Latin square and intersection of surface
โ Scribed by Alan P. Wang
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 592 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0096-3003
No coin nor oath required. For personal study only.
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## Abstract In this paper, it is shown that a latin square of order __n__ with __n__โโฅโ3 and __n__โโ โ6 can be embedded in a latin square of order __n__^2^ which has an orthogonal mate. A similar result for idempotent latin squares is also presented. ยฉ 2005 Wiley Periodicals, Inc. J Combin Designs 1
## Abstract An orthogonal latin square graph (OLSG) is one in which the vertices are latin squares of the same order and on the same symbols, and two vertices are adjacent if and only if the latin squares are orthogonal. If __G__ is an arbitrary finite graph, we say that __G__ is realizable as an O
We define a near-automorphism a of a Latin square L to be an isomorphism such that L and aL differ only within a 2ร2 subsquare. We prove that for all n โฅ 2 except n โ{3, 4}, there exists a Latin square which exhibits a near-automorphism. We also show that if a has the cycle structure (2, n-2), then
## Abstract We present the numbers of isotopy classes and main classes of Latin squares, and the numbers of isomorphism classes of quasigroups and loops, up to order 10. The best previous results were for Latin squares of order 8 (Kolesova, Lam, and Thiel, 1990), quasigroups of order 6 (Bower, 2000