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A013588 Smallest positive integer not the determinant of an n X n 0-1 matrix. 6


%S 2,2,3,4,6,10,19,41,103,269

%N Smallest positive integer not the determinant of an n X n 0-1 matrix.

%C 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.

%D 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.

%D 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.

%H W. P. Orrick, <a href="http://arXiv.org/abs/math.CO/0401179">The maximal {-1, 1}-determinant of order 15</a>.

%H G. R. Paseman, <a href="http://www.prado.com/~paseman/icm98sl.html">A Different Approach to Hadamard's Maximum Determinant Problem</a>

%H G. R. Paseman, <a href="http://www.prado.com/~paseman/icm.html">Related Material</a>

%H M. Zivkovic, <a href="http://arXiv.org/abs/math.CO/0511636">Classification of small (0,1) matrices</a>

%H <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>

%H <a href="/index/De#determinants">Index entries for sequences related to maximal determinants</a>

%e 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.

%Y Cf. A003432.

%K nice,hard,nonn

%O 1,1

%A Gerhard R. Paseman (paseman(AT)prado.com)

%E 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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Last modified October 17 22:48 EDT 2018. Contains 316297 sequences. (Running on oeis4.)