Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix

@article{Kocharovsky2021ExactRC,
  title={Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix},
  author={Vitaly Kocharovsky and Vl. V. Kocharovsky and V. Yu. Martyanov and Sergey V. Tarasov},
  journal={Entropy},
  year={2021},
  volume={23}
}
We present a finite-order system of recurrence relations for the permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k=1,2 and 3) and the method for deriving such recurrence relations, which is based on the permanents of the matrices with defects. The proposed system of linear recurrence equations with variable coefficients provides a powerful tool for the analysis of the circulant permanents, their fast, linear-time computing; and finding… Expand

References

SHOWING 1-10 OF 84 REFERENCES
Permanental compounds and permanents of (0, 1)-circulants
Abstract It was shown by the author in a recent paper that a recurrence relation for permanents of (0, 1)-circulants can be generated from the product of the characteristic polynomials of permanentalExpand
Efficient Computation of the Permanent of Block Factorizable Matrices
TLDR
It is shown that a factorization into a product of block diagonal matrices gives rise to a circuit acting on a Hilbert space with a tensor product structure and that the permanent is equal to the transition amplitude of this circuit and a product basis state. Expand
On permanental polynomials of certain random matrices
The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrixExpand
On the permanents of circulant and degenerate Schur matrices
Abstract We communicate three formulas for the permanents of degenerate Schur and circulant matrices. These combinatorial and integral formulas are intended for the analytical and asymptoticExpand
Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity
We reveal the analytic relations between a matrix permanent and major nature’s complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-bodyExpand
The μ-permanent of a tridiagonal matrix, orthogonal polynomials, and chain sequences
Abstract Let A = ( a ij ) be an n × n complex matrix. For any real μ , define the polynomial P μ ( A ) = ∑ σ ∈ S n a 1 σ ( 1 ) ⋯ a n σ ( n ) μ l ( σ ) , where l ( σ ) is the number of inversions ofExpand
Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices
We present a new efficient method for computing the permanent and Hafnian of certain banded Toeplitz matrices. The method covers non-trivial cases for which previous known methods do not apply. TheExpand
How fast can one compute the permanent of circulant matrices
Abstract In this paper we address the problem of computing the permanent of (0,1)-circulant matrices. We investigate structural properties of circulant matrices, showing that (i) if they are denseExpand
The Number of Terms in the Permanent and the Determinant of a Generic Circulant Matrix
Let A = (aij) be the generic n × n circulant matrix given by aij = xi + j, with subscripts on x interpreted mod n. Define d(n) (resp. p(n)) to be the number of terms in the determinant (resp.Expand
A note on permanents and generalized complementary basic matrices
Abstract We say that the product of a row vector and a column vector is intrinsic if there is at most one non-zero product of corresponding coordinates. Analogously we speak about intrinsic productExpand
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