%=======================================================================
%
%       Self-inverse permutations on n letters,
%       i.e. handshaking across a table, where not everybody is required
%       to shake, (or put in another way: some people may shake hands
%       with themselves).
%       Is enumerated by EIS A000085 (1,2,4,10,26,76,232,764,2620,9496,...)
%
% See also:
%
% http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000085
% http://www.research.att.com/~njas/sequences/a002694.gif
% http://www.iki.fi/~kartturi/matikka/ModFin/A001147.fnd
%
% http://arp.anu.edu.au/~jks/finder.html
%
%
%==========================================================================

sort {
        ELEM
        cardinality = 1
}


function {
        e:      ELEM,ELEM -> bool.
        f:      ELEM -> ELEM { cut }
}


clause {
        e(x,y) -> e(y,x).                       % Symmetric, if x shakes with y, then vice versa also.
        y=z; FALSE = e(x,y); FALSE = e(x,z).    % Each shakes with max one person.
        e(x,f(x)).                              % Everybody shakes hands with somebody.
}

setting {
        verbosity stats: full
        stack: maximal
}


end