%=======================================================================
%
%       
%       Handshaking across a table (everybody shaking), with
%       extra conditions.
%       Is enumerated by (0,1,0,2,0,5,0,14,0,43,0,143,0,510,0,1936,...)
%       whose bisection is NOT in OEIS.
%       (There are three sequences which begin as 1,2,5,14,43,143,...)
%
% See also:
%
% http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000110
% http://www.research.att.com/~njas/sequences/a002694.gif
% http://www.iki.fi/~kartturi/matikka/ModFin/A000110A.fnd
%
% http://arp.anu.edu.au/~jks/finder.html
%
%
%==========================================================================

sort {
        ELEM
        cardinality = 10
}


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).
        FALSE = (f(x) = y); FALSE = (y > x); f(x+1) < y.
        FALSE = (f(x) = y); FALSE = (y > x); FALSE = (f(x+1) < x).
}

setting {
        verbosity stats: full
        stack: maximal
}


end