Determinant versus permanent
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چکیده
منابع مشابه
Generalized matrix functions, determinant and permanent
In this paper, using permutation matrices or symmetric matrices, necessary and sufficient conditions are given for a generalized matrix function to be the determinant or the permanent. We prove that a generalized matrix function is the determinant or the permanent if and only if it preserves the product of symmetric permutation matrices. Also we show that a generalized matrix function is the de...
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The Permanent versus Determinant problem is the following: Given an n × n matrix X of indeterminates over a field of characteristic different from two, find the smallest matrix M whose coefficients are linear functions in the indeterminates such that the permanent of X equals the determinant of M. We prove that the dimensions of M are at most 2n − 1. The determinant and the permanent of an (n ×...
متن کاملDeterminant Versus Permanent
We study the problem of expressing permanents of matrices as determinants of (possibly larger) matrices. This problem has close connections to the complexity of arithmetic computations: the complexities of computing permanent and determinant roughly correspond to arithmetic versions of the classes NP and P respectively. We survey known results about their relative complexity and describe two re...
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Let Detn denote the closure of the GLn2(C)-orbit of the determinant polynomial detn with respect to linear substitution. The highest weights (partitions) of irreducible GL n 2(C)-representations occurring in the coordinate ring of Detn form a finitely generated monoid S(Detn). We prove that the saturation of S(Detn) contains all partitions λ with length at most n and size divisible by n. This i...
متن کاملDeterminant versus Permanent: salvation via generalization? The algebraic complexity of the Fermionant and the Immanant
The fermionant Fermn(x̄) = ∑ σ∈Sn (−k)c(π) ∏n i=1 xi,j can be seen as a generalization of both the permanent (for k = −1) and the determinant (for k = 1). We demonstrate that it is VNP-complete for any rational k , 1. Furthermore it is #P -complete for the same values of k. The immanant is also a generalization of the permanent (for a Young diagram with a single line) and of the determinant (whe...
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