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Conjugate orthogonal quasigroups

✍ Scribed by K.T. Phelps

Publisher
Elsevier Science
Year
1978
Tongue
English
Weight
576 KB
Volume
25
Category
Article
ISSN
0097-3165

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## Abstract A ternary quasigroup (or 3‐quasigroup) is a pair (__N, q__) where __N__ is an __n__‐set and __q__(__x, y, z__) is a ternary operation on __N__ with unique solvability. A 3‐quasigroup is called 2‐idempotent if it satisfies the generalized idempotent law: __q__(__x, x, y__) = __q__(__x, y

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Let us denote by COILS(v) a (3, 2, 1)-conjugate orthogonal idempotent Latin square of order v, and by ICOILS(v, n) an incomplete COILS(v) missing a sub-COILS(n). We shall investigate the existence of ICOILS(v, n). The construction of an ICOILS(8, 2) has already been instrumental in the construction

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We shall refer to a diagonal Latin square which is orthogonal to its (3, 2, 1)-conjugate and having its (3, 2, 1)-conjugate also a diagonal Latin square as a (3, 2, 1)-conjugate orthogonal diagonal Latin square, briefly CODLS. This article investigates the spectrum of CODLS and it is found that it c