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.
- Permanent supports a Method option. Possible settings include "MemoizedExpansion", "MixedCoefficient", "Glynn" and "Ryser". The default setting of Automatic switches among these methods depending on the matrix given.
Examplesopen allclose all
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:
Properties & Relations (4)
The determinant Det has the same terms as the permanent, except for sign changes:
Wolfram Research (2015), Permanent, Wolfram Language function, https://reference.wolfram.com/language/ref/Permanent.html (updated 2021).
Wolfram Language. 2015. "Permanent." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/Permanent.html.
Wolfram Language. (2015). Permanent. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Permanent.html