake, I.F., Stiffler, J.J. A construction method for generalized Room squares. Aeq. Math. 14, 83–94 (1976). https://doi.org/10.1007/BF01836209
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DOI: https://doi.org/10.1007/BF01836209