Paired-Permanent Determinant PPD Function

According to the symmetry properties of off fP), one can divide row and column indices of a PPD into two sets paired symmetry indices (PSI) z, z TV- 2S, and anti-symmetry indices (ASI) z, z TV-25. Furthermore, 2k-1 (2k) is refered to as the partner of z = 2k (2 k- ), denoted as z, if z is a PSI. Evidently, PPDs shares symmetries similar to the BTs, as follows  

A) is invariant under exchange between row (column) z and row (column) z, 

Various PPDs may be obtained by exchanging the row (column) indices for a given matrix A. The total number of the PPDs is 

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