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Search: id:A089472
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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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+0
7
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OFFSET
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1,1
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COMMENT
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a(1)..a(4) from Wouter Meeussen (wouter.meeussen(AT)pandora.be). a(7) verified by Gordon Royle (gordon(AT)maths.uwa.edu.au). 93<=a(8)<113=A003432(8) estimate from random search.
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REFERENCES
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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
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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
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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
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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 this_sequence A079429 A072299 A038204
Adjacent sequences: A089469 A089470 A089471 this_sequence A089473 A089474 A089475
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KEYWORD
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hard,more,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Nov 04 2003
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EXTENSIONS
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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. The estimate a(8) >= 93 is evidently in error. Lower bounds: a(11) >= 1623, a(12) >= 4605, a(13) >= 14365, a(14) >= 44535, a(15) >= 145273, a(16) >= 476947
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