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A089472
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Number of different values taken by the determinant of a real (0,1)-matrix of order n.
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7
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OFFSET
| 1,1
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COMMENTS
| Lower bounds: a(11) >= 1623, a(12) >= 4605, a(13) >= 14365, a(14) >= 44535, a(15) >= 145273, a(16) >= 476947
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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.
Gerhard R. Paseman, Partial Proof of the Determinant Spectrum for 7x7 0-1 Matrices.
M. Zivkovic, Classification of small (0,1) matrices.
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EXAMPLE
| a(7)=43 because a 7X7 (0,1)-matrix A_7 can produce the values abs(det(A_7))= {0,1,...,17,18,20,24,32}
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CROSSREFS
| Cf. A003432 largest determinant of (0, 1)-matrix, A013588 smallest integer not representible as determinant of (0, 1)-matrix, A089478 occurrence counts, A087983 number of different values taken by permanent of (0, 1)-matrix.
Sequence in context: A002231 A087769 A084736 * A079429 A072299 A038204
Adjacent sequences: A089469 A089470 A089471 * A089473 A089474 A089475
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KEYWORD
| hard,more,nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Nov 04 2003
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EXTENSIONS
| a(1)..a(4) from Wouter Meeussen (wouter.meeussen(AT)pandora.be).
a(7) verified by Gordon Royle (gordon(AT)maths.uwa.edu.au).
Extended by William Orrick, Jan 12 2006. a(8) and a(9) computed by Miodrag Zivkovic. a(8) independently confirmed by Antonis Charalambides. a(10) computed by William Orrick.
Edited by Max Alekseyev (maxale(AT)gmail.com), May 02 2011
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