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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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7
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OFFSET
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1,1
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COMMENTS
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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 first term needing verification is a(11) >= 739. a(12) = 2173 has been verified by Brent, Orrick, Osborn, and Zimmermann in 2010. Lower bounds for the next terms: a(13) >= 6739, a(14) >= 21278, a(15) >= 69259, a(16) >= 230309. - Hugo Pfoertner, Jan 03 2020
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LINKS
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EXAMPLE
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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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PROG
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(Python)
from itertools import product
from sympy import Matrix
s, k = set(Matrix(n, n, p).det() for p in product([0, 1], repeat=n**2)), 1
while k in s:
k += 1
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CROSSREFS
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KEYWORD
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nice,more,hard,nonn
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AUTHOR
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Gerhard R. Paseman (paseman(AT)prado.com)
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EXTENSIONS
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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.
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STATUS
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approved
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