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
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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
A351019
Minimal permanent of an n X n symmetric Toeplitz matrix using the integers 1 to n.
Original entry on oeis.org
1, 1, 5, 36, 480, 9991, 296913, 12099604, 637590728, 43090005714, 3550491371994, 359557627057876
Offset: 0
a(3) = 36:
2 1 3
1 2 1
3 1 2
a(4) = 480:
2 1 3 4
1 2 1 3
3 1 2 1
4 3 1 2
a(5) = 9991:
3 1 2 4 5
1 3 1 2 4
2 1 3 1 2
4 2 1 3 1
5 4 2 1 3
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from itertools import permutations
from sympy import Matrix
def A351019(n): return 1 if n == 0 else min(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).per() for p in permutations(range(1,n+1))) # Chai Wah Wu, Jan 31 2022
A358569
a(n) is the minimal permanent of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1).
Original entry on oeis.org
1, 0, 1, 16, 451, 17376, 1022546
Offset: 0
a(2) = 1:
[1, 0;
2, 1]
a(3) = 16:
[0, 1, 3;
2, 0, 1;
4, 2, 0]
A350939
Minimal permanent of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers.
Original entry on oeis.org
1, 2, 19, 496, 29609, 3009106, 498206489
Offset: 0
a(2) = 19:
2 3
5 2
a(3) = 496:
2 3 7
5 2 3
11 5 2
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a[n_] := Min[Table[Permanent[HankelMatrix[Join[Drop[per = Part[Permutations[Prime[Range[2 n - 1]]], i], n], {Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]], {i, (2 n - 1) !}]]; Join[{1}, Array[a, 5]] (* Stefano Spezia, Feb 06 2024 *)
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a(n) = my(v=[1..2*n-1], m=+oo, d); forperm(v, p, d = matpermanent(matrix(n, n, i, j, prime(p[i+j-1]))); if (dMichel Marcus, Feb 08 2024
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from itertools import permutations
from sympy import Matrix, prime
def A350939(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(prime(i) for i in range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A368351
a(n) is the minimal determinant of an n X n Hankel matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, -7, -105, -1810, -48098, -3051554, -175457984
Offset: 0
a(2) = -7:
2, 3;
3, 1.
a(3) = -105:
2, 4, 5;
4, 5, 1;
5, 1, 3.
a(4) = -1810:
4, 3, 7, 1;
3, 7, 1, 2;
7, 1, 2, 5;
1, 2, 5, 6.
A368352
a(n) is the maximal determinant of an n X n Hankel matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 5, 42, 2294, 71753, 2737409, 114381074
Offset: 0
a(2) = 5:
3, 1;
1, 2.
a(3) = 42:
2, 5, 3;
5, 3, 4;
3, 4, 1.
a(4) = 2294:
2, 3, 6, 7;
3, 6, 7, 1;
6, 7, 1, 5;
7, 1, 5, 4.
A351610
Minimal permanent of an n X n symmetric matrix using the integers 1 to n*(n + 1)/2.
Original entry on oeis.org
1, 1, 7, 163, 9850, 1243806, 284995981
Offset: 0
a(3) = 163:
1 2 3
2 5 4
3 4 6
a(4) = 9850:
1 2 3 4
2 8 5 6
3 5 9 7
4 6 7 10
A369943
a(n) is the number of distinct values of the permanent of an n X n Hankel matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 2, 49, 2117, 156189, 16943487
Offset: 0
-
a[n_] := CountDistinct[Table[Permanent[HankelMatrix[Join[Drop[per = Part[Permutations[Range[2 n - 1]], i], n],{Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]], {i, (2 n - 1) !}]]; Join[{1}, Array[a, 5]]
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a(n) = my(v=[1..2*n-1], list=List()); forperm(v, p, listput(list, matpermanent(matrix(n, n, i, j, p[i+j-1])));); #Set(list); \\ Michel Marcus, Feb 08 2024
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from itertools import permutations
from sympy import Matrix
def A369943(n): return len({Matrix([p[i:i+n] for i in range(n)]).per() for p in permutations(range(1,n<<1))}) # Chai Wah Wu, Feb 12 2024
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