Identifier
Values
[[3,0],[0]] => [[2,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0],[1]] => [[1,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0],[2]] => [[1,1,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0],[3]] => [[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[4,0],[0]] => [[2,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[3,0,0],[0,0],[0]] => [[3,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0],[1,0],[0]] => [[2,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0],[1,0],[1]] => [[1,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0],[2,0],[0]] => [[2,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0],[2,0],[2]] => [[1,1,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0],[3,0],[0]] => [[2,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0],[3,0],[1]] => [[1,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0],[3,0],[2]] => [[1,1,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0],[3,0],[3]] => [[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[5,0],[0]] => [[2,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0],[1]] => [[1,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0],[2]] => [[1,1,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0],[3]] => [[1,1,1,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0],[4]] => [[1,1,1,1,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0],[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[6,0],[0]] => [[2,2,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0],[1]] => [[1,2,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0],[2]] => [[1,1,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0],[3]] => [[1,1,1,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0],[4]] => [[1,1,1,1,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0],[5]] => [[1,1,1,1,1,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0],[6]] => [[1,1,1,1,1,1]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
>>> Load all 380 entries. <<<
[[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[7,0],[0]] => [[2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[7,0],[1]] => [[1,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[7,0],[2]] => [[1,1,2,2,2,2,2]] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[7,0],[3]] => [[1,1,1,2,2,2,2]] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[7,0],[4]] => [[1,1,1,1,2,2,2]] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[7,0],[5]] => [[1,1,1,1,1,2,2]] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[7,0],[6]] => [[1,1,1,1,1,1,2]] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[6,0,0],[0,0],[0]] => [[3,3,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[1,0],[0]] => [[2,3,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[1,0],[1]] => [[1,3,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[2,0],[0]] => [[2,2,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[2,0],[1]] => [[1,2,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[2,0],[2]] => [[1,1,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[3,0],[0]] => [[2,2,2,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[3,0],[1]] => [[1,2,2,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[3,0],[2]] => [[1,1,2,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[3,0],[3]] => [[1,1,1,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[4,0],[0]] => [[2,2,2,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[4,0],[1]] => [[1,2,2,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[4,0],[2]] => [[1,1,2,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[4,0],[3]] => [[1,1,1,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[4,0],[4]] => [[1,1,1,1,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[5,0],[0]] => [[2,2,2,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[5,0],[1]] => [[1,2,2,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[5,0],[2]] => [[1,1,2,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[5,0],[3]] => [[1,1,1,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[5,0],[4]] => [[1,1,1,1,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[5,0],[5]] => [[1,1,1,1,1,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[6,0],[0]] => [[2,2,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[6,0],[1]] => [[1,2,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[6,0],[2]] => [[1,1,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[6,0],[3]] => [[1,1,1,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[6,0],[4]] => [[1,1,1,1,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[6,0],[5]] => [[1,1,1,1,1,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[6,0,0],[6,0],[6]] => [[1,1,1,1,1,1]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[5,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[5,0,0,0],[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[3,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,6]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[3]] => [[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[4]] => [[1,1,1,1]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
search for individual values
searching the database for the individual values of this statistic
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Map
to semistandard tableau
Description
Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let $G$ be a Gelfand-Tsetlin pattern and let $\lambda^{(k)}$ be its $(n-k+1)$-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
$$ \lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)}, $$
where $\lambda^{(0)}$ is the empty partition.
Each skew shape $\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau $T(G)$ by inserting $k$ into the cells of the skew shape $\lambda^{(k)} / \lambda^{(k-1)}$, for $k=1,\dots,n$.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$