標題: | The minimum size of critical sets in latin squares |
作者: | Fu, CM Fu, HL Rodger, CA 應用數學系 Department of Applied Mathematics |
關鍵字: | latin squares;critical sets;design construction |
公開日期: | 15-八月-1997 |
摘要: | A critical set C of order n is a partial latin square of order n which is uniquely completable to a latin square, and omitting any entry of the partial latin square destroys this property. The size s(C) of a critical set C is the number of filled cells in the partial latin square. The size of a minimum critical set of order n is s(n). It is likely that s(n) is approximately 1/4n(2), though to date the best-known lower bound is that s(n)greater than or equal to n+1. In this paper, we obtain some conditions on C which force s(C)greater than or equal to[(n-1)/2](2). For n > 20, this is used to show that in generals(n)greater than or equal to[(7n-3)/6], thus improving the best-known result. (C) 1997 Elsevier Science B.V. |
URI: | http://hdl.handle.net/11536/366 |
ISSN: | 0378-3758 |
期刊: | JOURNAL OF STATISTICAL PLANNING AND INFERENCE |
Volume: | 62 |
Issue: | 2 |
起始頁: | 333 |
結束頁: | 337 |
顯示於類別: | 期刊論文 |