Processing math: 100%

Identifier
Values
=>
Cc0005;cc-rep-0 Cc0007;cc-rep-1 Cc0007;cc-rep
[1,0]=>[[1],[2]]=>[[1,2]]=>0 [1,0,1,0]=>[[1,3],[2,4]]=>[[1,2,4],[3]]=>2 [1,1,0,0]=>[[1,2],[3,4]]=>[[1,2,3,4]]=>0 [1,0,1,0,1,0]=>[[1,3,5],[2,4,6]]=>[[1,2,4,6],[3,5]]=>6 [1,0,1,1,0,0]=>[[1,3,4],[2,5,6]]=>[[1,2,4,5,6],[3]]=>2 [1,1,0,0,1,0]=>[[1,2,5],[3,4,6]]=>[[1,2,3,4,6],[5]]=>4 [1,1,0,1,0,0]=>[[1,2,4],[3,5,6]]=>[[1,2,3,5,6],[4]]=>3 [1,1,1,0,0,0]=>[[1,2,3],[4,5,6]]=>[[1,2,3,4,5,6]]=>0 [1,0,1,0,1,0,1,0]=>[[1,3,5,7],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7]]=>12 [1,0,1,0,1,1,0,0]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,4,6,7,8],[3,5]]=>6 [1,0,1,1,0,0,1,0]=>[[1,3,4,7],[2,5,6,8]]=>[[1,2,4,5,6,8],[3,7]]=>8 [1,0,1,1,0,1,0,0]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,5,7,8],[3,6]]=>7 [1,0,1,1,1,0,0,0]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,4,5,6,7,8],[3]]=>2 [1,1,0,0,1,0,1,0]=>[[1,2,5,7],[3,4,6,8]]=>[[1,2,3,4,6,8],[5,7]]=>10 [1,1,0,0,1,1,0,0]=>[[1,2,5,6],[3,4,7,8]]=>[[1,2,3,4,7,8],[5,6]]=>4 [1,1,0,1,0,0,1,0]=>[[1,2,4,7],[3,5,6,8]]=>[[1,2,3,5,6,8],[4,7]]=>9 [1,1,0,1,0,1,0,0]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,3,5,7,8],[4,6]]=>8 [1,1,0,1,1,0,0,0]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,5,6,7,8],[4]]=>3 [1,1,1,0,0,0,1,0]=>[[1,2,3,7],[4,5,6,8]]=>[[1,2,3,4,5,6,8],[7]]=>6 [1,1,1,0,0,1,0,0]=>[[1,2,3,6],[4,5,7,8]]=>[[1,2,3,4,5,7,8],[6]]=>5 [1,1,1,0,1,0,0,0]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,4,6,7,8],[5]]=>4 [1,1,1,1,0,0,0,0]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4,5,6,7,8]]=>0 [1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[[1,2,4,6,8,10],[3,5,7,9]]=>20 [1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,8],[2,4,6,9,10]]=>[[1,2,4,6,8,9,10],[3,5,7]]=>12 [1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,6,9],[2,4,7,8,10]]=>[[1,2,4,6,7,8,10],[3,5,9]]=>14 [1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,6,8],[2,4,7,9,10]]=>[[1,2,4,6,7,9,10],[3,5,8]]=>13 [1,0,1,0,1,1,1,0,0,0]=>[[1,3,5,6,7],[2,4,8,9,10]]=>[[1,2,4,6,7,8,9,10],[3,5]]=>6 [1,0,1,1,0,0,1,0,1,0]=>[[1,3,4,7,9],[2,5,6,8,10]]=>[[1,2,4,5,6,8,10],[3,7,9]]=>16 [1,0,1,1,0,0,1,1,0,0]=>[[1,3,4,7,8],[2,5,6,9,10]]=>[[1,2,4,5,6,9,10],[3,7,8]]=>8 [1,0,1,1,0,1,0,0,1,0]=>[[1,3,4,6,9],[2,5,7,8,10]]=>[[1,2,4,5,7,8,10],[3,6,9]]=>15 [1,0,1,1,0,1,0,1,0,0]=>[[1,3,4,6,8],[2,5,7,9,10]]=>[[1,2,4,5,7,9,10],[3,6,8]]=>14 [1,0,1,1,0,1,1,0,0,0]=>[[1,3,4,6,7],[2,5,8,9,10]]=>[[1,2,4,5,7,8,9,10],[3,6]]=>7 [1,0,1,1,1,0,0,0,1,0]=>[[1,3,4,5,9],[2,6,7,8,10]]=>[[1,2,4,5,6,7,8,10],[3,9]]=>10 [1,0,1,1,1,0,0,1,0,0]=>[[1,3,4,5,8],[2,6,7,9,10]]=>[[1,2,4,5,6,7,9,10],[3,8]]=>9 [1,0,1,1,1,0,1,0,0,0]=>[[1,3,4,5,7],[2,6,8,9,10]]=>[[1,2,4,5,6,8,9,10],[3,7]]=>8 [1,0,1,1,1,1,0,0,0,0]=>[[1,3,4,5,6],[2,7,8,9,10]]=>[[1,2,4,5,6,7,8,9,10],[3]]=>2 [1,1,0,0,1,0,1,0,1,0]=>[[1,2,5,7,9],[3,4,6,8,10]]=>[[1,2,3,4,6,8,10],[5,7,9]]=>18 [1,1,0,0,1,0,1,1,0,0]=>[[1,2,5,7,8],[3,4,6,9,10]]=>[[1,2,3,4,6,9,10],[5,7,8]]=>10 [1,1,0,0,1,1,0,0,1,0]=>[[1,2,5,6,9],[3,4,7,8,10]]=>[[1,2,3,4,7,8,10],[5,6,9]]=>12 [1,1,0,0,1,1,0,1,0,0]=>[[1,2,5,6,8],[3,4,7,9,10]]=>[[1,2,3,4,7,9,10],[5,6,8]]=>11 [1,1,0,0,1,1,1,0,0,0]=>[[1,2,5,6,7],[3,4,8,9,10]]=>[[1,2,3,4,7,8,9,10],[5,6]]=>4 [1,1,0,1,0,0,1,0,1,0]=>[[1,2,4,7,9],[3,5,6,8,10]]=>[[1,2,3,5,6,8,10],[4,7,9]]=>17 [1,1,0,1,0,0,1,1,0,0]=>[[1,2,4,7,8],[3,5,6,9,10]]=>[[1,2,3,5,6,9,10],[4,7,8]]=>9 [1,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,9],[3,5,7,8,10]]=>[[1,2,3,5,7,8,10],[4,6,9]]=>16 [1,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8],[3,5,7,9,10]]=>[[1,2,3,5,7,9,10],[4,6,8]]=>15 [1,1,0,1,0,1,1,0,0,0]=>[[1,2,4,6,7],[3,5,8,9,10]]=>[[1,2,3,5,7,8,9,10],[4,6]]=>8 [1,1,0,1,1,0,0,0,1,0]=>[[1,2,4,5,9],[3,6,7,8,10]]=>[[1,2,3,5,6,7,8,10],[4,9]]=>11 [1,1,0,1,1,0,0,1,0,0]=>[[1,2,4,5,8],[3,6,7,9,10]]=>[[1,2,3,5,6,7,9,10],[4,8]]=>10 [1,1,0,1,1,0,1,0,0,0]=>[[1,2,4,5,7],[3,6,8,9,10]]=>[[1,2,3,5,6,8,9,10],[4,7]]=>9 [1,1,0,1,1,1,0,0,0,0]=>[[1,2,4,5,6],[3,7,8,9,10]]=>[[1,2,3,5,6,7,8,9,10],[4]]=>3 [1,1,1,0,0,0,1,0,1,0]=>[[1,2,3,7,9],[4,5,6,8,10]]=>[[1,2,3,4,5,6,8,10],[7,9]]=>14 [1,1,1,0,0,0,1,1,0,0]=>[[1,2,3,7,8],[4,5,6,9,10]]=>[[1,2,3,4,5,6,9,10],[7,8]]=>6 [1,1,1,0,0,1,0,0,1,0]=>[[1,2,3,6,9],[4,5,7,8,10]]=>[[1,2,3,4,5,7,8,10],[6,9]]=>13 [1,1,1,0,0,1,0,1,0,0]=>[[1,2,3,6,8],[4,5,7,9,10]]=>[[1,2,3,4,5,7,9,10],[6,8]]=>12 [1,1,1,0,0,1,1,0,0,0]=>[[1,2,3,6,7],[4,5,8,9,10]]=>[[1,2,3,4,5,8,9,10],[6,7]]=>5 [1,1,1,0,1,0,0,0,1,0]=>[[1,2,3,5,9],[4,6,7,8,10]]=>[[1,2,3,4,6,7,8,10],[5,9]]=>12 [1,1,1,0,1,0,0,1,0,0]=>[[1,2,3,5,8],[4,6,7,9,10]]=>[[1,2,3,4,6,7,9,10],[5,8]]=>11 [1,1,1,0,1,0,1,0,0,0]=>[[1,2,3,5,7],[4,6,8,9,10]]=>[[1,2,3,4,6,8,9,10],[5,7]]=>10 [1,1,1,0,1,1,0,0,0,0]=>[[1,2,3,5,6],[4,7,8,9,10]]=>[[1,2,3,4,6,7,8,9,10],[5]]=>4 [1,1,1,1,0,0,0,0,1,0]=>[[1,2,3,4,9],[5,6,7,8,10]]=>[[1,2,3,4,5,6,7,8,10],[9]]=>8 [1,1,1,1,0,0,0,1,0,0]=>[[1,2,3,4,8],[5,6,7,9,10]]=>[[1,2,3,4,5,6,7,9,10],[8]]=>7 [1,1,1,1,0,0,1,0,0,0]=>[[1,2,3,4,7],[5,6,8,9,10]]=>[[1,2,3,4,5,6,8,9,10],[7]]=>6 [1,1,1,1,0,1,0,0,0,0]=>[[1,2,3,4,6],[5,7,8,9,10]]=>[[1,2,3,4,5,7,8,9,10],[6]]=>5 [1,1,1,1,1,0,0,0,0,0]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[[1,2,3,4,5,6,7,8,9,10]]=>0 [1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[[1,2,4,6,8,10,12],[3,5,7,9,11]]=>30 [1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>[[1,2,4,6,8,10,11,12],[3,5,7,9]]=>20 [1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>[[1,2,4,6,8,9,10,12],[3,5,7,11]]=>22 [1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>[[1,2,4,6,8,9,11,12],[3,5,7,10]]=>21 [1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>[[1,2,4,6,8,9,10,11,12],[3,5,7]]=>12 [1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>[[1,2,4,6,7,8,10,12],[3,5,9,11]]=>24 [1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>[[1,2,4,6,7,8,11,12],[3,5,9,10]]=>14 [1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>[[1,2,4,6,7,9,10,12],[3,5,8,11]]=>23 [1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>[[1,2,4,6,7,9,11,12],[3,5,8,10]]=>22 [1,0,1,0,1,1,0,1,1,0,0,0]=>[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>[[1,2,4,6,7,9,10,11,12],[3,5,8]]=>13 [1,0,1,0,1,1,1,0,0,0,1,0]=>[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>[[1,2,4,6,7,8,9,10,12],[3,5,11]]=>16 [1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>[[1,2,4,6,7,8,9,11,12],[3,5,10]]=>15 [1,0,1,0,1,1,1,0,1,0,0,0]=>[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>[[1,2,4,6,7,8,10,11,12],[3,5,9]]=>14 [1,0,1,0,1,1,1,1,0,0,0,0]=>[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>[[1,2,4,6,7,8,9,10,11,12],[3,5]]=>6 [1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>[[1,2,4,5,6,8,10,12],[3,7,9,11]]=>26 [1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>[[1,2,4,5,6,8,11,12],[3,7,9,10]]=>16 [1,0,1,1,0,0,1,1,0,0,1,0]=>[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>[[1,2,4,5,6,9,10,12],[3,7,8,11]]=>18 [1,0,1,1,0,0,1,1,0,1,0,0]=>[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>[[1,2,4,5,6,9,11,12],[3,7,8,10]]=>17 [1,0,1,1,0,0,1,1,1,0,0,0]=>[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>[[1,2,4,5,6,9,10,11,12],[3,7,8]]=>8 [1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>[[1,2,4,5,7,8,10,12],[3,6,9,11]]=>25 [1,0,1,1,0,1,0,0,1,1,0,0]=>[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>[[1,2,4,5,7,8,11,12],[3,6,9,10]]=>15 [1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>[[1,2,4,5,7,9,10,12],[3,6,8,11]]=>24 [1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>[[1,2,4,5,7,9,11,12],[3,6,8,10]]=>23 [1,0,1,1,0,1,0,1,1,0,0,0]=>[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>[[1,2,4,5,7,9,10,11,12],[3,6,8]]=>14 [1,0,1,1,0,1,1,0,0,0,1,0]=>[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>[[1,2,4,5,7,8,9,10,12],[3,6,11]]=>17 [1,0,1,1,0,1,1,0,0,1,0,0]=>[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>[[1,2,4,5,7,8,9,11,12],[3,6,10]]=>16 [1,0,1,1,0,1,1,0,1,0,0,0]=>[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>[[1,2,4,5,7,8,10,11,12],[3,6,9]]=>15 [1,0,1,1,0,1,1,1,0,0,0,0]=>[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>[[1,2,4,5,7,8,9,10,11,12],[3,6]]=>7 [1,0,1,1,1,0,0,0,1,0,1,0]=>[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>[[1,2,4,5,6,7,8,10,12],[3,9,11]]=>20 [1,0,1,1,1,0,0,0,1,1,0,0]=>[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>[[1,2,4,5,6,7,8,11,12],[3,9,10]]=>10 [1,0,1,1,1,0,0,1,0,0,1,0]=>[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>[[1,2,4,5,6,7,9,10,12],[3,8,11]]=>19 [1,0,1,1,1,0,0,1,0,1,0,0]=>[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>[[1,2,4,5,6,7,9,11,12],[3,8,10]]=>18 [1,0,1,1,1,0,0,1,1,0,0,0]=>[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>[[1,2,4,5,6,7,10,11,12],[3,8,9]]=>9 [1,0,1,1,1,0,1,0,0,0,1,0]=>[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>[[1,2,4,5,6,8,9,10,12],[3,7,11]]=>18 [1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>[[1,2,4,5,6,8,9,11,12],[3,7,10]]=>17 [1,0,1,1,1,0,1,0,1,0,0,0]=>[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>[[1,2,4,5,6,8,10,11,12],[3,7,9]]=>16 [1,0,1,1,1,0,1,1,0,0,0,0]=>[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>[[1,2,4,5,6,8,9,10,11,12],[3,7]]=>8 [1,0,1,1,1,1,0,0,0,0,1,0]=>[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>[[1,2,4,5,6,7,8,9,10,12],[3,11]]=>12 [1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>[[1,2,4,5,6,7,8,9,11,12],[3,10]]=>11 [1,0,1,1,1,1,0,0,1,0,0,0]=>[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>[[1,2,4,5,6,7,8,10,11,12],[3,9]]=>10 [1,0,1,1,1,1,0,1,0,0,0,0]=>[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>[[1,2,4,5,6,7,9,10,11,12],[3,8]]=>9 [1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>[[1,2,4,5,6,7,8,9,10,11,12],[3]]=>2 [1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>[[1,2,3,4,6,8,10,12],[5,7,9,11]]=>28 [1,1,0,0,1,0,1,0,1,1,0,0]=>[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>[[1,2,3,4,6,8,11,12],[5,7,9,10]]=>18 [1,1,0,0,1,0,1,1,0,0,1,0]=>[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>[[1,2,3,4,6,9,10,12],[5,7,8,11]]=>20 [1,1,0,0,1,0,1,1,0,1,0,0]=>[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>[[1,2,3,4,6,9,11,12],[5,7,8,10]]=>19 [1,1,0,0,1,0,1,1,1,0,0,0]=>[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>[[1,2,3,4,6,9,10,11,12],[5,7,8]]=>10 [1,1,0,0,1,1,0,0,1,0,1,0]=>[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>[[1,2,3,4,7,8,10,12],[5,6,9,11]]=>22 [1,1,0,0,1,1,0,0,1,1,0,0]=>[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>[[1,2,3,4,7,8,11,12],[5,6,9,10]]=>12 [1,1,0,0,1,1,0,1,0,0,1,0]=>[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>[[1,2,3,4,7,9,10,12],[5,6,8,11]]=>21 [1,1,0,0,1,1,0,1,0,1,0,0]=>[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>[[1,2,3,4,7,9,11,12],[5,6,8,10]]=>20 [1,1,0,0,1,1,0,1,1,0,0,0]=>[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>[[1,2,3,4,7,9,10,11,12],[5,6,8]]=>11 [1,1,0,0,1,1,1,0,0,0,1,0]=>[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>[[1,2,3,4,7,8,9,10,12],[5,6,11]]=>14 [1,1,0,0,1,1,1,0,0,1,0,0]=>[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>[[1,2,3,4,7,8,9,11,12],[5,6,10]]=>13 [1,1,0,0,1,1,1,0,1,0,0,0]=>[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>[[1,2,3,4,7,8,10,11,12],[5,6,9]]=>12 [1,1,0,0,1,1,1,1,0,0,0,0]=>[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>[[1,2,3,4,7,8,9,10,11,12],[5,6]]=>4 [1,1,0,1,0,0,1,0,1,0,1,0]=>[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>[[1,2,3,5,6,8,10,12],[4,7,9,11]]=>27 [1,1,0,1,0,0,1,0,1,1,0,0]=>[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>[[1,2,3,5,6,8,11,12],[4,7,9,10]]=>17 [1,1,0,1,0,0,1,1,0,0,1,0]=>[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>[[1,2,3,5,6,9,10,12],[4,7,8,11]]=>19 [1,1,0,1,0,0,1,1,0,1,0,0]=>[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>[[1,2,3,5,6,9,11,12],[4,7,8,10]]=>18 [1,1,0,1,0,0,1,1,1,0,0,0]=>[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>[[1,2,3,5,6,9,10,11,12],[4,7,8]]=>9 [1,1,0,1,0,1,0,0,1,0,1,0]=>[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>[[1,2,3,5,7,8,10,12],[4,6,9,11]]=>26 [1,1,0,1,0,1,0,0,1,1,0,0]=>[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>[[1,2,3,5,7,8,11,12],[4,6,9,10]]=>16 [1,1,0,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>[[1,2,3,5,7,9,10,12],[4,6,8,11]]=>25 [1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>[[1,2,3,5,7,9,11,12],[4,6,8,10]]=>24 [1,1,0,1,0,1,0,1,1,0,0,0]=>[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>[[1,2,3,5,7,9,10,11,12],[4,6,8]]=>15 [1,1,0,1,0,1,1,0,0,0,1,0]=>[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>[[1,2,3,5,7,8,9,10,12],[4,6,11]]=>18 [1,1,0,1,0,1,1,0,0,1,0,0]=>[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>[[1,2,3,5,7,8,9,11,12],[4,6,10]]=>17 [1,1,0,1,0,1,1,0,1,0,0,0]=>[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>[[1,2,3,5,7,8,10,11,12],[4,6,9]]=>16 [1,1,0,1,0,1,1,1,0,0,0,0]=>[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>[[1,2,3,5,7,8,9,10,11,12],[4,6]]=>8 [1,1,0,1,1,0,0,0,1,0,1,0]=>[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>[[1,2,3,5,6,7,8,10,12],[4,9,11]]=>21 [1,1,0,1,1,0,0,0,1,1,0,0]=>[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>[[1,2,3,5,6,7,8,11,12],[4,9,10]]=>11 [1,1,0,1,1,0,0,1,0,0,1,0]=>[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>[[1,2,3,5,6,7,9,10,12],[4,8,11]]=>20 [1,1,0,1,1,0,0,1,0,1,0,0]=>[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>[[1,2,3,5,6,7,9,11,12],[4,8,10]]=>19 [1,1,0,1,1,0,0,1,1,0,0,0]=>[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>[[1,2,3,5,6,7,10,11,12],[4,8,9]]=>10 [1,1,0,1,1,0,1,0,0,0,1,0]=>[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>[[1,2,3,5,6,8,9,10,12],[4,7,11]]=>19 [1,1,0,1,1,0,1,0,0,1,0,0]=>[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>[[1,2,3,5,6,8,9,11,12],[4,7,10]]=>18 [1,1,0,1,1,0,1,0,1,0,0,0]=>[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>[[1,2,3,5,6,8,10,11,12],[4,7,9]]=>17 [1,1,0,1,1,0,1,1,0,0,0,0]=>[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>[[1,2,3,5,6,8,9,10,11,12],[4,7]]=>9 [1,1,0,1,1,1,0,0,0,0,1,0]=>[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>[[1,2,3,5,6,7,8,9,10,12],[4,11]]=>13 [1,1,0,1,1,1,0,0,0,1,0,0]=>[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>[[1,2,3,5,6,7,8,9,11,12],[4,10]]=>12 [1,1,0,1,1,1,0,0,1,0,0,0]=>[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>[[1,2,3,5,6,7,8,10,11,12],[4,9]]=>11 [1,1,0,1,1,1,0,1,0,0,0,0]=>[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>[[1,2,3,5,6,7,9,10,11,12],[4,8]]=>10 [1,1,0,1,1,1,1,0,0,0,0,0]=>[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>[[1,2,3,5,6,7,8,9,10,11,12],[4]]=>3 [1,1,1,0,0,0,1,0,1,0,1,0]=>[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>[[1,2,3,4,5,6,8,10,12],[7,9,11]]=>24 [1,1,1,0,0,0,1,0,1,1,0,0]=>[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>[[1,2,3,4,5,6,8,11,12],[7,9,10]]=>14 [1,1,1,0,0,0,1,1,0,0,1,0]=>[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>[[1,2,3,4,5,6,9,10,12],[7,8,11]]=>16 [1,1,1,0,0,0,1,1,0,1,0,0]=>[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>[[1,2,3,4,5,6,9,11,12],[7,8,10]]=>15 [1,1,1,0,0,0,1,1,1,0,0,0]=>[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>[[1,2,3,4,5,6,10,11,12],[7,8,9]]=>6 [1,1,1,0,0,1,0,0,1,0,1,0]=>[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>[[1,2,3,4,5,7,8,10,12],[6,9,11]]=>23 [1,1,1,0,0,1,0,0,1,1,0,0]=>[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>[[1,2,3,4,5,7,8,11,12],[6,9,10]]=>13 [1,1,1,0,0,1,0,1,0,0,1,0]=>[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>[[1,2,3,4,5,7,9,10,12],[6,8,11]]=>22 [1,1,1,0,0,1,0,1,0,1,0,0]=>[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>[[1,2,3,4,5,7,9,11,12],[6,8,10]]=>21 [1,1,1,0,0,1,0,1,1,0,0,0]=>[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>[[1,2,3,4,5,7,10,11,12],[6,8,9]]=>12 [1,1,1,0,0,1,1,0,0,0,1,0]=>[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>[[1,2,3,4,5,8,9,10,12],[6,7,11]]=>15 [1,1,1,0,0,1,1,0,0,1,0,0]=>[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>[[1,2,3,4,5,8,9,11,12],[6,7,10]]=>14 [1,1,1,0,0,1,1,0,1,0,0,0]=>[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>[[1,2,3,4,5,8,10,11,12],[6,7,9]]=>13 [1,1,1,0,0,1,1,1,0,0,0,0]=>[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>[[1,2,3,4,5,8,9,10,11,12],[6,7]]=>5 [1,1,1,0,1,0,0,0,1,0,1,0]=>[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>[[1,2,3,4,6,7,8,10,12],[5,9,11]]=>22 [1,1,1,0,1,0,0,0,1,1,0,0]=>[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>[[1,2,3,4,6,7,8,11,12],[5,9,10]]=>12 [1,1,1,0,1,0,0,1,0,0,1,0]=>[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>[[1,2,3,4,6,7,9,10,12],[5,8,11]]=>21 [1,1,1,0,1,0,0,1,0,1,0,0]=>[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>[[1,2,3,4,6,7,9,11,12],[5,8,10]]=>20 [1,1,1,0,1,0,0,1,1,0,0,0]=>[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>[[1,2,3,4,6,7,10,11,12],[5,8,9]]=>11 [1,1,1,0,1,0,1,0,0,0,1,0]=>[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>[[1,2,3,4,6,8,9,10,12],[5,7,11]]=>20 [1,1,1,0,1,0,1,0,0,1,0,0]=>[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>[[1,2,3,4,6,8,9,11,12],[5,7,10]]=>19 [1,1,1,0,1,0,1,0,1,0,0,0]=>[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>[[1,2,3,4,6,8,10,11,12],[5,7,9]]=>18 [1,1,1,0,1,0,1,1,0,0,0,0]=>[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>[[1,2,3,4,6,8,9,10,11,12],[5,7]]=>10 [1,1,1,0,1,1,0,0,0,0,1,0]=>[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>[[1,2,3,4,6,7,8,9,10,12],[5,11]]=>14 [1,1,1,0,1,1,0,0,0,1,0,0]=>[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>[[1,2,3,4,6,7,8,9,11,12],[5,10]]=>13 [1,1,1,0,1,1,0,0,1,0,0,0]=>[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>[[1,2,3,4,6,7,8,10,11,12],[5,9]]=>12 [1,1,1,0,1,1,0,1,0,0,0,0]=>[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>[[1,2,3,4,6,7,9,10,11,12],[5,8]]=>11 [1,1,1,0,1,1,1,0,0,0,0,0]=>[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>[[1,2,3,4,6,7,8,9,10,11,12],[5]]=>4 [1,1,1,1,0,0,0,0,1,0,1,0]=>[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>[[1,2,3,4,5,6,7,8,10,12],[9,11]]=>18 [1,1,1,1,0,0,0,0,1,1,0,0]=>[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>[[1,2,3,4,5,6,7,8,11,12],[9,10]]=>8 [1,1,1,1,0,0,0,1,0,0,1,0]=>[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>[[1,2,3,4,5,6,7,9,10,12],[8,11]]=>17 [1,1,1,1,0,0,0,1,0,1,0,0]=>[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>[[1,2,3,4,5,6,7,9,11,12],[8,10]]=>16 [1,1,1,1,0,0,0,1,1,0,0,0]=>[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>[[1,2,3,4,5,6,7,10,11,12],[8,9]]=>7 [1,1,1,1,0,0,1,0,0,0,1,0]=>[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>[[1,2,3,4,5,6,8,9,10,12],[7,11]]=>16 [1,1,1,1,0,0,1,0,0,1,0,0]=>[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>[[1,2,3,4,5,6,8,9,11,12],[7,10]]=>15 [1,1,1,1,0,0,1,0,1,0,0,0]=>[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>[[1,2,3,4,5,6,8,10,11,12],[7,9]]=>14 [1,1,1,1,0,0,1,1,0,0,0,0]=>[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>[[1,2,3,4,5,6,9,10,11,12],[7,8]]=>6 [1,1,1,1,0,1,0,0,0,0,1,0]=>[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>[[1,2,3,4,5,7,8,9,10,12],[6,11]]=>15 [1,1,1,1,0,1,0,0,0,1,0,0]=>[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>[[1,2,3,4,5,7,8,9,11,12],[6,10]]=>14 [1,1,1,1,0,1,0,0,1,0,0,0]=>[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>[[1,2,3,4,5,7,8,10,11,12],[6,9]]=>13 [1,1,1,1,0,1,0,1,0,0,0,0]=>[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>[[1,2,3,4,5,7,9,10,11,12],[6,8]]=>12 [1,1,1,1,0,1,1,0,0,0,0,0]=>[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>[[1,2,3,4,5,7,8,9,10,11,12],[6]]=>5 [1,1,1,1,1,0,0,0,0,0,1,0]=>[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>[[1,2,3,4,5,6,7,8,9,10,12],[11]]=>10 [1,1,1,1,1,0,0,0,0,1,0,0]=>[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>[[1,2,3,4,5,6,7,8,9,11,12],[10]]=>9 [1,1,1,1,1,0,0,0,1,0,0,0]=>[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>[[1,2,3,4,5,6,7,8,10,11,12],[9]]=>8 [1,1,1,1,1,0,0,1,0,0,0,0]=>[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>[[1,2,3,4,5,6,7,9,10,11,12],[8]]=>7 [1,1,1,1,1,0,1,0,0,0,0,0]=>[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>[[1,2,3,4,5,6,8,9,10,11,12],[7]]=>6 [1,1,1,1,1,1,0,0,0,0,0,0]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[[1,2,3,4,5,6,7,8,9,10,11,12]]=>0
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Description
The (standard) major index of a standard tableau.
A descent of a standard tableau T is an index i such that i+1 appears in a row strictly below the row of i. The (standard) major index is the the sum of the descents.
Map
to two-row standard tableau
Description
Return a standard tableau of shape (n,n) where n is the semilength of the Dyck path.
Given a Dyck path D, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
Map
catabolism
Description
Remove the first row of the standard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry k into tableau T is as follows:
If k is larger than all entries in the first column, place k at the bottom of the first column and the procedure is finished. Otherwise, place k in the first column, replacing the smallest entry, y, greater than k. Now insert y into the second column using the same procedure: if y is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place y in the second column, replacing, or 'bumping', the smallest entry, z, larger than y. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).