In computational complexity theory, the complexity class #P (pronounced "number P" or, sometimes "sharp P" or "hash P") is the set of the counting problems associated with the decision problems in the set NP. More formally, #P is the class of function problems of the form "compute ƒ(x)", where ƒ is the number of accepting paths of a nondeterministic Turing machine running in polynomial time. Unlike most well-known complexity classes, it is not a class of decision problems but a class of function problems.
== Relation to decision problems ==
An NP decision problem is often of the form "Are there...
The #P-completeness of 01-permanent, sometimes known as Valiant's theorem, is a mathematical proof about the permanent of matrices, considered a seminal result in computational complexity theory. In a 1979 scholarly paper, Leslie Valiant proved that the computational problem of computing the permanent of a matrix is #P-hard, even if the matrix is restricted to have entries that are all 0 or 1. In this restricted case, computing the permanent is even #P-complete, because it corresponds to the #P problem of counting the number of permutation matrices one can get by changing ones into zeroes.
Valiant...
Immanant redirects here; it should not be confused with the philosophical immanent.
In mathematics, the immanant of a matrix was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent.
Let
λ
=
(
λ
1
,
λ
2
,
…
)
{\displaystyle \lambda =(\lambda _{1},\lambda _{2},\ldots )}
be a partition of
...
