A counterexample to a direct product construction of Room squares
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TLDR
In this paper, it was shown that the direct product of two Room pairs of quasigroups is not a Room pair as was previously believed, and therefore, there is no room pair in the product.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1969-11-01 and is currently open access. It has received 8 citations till now. The article focuses on the topics: Counterexample & Direct product.read more
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Journal ArticleDOI
The existence of Room squares
TL;DR: In this article, the authors give a condensed proof of the existence of room squares for positive odd sides except 3 and 5, and some areas of current research on room squares are also discussed.
Journal ArticleDOI
On furnishing Room squares
TL;DR: In this article, it was shown that for v = 6t+1=pn, p a prime, there exists a Room square of order v+1, where v is the number of rooms in the room.
Book ChapterDOI
Algebraic Speculations About Steiner Systems
TL;DR: In this paper, the algebraic speculations about Steiner systems are discussed and two examples of algebraic techniques that provided the initial proofs of significant results in combinatorial design theory and one case where more algebraic knowledge are prevented an embarrassing mistake.
Journal ArticleDOI
A multiplication theorem for Room Squares
TL;DR: It is proved that a Room Square of side m can be combined with a Roomsquare of side n to produce a RoomSquare of sidemn.