“School of Mathematics”
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| Paper IPM / M / 2346 |
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| Abstract: | |||||
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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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