A350931
Maximal determinant of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 7, 105, 2294, 71753, 3051554, 175457984
Offset: 0
a(2) = 7:
[3 1]
[2 3]
a(3) = 105:
[5 1 3]
[4 5 1]
[2 4 5]
-
from itertools import permutations
from sympy import Matrix
def A350931(n): return max(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).det() for p in permutations(range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A350937
Minimal permanent of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 7, 89, 2287, 89025, 5141775, 404316249
Offset: 0
a(2) = 7:
1 2
3 1
a(3) = 89:
1 2 4
3 1 2
5 3 1
-
from itertools import permutations
from sympy import Matrix
def A350937(n): return 1 if n == 0 else min(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).per() for p in permutations(range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A350938
Maximal permanent of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 11, 296, 14502, 1153889, 134713213, 21788125930
Offset: 0
a(2) = 11:
3 1
2 3
a(3) = 296:
5 3 2
4 5 3
1 4 5
-
from itertools import permutations
from sympy import Matrix
def A350938(n): return 1 if n == 0 else max(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).per() for p in permutations(range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A350930
Minimal determinant of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, -5, -42, -1810, -48098, -2737409, -114381074
Offset: 0
a(2) = -5:
[1 2]
[3 1]
a(3) = -42:
[3 4 1]
[5 3 4]
[2 5 3]
-
from itertools import permutations
from sympy import Matrix
def A350930(n): return min(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).det() for p in permutations(range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A323255
The permanent of an n X n Toeplitz matrix M(n) whose first row consists of successive positive integer numbers 2*n - 1, n - 1, ..., 1 and whose first column consists of 2*n - 1, 2*n - 2, ..., n.
Original entry on oeis.org
1, 1, 11, 248, 9968, 638772, 60061657, 7798036000, 1336715859150, 292406145227392, 79483340339739367, 26280500564448081664, 10386012861097225139356, 4834639222955142417477888, 2618110215141486526589786501, 1631888040186649673361825042432, 1159983453675106278249250918734938
Offset: 0
For n = 1 the matrix M(1) is
1
with permanent a(1) = 1.
For n = 2 the matrix M(2) is
3, 1
2, 3
with permanent a(2) = 11.
For n = 3 the matrix M(3) is
5, 2, 1
4, 5, 2
3, 4, 5
with permanent a(3) = 248.
Cf.
A323254 (determinant of matrix M(n)).
-
b[i_]:=i; a[n_]:=If[n==0, 1, Permanent[ToeplitzMatrix[Join[{b[2*n-1]}, Array[b, n-1, {2*n-2,n }]], Join[{b[2*n-1]},Array[b, n-1, {n-1,1}]]]]]; Array[a, 16, 0]
-
tm(n) = {my(m = matrix(n, n, i, j, if (j==1, 2*n-i, n-j+1))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m;}
a(n) = matpermanent(tm(n)); \\ Stefano Spezia, Dec 11 2019
Showing 1-5 of 5 results.
Comments