A089472
Number of different values taken by the determinant of a real (0,1)-matrix of order n.
Original entry on oeis.org
1, 2, 3, 5, 7, 11, 19, 43, 91, 227, 587
Offset: 0
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}
- 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.
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).
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.
A089479
Triangle T(n,k) read by rows, where T(n,k) = number of times the permanent of a real n X n (0,1)-matrix takes the value k, for n >= 0, 0 <= k <= n!.
Original entry on oeis.org
0, 1, 1, 1, 9, 6, 1, 265, 150, 69, 18, 9, 0, 1, 27713, 13032, 10800, 4992, 4254, 1440, 1536, 576, 648, 24, 288, 96, 48, 0, 72, 0, 0, 0, 16, 0, 0, 0, 0, 0, 1, 10363361, 3513720, 4339440, 2626800, 3015450, 1451400, 1872800, 962400, 1295700, 425400, 873000
Offset: 0
Triangle begins:
0, 1;
1, 1;
9, 6, 1;
265, 150, 69, 18, 9, 0, 1;
27713, 13032, 10800, 4992, 4254, 1440, 1536, 576, 648, 24, 288,
96, 48, 0, 72, 0, 0, 0, 16, 0, 0, 0, 0, 0, 1;
...
T(n,0) =
A088672(n), T(n,1) =
A089482(n). The n-th row of the table contains
A087983(n) nonzero entries. For n>2
A089477(n) gives the position of the first zero entry in the n-th row.
Cf.
A089480 (occurrence counts for permanents of non-singular (0,1)-matrices),
A089481 (occurrence counts for permanents of singular (0,1)-matrices).
A051752
Number of n X n (real) {0,1}-matrices having determinant A003432(n).
Original entry on oeis.org
1, 1, 3, 3, 60, 3600, 529200, 75600, 195955200, 13716864000
Offset: 0
- Eric Weisstein's World of Mathematics, Hadamard's Maximum Determinant Problem.
- Eric Weisstein's World of Mathematics, (0, 1)-Matrix
- Luke Zeng, Shawn Xin, Avadesian Xu, Thomas Pang, Tim Yang, Maolin Zheng, Seele's New Anti-ASIC Consensus Algorithm with Emphasis on Matrix Computation, arXiv:1905.04565 [cs.CR], 2019.
- Miodrag Zivkovic, Classification of small (0,1) matrices, arXiv:math/0511636 [math.CO], 2005.
- Miodrag Zivkovic, Classification of small (0,1) matrices, Linear Algebra and its Applications, 414 (2006), 310-346.
a(5) = 3600 from Daniel P. Corson (danl(AT)MIT.EDU), Jan 09 2000
a(6) = 529200, a(7) = 75600 from Ulrich Hermisson (uhermiss(AT)rz.uni-leipzig.de), Feb 25 2003
More terms from Miodrag Zivkovic (ezivkovm(AT)matf.bg.ac.yu), Feb 28 2006
Showing 1-3 of 3 results.
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