Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651270 | Discrete Mathematics | 2006 | 23 Pages |
Abstract
Two Latin squares of order vv are r-orthogonal if their superposition produces exactly r distinct ordered pairs. If the second square is the transpose of the first one, we say that the first square is r-self-orthogonal, denoted by r -SOLS(v)(v). It has been proved that for any integer v⩾28v⩾28, there exists an r -SOLS(v)(v) if and only if v⩽r⩽v2v⩽r⩽v2 and r∉{v+1,v2-1}r∉{v+1,v2-1}. In this paper, we give an almost complete solution for the existence of r-self-orthogonal Latin squares.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yunqing Xu, Yanxun Chang,