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def rowvacuation(P,I): r = P.rank() f = P.rank_function() my_order_ideal = I for i in range(r+1): for j in range(r+1-i): s = r+1-j-1 for x in P: if f(x)==s: my_order_ideal = P.order_ideal_toggle(my_order_ideal,x) return my_order_ideal
a = 2 b = 2 P = Posets.ChainPoset(a).product(Posets.ChainPoset(b)) P.show() for I in P.order_ideals_lattice(facade=true): print I print rowvacuation (P,I) print
{} {(0, 1), (1, 0), (0, 0), (1, 1)} {(0, 0)} {(0, 1), (1, 0), (0, 0)} {(1, 0), (0, 0)} {(1, 0), (0, 0)} {(0, 1), (0, 0)} {(0, 1), (0, 0)} {(0, 1), (1, 0), (0, 0)} {(0, 0)} {(0, 1), (1, 0), (0, 0), (1, 1)} {}
n=4 P = Posets.BooleanLattice(n) P.show() for I in P.order_ideals_lattice(facade=true): J=rowvacuation (P,I) print I print J print I.cardinality()+J.cardinality() print
{} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} 16 {0} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} 16 {0, 8} {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14} 16 {0, 4} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14} 16 {0, 1} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} 16 {0, 1, 4} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13} 16 {0, 1, 4, 5} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13} 16 {0, 1, 8} {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13} 16 {0, 1, 8, 9} {0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13} 16 {0, 2} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14} 16 {0, 2, 4} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14} 16 {0, 2, 4, 6} {0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14} 16 {0, 8, 2} {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14} 16 {0, 8, 2, 10} {0, 1, 2, 3, 4, 6, 8, 9, 10, 11, 12, 14} 16 {0, 1, 2} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} 16 {0, 1, 2, 8} {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12} 16 {0, 1, 2, 3} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} 16 {0, 1, 2, 3, 8} {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11} 16 {0, 1, 2, 4} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12} 16 {0, 1, 2, 4, 5} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12} 16 {0, 1, 2, 4, 6} {0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12} 16 {0, 1, 2, 4, 5, 6} {0, 1, 2, 3, 4, 5, 6, 7, 8, 12} 16 {0, 1, 2, 10, 8} {0, 1, 2, 3, 4, 6, 8, 9, 10, 11, 12} 16 {0, 1, 2, 3, 8, 10} {0, 1, 2, 3, 4, 6, 8, 9, 10, 11} 16 {0, 1, 2, 8, 9} {0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 12} 16 {0, 1, 2, 8, 9, 10} {0, 1, 2, 3, 4, 8, 9, 10, 11, 12} 16 {0, 1, 2, 3, 8, 9} {0, 1, 2, 3, 4, 5, 8, 9, 10, 11} 16 {0, 1, 2, 3, 8, 9, 10} {0, 1, 2, 3, 4, 8, 9, 10, 11} 16 {0, 8, 4} {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14} 16 {0, 8, 4, 12} {0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14} 