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 A063437 Cardinality of largest critical set in any Latin square of order n. 1
 0, 1, 3, 7, 11, 18 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. a(9) >= 45. - Richard Bean (rwb(AT)eskimo.com), May 01 2002 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 REFERENCES Richard Bean and E. S. Mahmoodian, A new bound on the size of the largest critical set in a Latin square, Discrete Math., 267 (2003), 13-21. R. Bean and Ebadollah S. Mahmoodian, A new bound on the size of the largest critical set in Latin squares, Discrete Math, to appear. LINKS Richard Bean and E. S. Mahmoodian, A new bound on the size of the largest critical set in a Latin square Mahya Ghandehari, Hamed Hatami and Ebadollah S. Mahmoodian, On the size of the minimum critical set of a Latin square, Journal of Discrete Mathematics. 293(1-3) (2005) pp. 121-127 Hamed Hatami and Ebadollah S. Mahmoodian, A lower bound for the size of the largest critical sets in Latin squares, Bulletin of the Institute of Combinatorics and its Applications (Canada). 38 (2003) pp. 19-22 CROSSREFS Sequence in context: A072456 A138659 A020590 * A190711 A210977 A049792 Adjacent sequences:  A063434 A063435 A063436 * A063438 A063439 A063440 KEYWORD nonn AUTHOR Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 24 2001 EXTENSIONS 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. STATUS approved

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