A350565 a(n) is the minimum permanent of an n X n matrix using the integers 1 to n^2.
1, 1, 10, 436, 52197, 13300936, 6192060119
Offset: 0
Examples
a(2) = 10:
[1, 3;
2, 4]
.
a(3) = 436:
[1, 3, 2;
4, 8, 6;
5, 9, 7]
.
a(4) = 52197:
[1, 2, 4, 3;
6, 9, 15, 12;
5, 8, 13, 11;
7, 10, 16, 14]
.
a(5) = 13300936:
[16, 8, 24, 21, 12;
18, 9, 25, 23, 13;
3, 1, 5, 4, 2;
14, 6, 20, 17, 10;
15, 7, 22, 19, 11]
.
a(6) = 6192060119:
[36, 35, 33, 31, 27, 6;
11, 10, 9, 8, 7, 1;
34, 32, 30, 28, 25, 5;
22, 21, 19, 18, 16, 3;
29, 26, 24, 23, 20, 4;
17, 15, 14, 13, 12, 2]
Links
- Carl-Erik Fröberg, On a combinatorial problem related to permanents, BIT 28 (1988), No. 3, 406-411.
Programs
-
Python
from itertools import permutations from sympy import Matrix def A350565(n): return 1 if n == 0 else min(Matrix(n,n,p).per() for p in permutations(range(1,n**2+1))) # Chai Wah Wu, Jan 21 2022
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