16 {0, 8, 2, 4} {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14} 16 {0, 8, 2, 4, 6} {0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 14} 16 {0, 8, 2, 4, 12} {0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 14} 16 {0, 2, 4, 6, 8, 12} {0, 1, 2, 4, 5, 6, 8, 10, 12, 14} 16 {0, 8, 2, 4, 10} {0, 1, 2, 3, 4, 6, 8, 9, 10, 12, 14} 16 {0, 2, 4, 6, 8, 10} {0, 1, 2, 3, 4, 6, 8, 10, 12, 14} 16 {0, 2, 4, 8, 10, 12} {0, 1, 2, 4, 6, 8, 9, 10, 12, 14} 16 {0, 2, 4, 6, 8, 10, 12} {0, 1, 2, 4, 6, 8, 10, 12, 14} 16 {0, 2, 4, 6, 8, 10, 12, 14} {0, 2, 4, 6, 8, 10, 12, 14} 16 {0, 1, 4, 8} {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13} 16 {0, 1, 4, 8, 12} {0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 13} 16 {0, 1, 4, 5, 8} {0, 1, 2, 3, 4, 5, 6, 8, 9, 12, 13} 16 {0, 1, 4, 5, 8, 12} {0, 1, 2, 4, 5, 6, 8, 9, 12, 13} 16 {0, 1, 4, 8, 9} {0, 1, 2, 3, 4, 5, 8, 9, 10, 12, 13} 16 {0, 1, 4, 8, 9, 12} {0, 1, 2, 4, 5, 8, 9, 10, 12, 13} 16 {0, 1, 4, 5, 8, 9} {0, 1, 2, 3, 4, 5, 8, 9, 12, 13} 16 {0, 1, 4, 5, 8, 9, 12} {0, 1, 2, 4, 5, 8, 9, 12, 13} 16 {0, 1, 4, 5, 8, 9, 12, 13} {0, 1, 4, 5, 8, 9, 12, 13} 16 {0, 1, 2, 4, 8} {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12} 16 {0, 1, 2, 4, 8, 10} {0, 1, 2, 3, 4, 6, 8, 9, 10, 12} 16 {0, 1, 2, 4, 8, 12} {0, 1, 2, 4, 5, 6, 8, 9, 10, 12} 16 {0, 1, 2, 4, 8, 10, 12} {0, 1, 2, 4, 6, 8, 9, 10, 12} 16 {0, 1, 2, 4, 8, 9} {0, 1, 2, 3, 4, 5, 8, 9, 10, 12} 16 {0, 1, 2, 4, 8, 9, 10} {0, 1, 2, 3, 4, 8, 9, 10, 12} 16 {0, 1, 2, 4, 8, 9, 12} {0, 1, 2, 4, 5, 8, 9, 10, 12} 16 {0, 1, 2, 4, 8, 9, 10, 12} {0, 1, 2, 4, 8, 9, 10, 12} 16 {0, 1, 2, 4, 5, 8} {0, 1, 2, 3, 4, 5, 6, 8, 9, 12} 16 {0, 1, 2, 4, 5, 8, 12} {0, 1, 2, 4, 5, 6, 8, 9, 12} 16 {0, 1, 2, 4, 5, 8, 10} {0, 1, 2, 3, 4, 6, 8, 9, 12} 16 {0, 1, 2, 4, 5, 8, 9} {0, 1, 2, 3, 4, 5, 8, 9, 12} 16 {0, 1, 2, 4, 5, 8, 9, 10} {0, 1, 2, 3, 4, 6, 8, 12} 16 {0, 1, 2, 4, 5, 8, 9, 12} {0, 1, 2, 4, 5, 8, 9, 12} 16 {0, 1, 2, 4, 5, 8, 9, 12, 13} {0, 1, 4, 5, 8, 9, 12} 16 {0, 1, 2, 3, 8, 9, 10, 11} {0, 1, 2, 3, 8, 9, 10, 11} 16 {0, 1, 2, 3, 4} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} 16 {0, 1, 2, 3, 4, 5} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} 16 {0, 1, 2, 3, 4, 6} {0, 1, 2, 3, 4, 5, 6, 7, 8, 10} 16 {0, 1, 2, 3, 4, 5, 6} {0, 1, 2, 3, 4, 5, 6, 7, 8} 16 {0, 1, 2, 3, 4, 5, 6, 7} {0, 1, 2, 3, 4, 5, 6, 7} 16 {0, 1, 2, 3, 4, 8} {0, 1, 2, 3, 4, 5, 6, 8, 9, 10} 16 {0, 1, 2, 3, 4, 8, 10} {0, 1, 2, 3, 4, 6, 8, 9, 10} 16 {0, 1, 2, 3, 4, 8, 9} {0, 1, 2, 3, 4, 5, 8, 9, 10} 16 {0, 1, 2, 3, 4, 8, 9, 10} {0, 1, 2, 3, 4, 8, 9, 10} 16 {0, 1, 2, 3, 4, 8, 9, 10, 11} {0, 1, 2, 3, 8, 9, 10} 16 {0, 1, 2, 3, 4, 5, 8} {0, 1, 2, 3, 4, 5, 6, 8, 9} 16 {0, 1, 2, 3, 4, 5, 8, 10} {0, 1, 2, 4, 6, 8, 9, 12} 16 {0, 1, 2, 3, 4, 5, 8, 9} {0, 1, 2, 3, 4, 5, 8, 9} 16 {0, 1, 2, 3, 4, 5, 8, 9, 10} {0, 1, 2, 3, 4, 8, 9} 16 {0, 1, 2, 3, 4, 5, 8, 9, 10, 11} {0, 1, 2, 3, 8, 9} 16 {0, 1, 2, 3, 4, 8, 12} {0, 1, 2, 4, 5, 6, 8, 9, 10} 16 {0, 1, 2, 3, 4, 5, 8, 12} {0, 1, 2, 4, 6, 8, 9, 10} 16 {0, 1, 2, 3, 4, 8, 10, 12} {0, 1, 2, 4, 5, 6, 8, 9} 16 {0, 1, 2, 3, 4, 8, 9, 12} {0, 1, 2, 4, 5, 6, 8, 10} 16 {0, 1, 2, 3, 4, 8, 9, 10, 12} {0, 1, 2, 4, 8, 9, 10} 16 {0, 1, 2, 3, 4, 8, 9, 10, 11, 12} {0, 1, 2, 8, 9, 10} 16 {0, 1, 2, 3, 4, 5, 8, 9, 12} {0, 1, 2, 4, 5, 8, 9} 16 {0, 1, 2, 3, 4, 5, 8, 9, 12, 13} {0, 1, 4, 5, 8, 9} 16 {0, 1, 2, 4, 6, 8} {0, 1, 2, 3, 4, 5, 6, 8, 10, 12} 16 {0, 1, 2, 3, 4, 6, 8} {0, 1, 2, 3, 4, 5, 6, 8, 10} 16 {0, 1, 2, 4, 5, 6, 8} {0, 1, 2, 3, 4, 5, 6, 8, 12} 16 {0, 1, 2, 3, 4, 5, 6, 8} {0, 1, 2, 3, 4, 5, 6, 8} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8} {0, 1, 2, 3, 4, 5, 6} 16 {0, 1, 2, 4, 6, 8, 9} {0, 1, 2, 3, 4, 5, 8, 10, 12} 16 {0, 1, 2, 3, 4, 6, 8, 9} {0, 1, 2, 4, 5, 8, 10, 12} 16 {0, 1, 2, 4, 5, 6, 8, 9} {0, 1, 2, 3, 4, 8, 10, 12} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9} {0, 1, 2, 3, 4, 5, 8} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} {0, 1, 2, 3, 4, 5} 16 {0, 1, 2, 4, 6, 8, 10} {0, 1, 2, 3, 4, 6, 8, 10, 12} 16 {0, 1, 2, 4, 5, 6, 8, 10} {0, 1, 2, 3, 4, 8, 9, 12} 16 {0, 1, 2, 4, 6, 8, 9, 10} {0, 1, 2, 3, 4, 5, 8, 12} 16 {0, 1, 2, 3, 4, 6, 8, 10} {0, 1, 2, 3, 4, 6, 8, 10} 16 {0, 1, 2, 3, 4, 6, 8, 9, 10} {0, 1, 2, 3, 4, 8, 10} 16 {0, 1, 2, 3, 4, 6, 8, 9, 10, 11} {0, 1, 2, 3, 8, 10} 16 {0, 1, 2, 3, 4, 5, 6, 8, 10} {0, 1, 2, 3, 4, 6, 8} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 10} {0, 1, 2, 3, 4, 6} 16 {0, 1, 2, 4, 6, 8, 12} {0, 1, 2, 4, 5, 6, 8, 10, 12} 16 {0, 1, 2, 4, 6, 8, 10, 12} {0, 1, 2, 4, 6, 8, 10, 12} 16 {0, 1, 2, 4, 6, 8, 10, 12, 14} {0, 2, 4, 6, 8, 10, 12} 16 {0, 1, 2, 4, 5, 6, 8, 12} {0, 1, 2, 4, 5, 6, 8, 12} 16 {0, 1, 2, 4, 6, 8, 9, 12} {0, 1, 2, 3, 4, 5, 8, 10} 16 {0, 1, 2, 4, 5, 6, 8, 9, 12} {0, 1, 2, 4, 5, 8, 12} 16 {0, 1, 2, 4, 5, 6, 8, 9, 12, 13} {0, 1, 4, 5, 8, 12} 16 {0, 1, 2, 4, 6, 8, 9, 10, 12} {0, 1, 2, 4, 8, 10, 12} 16 {0, 1, 2, 4, 6, 8, 9, 10, 12, 14} {0, 2, 4, 8, 10, 12} 16 {0, 1, 2, 3, 4, 6, 8, 12} {0, 1, 2, 4, 5, 8, 9, 10} 16 {0, 1, 2, 3, 4, 5, 6, 8, 12} {0, 1, 2, 4, 5, 6, 8} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 12} {0, 1, 2, 4, 5, 6} 16 {0, 1, 2, 3, 4, 6, 8, 10, 12} {0, 1, 2, 4, 6, 8, 10} 16 {0, 1, 2, 3, 4, 6, 8, 10, 12, 14} {0, 2, 4, 6, 8, 10} 16 {0, 1, 2, 3, 4, 6, 8, 9, 12} {0, 1, 2, 4, 5, 8, 10} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 12} {0, 1, 2, 4, 5, 8} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12} {0, 1, 2, 4, 5} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 12, 13} {0, 1, 4, 5, 8} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13} {0, 1, 4, 5} 16 {0, 1, 2, 3, 4, 6, 8, 9, 10, 12} {0, 1, 