A089472 Number of different values taken by the determinant of a real (0,1)-matrix of order n.

1, 2, 3, 5, 7, 11, 19, 43, 91, 227, 587

Offset: 0

Author

Hugo Pfoertner, Nov 04 2003

Keywords

• nonn
• hard
• more

Comments

Lower bounds: a(11) >= 1623, a(12) >= 4605, a(13) >= 14365, a(14) >= 44535, a(15) >= 145273, a(16) >= 476947

Examples

			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}
		

Links

• 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.
• 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.
• 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.
• M. Zivkovic, Classification of small (0,1) matrices, arXiv:math/0511636 [math.CO], 2005.

Crossrefs

Cf. A003432 (largest determinant of (0, 1)-matrix), A013588 (smallest integer not representable as determinant of (0, 1)-matrix), A089478 (occurrence counts), A087983 (number of different values taken by permanent of (0, 1)-matrix).

Extensions

a(1)..a(4) from Wouter Meeussen.

a(7) verified by Gordon F. Royle.

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, May 02 2011

a(0)=1 prepended by Alois P. Heinz, Mar 16 2019