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… 
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