2, 4, 8, 10} 16 {0, 1, 2, 3, 4, 6, 8, 9, 10, 12, 14} {0, 8, 2, 4, 10} 16 {0, 1, 2, 3, 4, 6, 8, 9, 10, 11, 12} {0, 1, 2, 10, 8} 16 {0, 1, 2, 3, 4, 6, 8, 9, 10, 11, 12, 14} {0, 8, 2, 10} 16 {0, 1, 2, 4, 5, 8, 10, 12} {0, 1, 2, 3, 4, 6, 8, 9} 16 {0, 1, 2, 4, 5, 8, 9, 10, 12} {0, 1, 2, 4, 8, 9, 12} 16 {0, 1, 2, 4, 5, 8, 9, 10, 12, 13} {0, 1, 4, 8, 9, 12} 16 {0, 1, 2, 4, 5, 6, 8, 10, 12} {0, 1, 2, 4, 6, 8, 12} 16 {0, 1, 2, 4, 5, 6, 8, 10, 12, 14} {0, 2, 4, 6, 8, 12} 16 {0, 1, 2, 3, 4, 5, 8, 10, 12} {0, 1, 2, 4, 6, 8, 9} 16 {0, 1, 2, 3, 4, 5, 8, 9, 10, 12} {0, 1, 2, 4, 8, 9} 16 {0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 12} {0, 1, 2, 8, 9} 16 {0, 1, 2, 3, 4, 5, 8, 9, 10, 12, 13} {0, 1, 4, 8, 9} 16 {0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13} {0, 1, 8, 9} 16 {0, 1, 2, 3, 4, 5, 6, 8, 10, 12} {0, 1, 2, 4, 6, 8} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12} {0, 1, 2, 4, 6} 16 {0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 14} {0, 8, 2, 4, 6} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14} {0, 2, 4, 6} 16 {0, 1, 2, 4, 5, 6, 8, 9, 10} {0, 1, 2, 3, 4, 8, 12} 16 {0, 1, 2, 4, 5, 6, 8, 9, 10, 12} {0, 1, 2, 4, 8, 12} 16 {0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 13} {0, 1, 4, 8, 12} 16 {0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 14} {0, 8, 2, 4, 12} 16 {0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14} {0, 8, 4, 12} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 10} {0, 1, 2, 3, 4, 8} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11} {0, 1, 2, 3, 8} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} {0, 1, 2, 3, 4} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} {0, 1, 2, 3} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12} {0, 1, 2, 4, 8} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12} {0, 1, 2, 4} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14} {0, 8, 2, 4} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14} {0, 2, 4} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12} {0, 1, 2, 8} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14} {0, 8, 2} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} {0, 1, 2} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14} {0, 2} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13} {0, 1, 4, 8} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14} {0, 8, 4} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13} {0, 1, 4} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14} {0, 4} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13} {0, 1, 8} 16 {0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14} {0, 8} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} {0, 1} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} {0} 16 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} {} 16