A350937 Minimal permanent of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.

1, 1, 7, 89, 2287, 89025, 5141775, 404316249

Offset: 0

Author

Stefano Spezia, Jan 26 2022

Keywords

• nonn
• hard
• more

Comments

At least up to a(7) the minimal permanent is attained by a matrix which has 1, 3, 5, ... as first row and 1, 2, 4, 6,... as first column. - Giovanni Resta, Oct 13 2022

Also minimal permanent of an n X n Hankel matrix using the integers 1 to 2*n - 1. - Stefano Spezia, Dec 22 2023

Examples

			a(2) = 7:
    1    2
    3    1
a(3) = 89:
    1    2    4
    3    1    2
    5    3    1
		

Links

• Lucas A. Brown, A350937+8.sage
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A322908, A323254, A350930, A350938 (maximal).

Programs

Python

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

Extensions

a(5) from Alois P. Heinz, Jan 26 2022

a(6) from Lucas A. Brown, Sep 04 2022

a(7) from Giovanni Resta, Oct 13 2022