A336764 Maximum number of order 3 subsquares in a Latin square of order n.

0, 0, 1, 0, 0, 4, 7

Offset: 1

Author

Omar Aceval Garcia, Cameron Byer, Eugene Fiorini, Nicholas Hanson, Brian G. Kronenthal, Lindsey Wise, Aug 03 2020

Keywords

• nonn
• hard
• more

Comments

A subsquare of a Latin square is a submatrix (not necessarily consisting of adjacent entries) which is itself a Latin square. (I. M. Wanless, Latin Squares with One Subsquare, Wiley and Sons)

Links

• R. Bean, Critical sets in Latin squares and Associated Structures, Ph.D. Thesis, The University of Queensland, 2001.
• K. Heinrich and W. Wallis, The Maximum Number of Intercalates in a Latin Square, Combinatorial Math. VIII, Proc. 8th Australian Conf. Combinatorics, 1980, 221-233.
• I. M. Wanless, Latin Squares with One Subsquare, Journal of Combinatorial Designs, 9 (2001), 128-146.

Crossrefs

Cf. A092237, A091323, A090741, A307163, A307164.

Formula

a(3^n) = 9*a(3^(n-1)) + 27^(n-1) (conjectured).