Declarations of functions associated with group_W.
Version of Sunday 15 September 2024.

The following declarations, all private, are found in file group_A/permzbi_A5.h:

    class SJT {
        friend bool permzbi::next_perm_SJT_modify (int begin, int end);
        friend bool permzbi::prev_perm_SJT_modify (int begin, int end);

        /* W1 */ static int  sign (SVI const & per, int const hi);
        /* W1 */ static int  seek (SVI const & per, int const hi);
        /* W1 */ static bool is_ident (SVI & per);        
        /* W1 */ static bool next (SVI & per);
        /* W1 */ static bool prev (SVI & per);           
   };

These functions support calculations for the SJT sequence of permutations as invoked from class permzbi. However, they are declared outside of class permzbi because the SJT code is lengthy, and class permzbi is already too complicated.

For any permzbi P with at least two components:

• the difference between
  • P
  • P.next_perm_SJT_create().p
  is that exactly two components have been exchanged, and they are consecutive.
• the difference between
  • P.inverse()
  • P.inverse().next_perm_SJT_create().p
  is that exactly two components have been exchanged, but they might not be consecutive.