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A063437
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Cardinality of largest critical set in any Latin square of order n.
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1
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OFFSET
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1,3
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COMMENTS
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A critical set in an n X n array is a set C of given entries such that there exists a unique extension of C to an n X n Latin square and no proper subset of C has this property.
The next terms satisfy a(7) >= 25, a(8) >= 37, a(9) >= 44, a(10) >= 57. In the reference it is proved that, for all n, a(n) <= n^2 - 3n + 3.
For n sufficiently large (>= 295), a(n) >= (n^2)*(1-(2 + log 2)/log n) + n*(1 + (log(8*Pi)/log n) - (log 2}/(log n). Bean and Mahmoodian also show a(n) <= n^2 - 3n + 3. - Jonathan Vos Post, Jan 03 2007
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LINKS
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 24 2001
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STATUS
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approved
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