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Paper   IPM / M / 2346
School of Mathematics
  Title:   A lower bound for the size of the largest critical sets in Latin squares
1.  H. Hatami
2.  E. S. Mahmoodian
  Status:   Published
  Journal: Bull. Inst. Combin. Appl.
  Vol.:  38
  Year:  2003
  Pages:   19-22
  Supported by:  IPM
A critical set in an n×n array is a set C of given entries, such that there exists a unique extension of C to an n×n Latin square and no proper subset of C has this property. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). We give a lower bound for lcs(n) by showing that lcs (n) ≥ n2 ( 1 −[(2 + ln 2)/(ln n)] ) + n ( 1 +[(ln (8 π))/(ln n)] ) −[(ln 2 )/( ln n)].

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