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A013588
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Smallest positive integer not the determinant of an n X n 0-1 matrix.
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5
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OFFSET
| 1,1
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COMMENTS
| This majorizes the sequence of maximal determinants only up to the 6th term. It is conjectured that the sequence of maximal determinants majorizes this for all later terms. The 8th term has not been independently verified.
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REFERENCES
| R. Craigen, The Range of the Determinant Function on the Set of n X n (0,1)-Matrices, J. Combin. Math. Combin. Computing, 8 (1990) pp. 161-171.
Miodrag Zivkovic, Massive computation as a problem solving tool. In Proceedings of the 10th Congress of Yugoslav Mathematicians (Belgrade, 2001), pages 113-128. Univ. Belgrade Fac. Math., Belgrade, 2001.
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LINKS
| W. P. Orrick, The maximal {-1, 1}-determinant of order 15.
G. R. Paseman, A Different Approach to Hadamard's Maximum Determinant Problem
G. R. Paseman, Related Material
M. Zivkovic, Classification of small (0,1) matrices
Index entries for sequences related to binary matrices
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EXAMPLE
| There is no 3 X 3 0-1 matrix with determinant 3, as such a matrix must have a row with at least one 0 in it.
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CROSSREFS
| Cf. A003432.
Sequence in context: A039829 A143588 A032245 * A108150 A066015 A065482
Adjacent sequences: A013585 A013586 A013587 * A013589 A013590 A013591
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KEYWORD
| nice,hard,nonn
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AUTHOR
| Gerhard R. Paseman (paseman(AT)prado.com)
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EXTENSIONS
| Extended by William Orrick, Jan 12 2006. a(7), a(8) and a(9) computed by Miodrag Zivkovic. a(7) and a(8) independently confirmed by Antonis Charalambides. a(10) computed by William Orrick. Lower bounds: a(11) >= 739, a(12) >= 2173, a(13) >= 6739, a(14) >= 21278, a(15) >= 69259, a(16) >= 230309
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