Incomplete self-orthogonal latin squares ISOLS(6m + 6, 2m) exist for all m
نویسندگان
چکیده
Heinrich, K., L. Wu and L. Zhu, Incomplete self-orthogonal latin squares ISOLS(6m + 6, 2m) exist fo all m, Discrete Mathematics 87 (1991) 281-290. 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 2 3n + 1. We show that an ISOLS(6m + 6, 2m) exists for all values of m and thus only the existence of an ISOLS(6m + 2,2m), m 2 2, remains in doubt.
منابع مشابه
A few more incomplete self-orthogonal Latin squares and related designs
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 ...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 87 شماره
صفحات -
تاریخ انتشار 1991