Declarations of functions associated with group_R.
Version of Saturday 14 September 2024.

    /* R1 */ int  qty_deranged (permzbi const & a);
    /* R1 */ int  qty_deranged (permzbi const & a, permzbi const & b);
    /* R1 */ bool all_deranged (permzbi const & a);
    /* R1 */ bool all_deranged (permzbi const & a, permzbi const & b);
    /* R1 */ int  conjunctions (std::initializer_list ilp); 
    /* R1 */ bool are_disjoint (std::initializer_list ilp); 

Although the two-parameter version of qty_deranged could have been made a member function, the asymmetric syntax of calling it would have seemed awkward, so it is a non-member. Then to be consistent, qty_deranged with only one parameter needed also to be a non-member function. The same comments of course apply to all_deranged.

    /* R2 */ double correlation (permzbi const & a, permzbi const & b);
    /* R2 */ double angle (permzbi const & a, permzbi const & b);

correlation gives the Pearson correlation coefficient. Note that Spearman's rank correlation coefficient would have the same value, because a permutation of consecutive integers is self-ranking.

Function angle gives the angle in radians between the two permutations, interpreting them as vectors.