# Questions tagged [permanent]

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### Complexity of computing generalised determinants. (P - #P transition)

Computing the determinant of a matrix can be done in polynomial time, while computing the permanent is known to be #P-hard. Let $A$ be an $n \times n$ matrix. Define a generalised determinant function ...
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### Is Permanent $+$-reducible?

Suppose we have two bipartite graphs $G_1$ and $G_2$ with perfect matching count $P_1$ and $P_2$ respectively then their disjoint union gives a bipartite graph with perfect matching $P_1P_2$. Is ...
84 views

### On permanent mod $3^t$ computation

By $'$ I mean transpose. I gather the info here from rjlipton.wordpress.com/2014/12/21/modulating-the-permanent. We know that if $U\in\Bbb F_{3^t}^{n\times n}$ satisfies $UU'=I_n$ in $\Bbb F_{3^t}$ ...
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### A succinct version of permanent that is $EXP$-complete

Succinct version of permanent is $NEXP$-hard (https://eccc.weizmann.ac.il/report/2012/086/) and so unlikely to be $EXP$-complete. Permanent mod $2$ is in $\oplus L$ and so succinct version is ...
71 views

### Approximating max degree $3$ perfect matching count?

We do not have a deterministic constant factor approximation scheme for general $n\times n$ $0/1$ permanent. What is the best factor in deterministic approximation schemes if we only care counting ...
134 views

### What is known about counting bipartite perfect matching with average degree in $[2,3]$ and max degree $3$?

We know counting perfect matching for bipartite graphs with vertex degree $2$ is in $P$ while counting perfect matching for graphs with vertex degree $3$ is in $\#P$. We also know there are degree $3$...
142 views

### Application of weak determinantal identities to GCT?

In general determinants have many identities. Would it help the $GCT$ program by invoking the paradigm of identities such as to state that if the permanent is converted to determinant then it has to ...
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### On the permanent mod $p$

Computing the permanent $\bmod p$ of an $n\times n$ $0/1$-matrix is $\#P$-complete if $p$ is a prime $p>n$. We have an FPTAS for approximating the $0/1$ integer matrix permanent over the reals. ...
137 views

### Quantum algorithms for generalizations of determinants

There are a wide variety of determent-like constructions. Some like the permanent or immanents are variations on the ordinary determinant for matrices over fields or commutative rings. Some like ...
173 views

### Implications of a recent negative result to geometric complexity

A paper was posted in arxiv http://arxiv.org/pdf/1512.03798.pdf titled 'Rectangular Kronecker coefficients and plethysms in geometric complexity theory' by Christian Ikenmeyer and Greta Panova with ...
1k views

### Matrix permanent is 0

Valiant's theorem says that computing the permanent of an $n\times n$ matrix is #P-hard. Is the problem of determining if a permanent is 0 any easier? This arises in the context of sequence A006063 in ...
257 views

### The complexity of decomposing a bi-stochastic matrix

A bistochastic matrix $A$ is a matrix with positive entries in which each row/column sums to $1$. By the Birkhoff von-Neumann theorem $A$ is a convex combination of permutation matrices. Further, by ...
511 views

### Conditional results implying difficulty of improving upper/lower bounds for permanent

Let $A$ be a given square matrix. Is there any evidence that beating quadratic lower bounds for $B$ such that $\text{det}(B) = \text{per}(A)$ could be hard? Is there any plausible conjecture which ...