hadamard_6
POLIPlibrary for polynomially constrained
| ||
hadamard_6| Name | hadamard_6 |
| Classification | nc|b|d6 |
| Problem type | hadamard |
| Description | Maximize determinant of 6 times 6 binary matrix |
| Objective sense | max |
| Variables | 36 (36 binary, 0 general integer, 0 continuous) |
| Nonlinear variables | 36 |
| Constraints | 0 |
| Nonlinear constraints | 0 |
| Linear nonzeros | 0 |
| Nonlinear nonzeros | 720 |
| Download | hadamard_6.pip.gz |
| Best known solution | |
| Best known objective | 9 |
| Best known bound | 9 |
| Originator | Marc Pfetsch |
| Formulator | Marc Pfetsch |
| Donator | Marc Pfetsch |
| References | |
| Links | |
| Additional information | Let a(n) be the maximal determinant of a 0/1-matrix of size
n by n. Hadamard proved that a(n) ≤
2(-n) (n+1)((n+1)/2). A Hadamard matrix
attains this bound. The Hadamard conjecture states that this is the
case if and only if n+1 is 1 or 2 or a multiple of 4. The
values of a(n) for small n are known. See the on-line encyclopedia of integer
sequences for more information.
|
© by maintainers | last update LAST_CHANGE | imprint