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Incomplete conjugate orthogonal idempotent latin squares

✍ Scribed by F.E Bennett; L Zhu

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 914 KB
Volume: 65
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90207-x

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✦ Synopsis

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 of a COILS(26), the existence of Which was unknown for some time. A necessary condition for the existence of an. ICOILS(v, n) is v ~> 3n + 1. In this paper, it is shown that for all n ~> 1, an ICOILS(v, n) exists if v = 3n + 1 or v ~>8n + 42. Moreover, for 2 ~< n <~ 6, it is shown that an ICOILS(v; n) exists for all v ~> 3n + 1 with very few possible exceptions.

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