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Incomplete self-orthogonal latin squares ISOLS(6m+ 6, 2m) exist for allm

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
87
Issue
3
Identifiers
DOI: 10.1016/0012-365x(91)90137-q

Abstract

Abstract 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 ⩾ 3 n + 1. We show that an ISOLS(6 m + 6, 2 m) exists for all values of m and thus only the existence of an ISOLS(6 m + 6, 2 m), m ⩾ 2, remains in doubt.

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