A087983
Number of different values taken by permanent of n X n (0,1)-matrix.
Original entry on oeis.org
1, 2, 3, 6, 16, 51, 220, 1179, 7980
Offset: 0
For a 4 X 4 matrix the 16 possible permanents and their multiplicieties are:
{{0, 27713}, {1, 13032}, {2, 10800}, {3, 4992}, {4, 4254}, {5, 1440}, {6, 1536}, {7, 576}, {8, 648}, {9, 24}, {10, 288}, {11, 96}, {12, 48}, {14, 72}, {18, 16}, {24, 1}}
A013588
Smallest positive integer not the determinant of an n X n {0,1}-matrix.
Original entry on oeis.org
2, 2, 3, 4, 6, 10, 19, 41, 103, 269
Offset: 1
Gerhard R. Paseman (paseman(AT)prado.com)
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.
- Swee Hong Chan and Igor Pak, Computational complexity of counting coincidences, arXiv:2308.10214 [math.CO], 2023. See p. 18.
- 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.
- William P. Orrick, The maximal {-1, 1}-determinant of order 15, arXiv:math/0401179 [math.CO], 2004.
- William P. Orrick, Spectrum of the determinant function.
- G. R. Paseman, A Different Approach to Hadamard's Maximum Determinant Problem
- G. R. Paseman, Related Material
- Rikhav Shah, Determinants of binary matrices achieve every integral value up to Ω(2^n/n), Linear Algebra and its Applications, Volume 645, 2022, pp. 229-236.
- Miodrag Živković, 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.
- Miodrag Živković, Classification of small (0,1) matrices, arXiv:math/0511636 [math.CO], 2005.
- Index entries for sequences related to binary matrices
- Index entries for sequences related to maximal determinants
-
from itertools import product
from sympy import Matrix
def A013588(n):
s, k = set(Matrix(n,n,p).det() for p in product([0,1],repeat=n**2)), 1
while k in s:
k += 1
return k # Chai Wah Wu, Oct 01 2021
Extended by
William P. 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.
A118985
Number of different values taken by the determinant of a symmetric real (0,1)-matrix of order n.
Original entry on oeis.org
1, 2, 3, 5, 7, 11, 19, 40, 91, 214, 577
Offset: 0
Cf.
A006125 (number of symmetric real (0,1)-matrices of order (n-1)).
A089478
Triangle T(n,k) read by rows, where T(n,k) = number of times the determinant of a real n X n (0,1)-matrix takes the value k, for n >= 0, 0 <= k <= A003432(n).
Original entry on oeis.org
0, 1, 1, 1, 10, 3, 338, 84, 3, 42976, 10020, 1200, 60, 21040112, 4851360, 1213920, 144720, 43560, 3600, 39882864736, 9240051240, 3868663680, 768723480, 418703040, 63612360, 46569600, 6438600, 5014800, 529200, 292604283435872
Offset: 0
a(4) = T(2,1) = 3 because there are 3 different (0,1)-matrices with determinant=1:
((1,0),(0,1)), ((1,1),(0,1)), ((1,0),(1,1)).
Triangle T(n,k) begins:
0, 1;
1, 1;
10, 3;
338, 84, 3;
42976, 10020, 1200, 60;
21040112, 4851360, 1213920, 144720, 43560, 3600;
...
The n-th row of the table contains
A089472(n) nonzero entries.
A118987
Number of different values taken by the determinant of a symmetric real (+1,-1)-matrix of order n.
Original entry on oeis.org
1, 2, 2, 3, 5, 7, 11, 19, 40, 91, 214
Offset: 0
Cf.
A006125 (number of symmetric real (+1,-1)-matrices of order (n-1)).
A099834
Maximum number of different determinants that can be produced by permuting the elements of a 3 X 3 integer matrix with nonnegative entries <= n.
Original entry on oeis.org
5, 15, 53, 109, 209, 351, 573, 811, 1193, 1509, 1971, 2501, 3183, 3769, 4511, 5025, 5641, 6165, 6600, 6964, 7354, 7696, 7960, 8110, 8404, 8606, 8704, 8846, 8962, 9125, 9210, 9284, 9362, 9420
Offset: 1
a(10)=1509: A corresponding set of matrix elements is {10,9,9,8,7,5,2,1,0}.
Cf.
A099815 largest determinant that can be produced by the optimal set of matrix elements.
A108150
Number of different nonnegative values taken by the determinant of a real (0,1)-matrix of order n.
Original entry on oeis.org
1, 2, 2, 3, 4, 6, 10, 22, 46, 114, 294
Offset: 0
- For references and links see A089472.
A373915
Determinants of symmetric real {0,1}-matrices of order 9 that only occur as positive values.
Original entry on oeis.org
89, 94, 95, 97, 98, 99, 101, 102, 105, 110, 116, 125, 144
Offset: 1
A306837
Number of unimodular n X n matrices with elements {0, 1}.
Original entry on oeis.org
1, 6, 168, 20040, 9702720, 18480102480, 135491563468800, 3766962568171582080
Offset: 1
Number of different values taken by the determinant is in
A089472.
A363862 gives equivalence classes up to row and column permutation.
A373916
Numbers that are the determinant of real {0,1}-matrices of order 10, but not of symmetric such matrices.
Original entry on oeis.org
253, 268, 274, 294, 304
Offset: 1
Showing 1-10 of 12 results.
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