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[m,Modulus->n] computes the permanent modulo n.
- 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
This is faster than computing Mod[Permanent[m],47]:
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 (5)
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 2022).
Wolfram Language. 2015. "Permanent." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. 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