%=======================================================================
%
%       
%       Handshaking across a table (everybody shaking), with
%       an extra condition. Failed attempt of A000108A.fnd
%       SEEMS (Check it!) to be enumerated by EIS A000110 (Bell numbers),
%       but aerated (0,1,0,2,0,5,0,15,0,52,0,203,0,877,0,4140,0,21147,...)
%       because we get no solutions when there are odd number of shakers.
%
% See also:
%
% http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000110
% http://www.iki.fi/~kartturi/matikka/ModFin/A000108A.fnd
% http://www.research.att.com/~njas/sequences/a002694.gif
% http://mathforum.org/advanced/robertd/bell.html
% http://www.iki.fi/~kartturi/matikka/ModFin/A001147A.fnd
%
% http://arp.anu.edu.au/~jks/finder.html
%
%
%==========================================================================

sort {
        ELEM
        cardinality = 16
}


function {
        f:      ELEM -> ELEM { bijective }
}


clause {
        f(x) = x -> FALSE.                      % No fixed points.
        f(x) = y -> f(y) = x.                   % Just transpositions, no larger cycles.
        FALSE = (f(x) = y); FALSE = (y > x); f(y-1) > x.
        FALSE = (f(x) = y); FALSE = (y > x); FALSE = (f(y-1) > y).
}

setting {
        verbosity stats: full
        stack: maximal
}


end