Permanent
Permanent[m]
gives the permanent of the square matrix m.
Details and Options

- Permanent works with both numeric and symbolic matrices.
- The permanent of an
matrix m is given by
, where the
are the permutations of
elements.
Examples
open allclose allScope (1)
Applications (3)
The permanent of a square matrix of all ones is the factorial of the dimension:
The permanent of a square matrix of all ones minus the identity matrix counts the number of derangements of the corresponding dimension:
Given n sets, each containing a subset of (1 …n), the number of ways to choose a distinct element from each subset is equal to the permanent of the 0‐1 matrix where the (i,j) position contains a 1 exactly when subset i contains j:
There are two ways to create sets with distinct elements from each subset:
Properties & Relations (4)
The permanent is a polynomial of its entries. Degree 2 for a matrix:
The determinant Det has the same terms as the permanent, except for sign changes:
The permanent is the outer product of the matrix rows, with terms having the repeated column index removed:
Text
Wolfram Research (2015), Permanent, Wolfram Language function, https://reference.wolfram.com/language/ref/Permanent.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 2015. "Permanent." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Permanent.html.
APA
Wolfram Language. (2015). Permanent. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Permanent.html