On the existence of three dimensional Room frames and Howell cubes
نویسندگان
چکیده
منابع مشابه
On the existence of three dimensional Room frames and Howell cubes
A Howell design of side s and order 2n+2, or more briefly an H(s, 2n+2) isan s× s array in which each cell is either empty or contains an unordered pairof elements from some 2n+2 set V such that (1) every element of V occurs inprecisely one cell of each row and each column, and (2) every unordered pairof elements from V is in at most one cell of the array. It follows immediately...
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A Room t-cube is standardized if it also satisfies (iv) the ith diagonal cell contains the pair of symbols {co, i}. There are several other equivalent forms that are taken by Room t-cubes, one in terms of graphs and one in terms of Latin squares. The first of these forms is as a set of orthogonal one-factorizations of K,,. Let G be a graph with an even number of vertices. A one-factor in G is a...
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Partitionable skew Room frames of type hn have played an important role in the constructions of 4-frames, (K4 − e)-frames and super-simple (4, 2)-frames. In this paper, we investigate the existence of partitionable skew Room frames of type hn. The necessary conditions for the existence of such a design are that h(n − 1) ≡ 0 (mod 4) and h 5. It is proved that these necessary conditions are also ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.02.017