A few more incomplete self-orthogonal Latin squares and related designs
نویسندگان
چکیده
An incomplete self-orthogonal Latin square of order v with an empty subarray of order n, an ISOLS(v, n), can exist only if v ~ 3n + 1. This necessary condition is known to be sufficient apart from 2 known exceptions (v, n) = (6,1) and (8,2) plus 14 possible exceptions (v, n) with v = 3n + 2. In this paper, we construct eleven new ISOLS(3n + 2, n) reducing unknown n to 6, 8,10 only. This result is then used to improve the existence of HSOLS of type 3 u1• To do this, two newly found unipotent SOLSSOMs, SOLSSOM(66) and SOLSSOM(70) are also useful. "'Research supported in part by NSERC Grant OGP 0005320 for the second author; NSF Grants CCR-9504205 and CCR-9357851 for the third author; and NSFC Grant 19831050 for the
منابع مشابه
Incomplete self-orthogonal latin squares ISOLS(6m + 6, 2m) exist for all m
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 21 شماره
صفحات -
تاریخ انتشار 2000