Search: id:A013588
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%I A013588
%S A013588 2,2,3,4,6,10,19,41,103,269
%N A013588 Smallest positive integer not the determinant of an n X n 0-1 matrix.
%C A013588 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 A013588 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 A013588 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 A013588 W. P. Orrick, <a href="http://arXiv.org/abs/math.CO/0401179">The maximal 
               {-1, 1}-determinant of order 15</a>.
%H A013588 G. R. Paseman, <a href="http://www.prado.com/~paseman/icm98sl.html">A 
               Different Approach to Hadamard's Maximum Determinant Problem</a>
%H A013588 G. R. Paseman, <a href="http://www.prado.com/~paseman/icm.html">Related 
               Material</a>
%H A013588 M. Zivkovic, <a href="http://arXiv.org/abs/math.CO/0511636">Classification 
               of small (0,1) matrices</a>
%H A013588 <a href="Sindx_Mat.html#binmat">Index entries for sequences related to 
               binary matrices</a>
%e A013588 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 A013588 Cf. A003432.
%Y A013588 Sequence in context: A039829 A143588 A032245 this_sequence A108150 A066015 
               A065482
%Y A013588 Adjacent sequences: A013585 A013586 A013587 this_sequence A013589 A013590 
               A013591
%K A013588 nice,hard,nonn
%O A013588 1,1
%A A013588 Gerhard R. Paseman (paseman(AT)prado.com)
%E A013588 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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