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    請使用永久網址來引用或連結此文件: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/41347

    題名: The minimum size of critical sets in Latin squares
    其他題名: 拉丁方陣最小臨界集合的個數
    作者: 高金美;Fu, Chin-mei;Fu, Hung-lin;Rodger, C. A.
    貢獻者: 淡江大學數學學系
    關鍵詞: Latin squares;Critical sets;Design construction
    日期: 1997-08-15
    上傳時間: 2010-01-28 07:21:32 (UTC+8)
    出版者: Elsevier
    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 14n2, though to date the best-known lower bound is that s(n) ⩾ n + 1. In this paper, we obtain some conditions on C which force s(C) ⩾ [(n − 1)2]2. For n > 20, this is used to show that in general s(n) ⩾ [(7n − 3)6], thus improving the best-known result.
    關聯: Journal of Statistical Planning and Inference 62(2), pp.333-337
    DOI: 10.1016/S0378-3758(96)00187-5
    顯示於類別:[數學學系暨研究所] 期刊論文


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