

A013588


Smallest positive integer not the determinant of an n X n 01 matrix.


6




OFFSET

1,1


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.


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. 161171.
Miodrag Zivkovic, Massive computation as a problem solving tool. In Proceedings of the 10th Congress of Yugoslav Mathematicians (Belgrade, 2001), pages 113128. Univ. Belgrade Fac. Math., Belgrade, 2001.


LINKS

Table of n, a(n) for n=1..10.
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
Index entries for sequences related to maximal determinants


EXAMPLE

There is no 3 X 3 01 matrix with determinant 3, as such a matrix must have a row with at least one 0 in it.


CROSSREFS

Cf. A003432.
Sequence in context: A284908 A103599 A032245 * A108150 A066015 A065482
Adjacent sequences: A013585 A013586 A013587 * A013589 A013590 A013591


KEYWORD

nice,hard,nonn


AUTHOR

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


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


STATUS

approved



