Existence of HSOLSSOMs of type |
| |
| Authors: | RJR Abel Frank E Bennett Hantao Zhang |
| |
| Institution: | aSchool of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia;bDepartment of Mathematics, Mount Saint Vincent University, Halifax, NS, Canada B3M 2J6;cComputer Science Department, The University of Iowa, Iowa City, IA 52242, USA |
| |
| Abstract: | In this paper we investigate the existence of holey self-orthogonal Latin squares with a symmetric orthogonal mate of type 2nu1 (HSOLSSOM(2nu1)). For u 2, necessary conditions for existence of such an HSOLSSOM are that u must be even and n3u/2+1. Xu Yunqing and Hu Yuwang have shown that these HSOLSSOMs exist whenever either (1) n 9 and n3u/2+1 or (2) n263 and n2(u-2). In this paper we show that in (1) the condition n9 can be extended to n30 and that in (2), the condition n263 can be improved to n4, except possibly for 19 pairs (n,u), the largest of which is (53,28). |
| |
| Keywords: | Holey self-orthogonal Latin squares Symmetric orthogonal mates |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
