edit this statistic or download as text // json
Identifier
Values
=>
[1]=>6 [1,2]=>18 [2,1]=>12 [1,2,3]=>54 [1,3,2]=>36 [2,1,3]=>36 [2,3,1]=>36 [3,1,2]=>36 [3,2,1]=>24 [1,2,3,4]=>162 [1,2,4,3]=>108 [1,3,2,4]=>108 [1,3,4,2]=>108 [1,4,2,3]=>108 [1,4,3,2]=>72 [2,1,3,4]=>108 [2,1,4,3]=>72 [2,3,1,4]=>36 [2,3,4,1]=>108 [2,4,1,3]=>36 [2,4,3,1]=>72 [3,1,2,4]=>108 [3,1,4,2]=>72 [3,2,1,4]=>72 [3,2,4,1]=>72 [3,4,1,2]=>36 [3,4,2,1]=>72 [4,1,2,3]=>108 [4,1,3,2]=>72 [4,2,1,3]=>72 [4,2,3,1]=>72 [4,3,1,2]=>72 [4,3,2,1]=>48 [1,2,3,4,5]=>486 [1,2,3,5,4]=>324 [1,2,4,3,5]=>324 [1,2,4,5,3]=>324 [1,2,5,3,4]=>324 [1,2,5,4,3]=>216 [1,3,2,4,5]=>324 [1,3,2,5,4]=>216 [1,3,4,2,5]=>108 [1,3,4,5,2]=>324 [1,3,5,2,4]=>108 [1,3,5,4,2]=>216 [1,4,2,3,5]=>324 [1,4,2,5,3]=>216 [1,4,3,2,5]=>216 [1,4,3,5,2]=>216 [1,4,5,2,3]=>108 [1,4,5,3,2]=>216 [1,5,2,3,4]=>324 [1,5,2,4,3]=>216 [1,5,3,2,4]=>216 [1,5,3,4,2]=>216 [1,5,4,2,3]=>216 [1,5,4,3,2]=>144 [2,1,3,4,5]=>324 [2,1,3,5,4]=>216 [2,1,4,3,5]=>216 [2,1,4,5,3]=>216 [2,1,5,3,4]=>216 [2,1,5,4,3]=>144 [2,3,1,4,5]=>108 [2,3,1,5,4]=>72 [2,3,4,1,5]=>108 [2,3,4,5,1]=>324 [2,3,5,1,4]=>108 [2,3,5,4,1]=>216 [2,4,1,3,5]=>108 [2,4,1,5,3]=>72 [2,4,3,1,5]=>72 [2,4,3,5,1]=>216 [2,4,5,1,3]=>108 [2,4,5,3,1]=>216 [2,5,1,3,4]=>108 [2,5,1,4,3]=>72 [2,5,3,1,4]=>72 [2,5,3,4,1]=>216 [2,5,4,1,3]=>72 [2,5,4,3,1]=>144 [3,1,2,4,5]=>324 [3,1,2,5,4]=>216 [3,1,4,2,5]=>216 [3,1,4,5,2]=>216 [3,1,5,2,4]=>216 [3,1,5,4,2]=>144 [3,2,1,4,5]=>216 [3,2,1,5,4]=>144 [3,2,4,1,5]=>72 [3,2,4,5,1]=>216 [3,2,5,1,4]=>72 [3,2,5,4,1]=>144 [3,4,1,2,5]=>108 [3,4,1,5,2]=>72 [3,4,2,1,5]=>72 [3,4,2,5,1]=>72 [3,4,5,1,2]=>108 [3,4,5,2,1]=>216 [3,5,1,2,4]=>108 [3,5,1,4,2]=>72 [3,5,2,1,4]=>72 [3,5,2,4,1]=>72 [3,5,4,1,2]=>72 [3,5,4,2,1]=>144 [4,1,2,3,5]=>324 [4,1,2,5,3]=>216 [4,1,3,2,5]=>216 [4,1,3,5,2]=>216 [4,1,5,2,3]=>216 [4,1,5,3,2]=>144 [4,2,1,3,5]=>216 [4,2,1,5,3]=>144 [4,2,3,1,5]=>72 [4,2,3,5,1]=>216 [4,2,5,1,3]=>72 [4,2,5,3,1]=>144 [4,3,1,2,5]=>216 [4,3,1,5,2]=>144 [4,3,2,1,5]=>144 [4,3,2,5,1]=>144 [4,3,5,1,2]=>72 [4,3,5,2,1]=>144 [4,5,1,2,3]=>108 [4,5,1,3,2]=>72 [4,5,2,1,3]=>72 [4,5,2,3,1]=>72 [4,5,3,1,2]=>72 [4,5,3,2,1]=>144 [5,1,2,3,4]=>324 [5,1,2,4,3]=>216 [5,1,3,2,4]=>216 [5,1,3,4,2]=>216 [5,1,4,2,3]=>216 [5,1,4,3,2]=>144 [5,2,1,3,4]=>216 [5,2,1,4,3]=>144 [5,2,3,1,4]=>72 [5,2,3,4,1]=>216 [5,2,4,1,3]=>72 [5,2,4,3,1]=>144 [5,3,1,2,4]=>216 [5,3,1,4,2]=>144 [5,3,2,1,4]=>144 [5,3,2,4,1]=>144 [5,3,4,1,2]=>72 [5,3,4,2,1]=>144 [5,4,1,2,3]=>216 [5,4,1,3,2]=>144 [5,4,2,1,3]=>144 [5,4,2,3,1]=>144 [5,4,3,1,2]=>144 [5,4,3,2,1]=>96 [1,2,3,4,5,6]=>1458 [1,2,3,4,6,5]=>972 [1,2,3,5,4,6]=>972 [1,2,3,5,6,4]=>972 [1,2,3,6,4,5]=>972 [1,2,3,6,5,4]=>648 [1,2,4,3,5,6]=>972 [1,2,4,3,6,5]=>648 [1,2,4,5,3,6]=>324 [1,2,4,5,6,3]=>972 [1,2,4,6,3,5]=>324 [1,2,4,6,5,3]=>648 [1,2,5,3,4,6]=>972 [1,2,5,3,6,4]=>648 [1,2,5,4,3,6]=>648 [1,2,5,4,6,3]=>648 [1,2,5,6,3,4]=>324 [1,2,5,6,4,3]=>648 [1,2,6,3,4,5]=>972 [1,2,6,3,5,4]=>648 [1,2,6,4,3,5]=>648 [1,2,6,4,5,3]=>648 [1,2,6,5,3,4]=>648 [1,2,6,5,4,3]=>432 [1,3,2,4,5,6]=>972 [1,3,2,4,6,5]=>648 [1,3,2,5,4,6]=>648 [1,3,2,5,6,4]=>648 [1,3,2,6,4,5]=>648 [1,3,2,6,5,4]=>432 [1,3,4,2,5,6]=>324 [1,3,4,2,6,5]=>216 [1,3,4,5,2,6]=>324 [1,3,4,5,6,2]=>972 [1,3,4,6,2,5]=>324 [1,3,4,6,5,2]=>648 [1,3,5,2,4,6]=>324 [1,3,5,2,6,4]=>216 [1,3,5,4,2,6]=>216 [1,3,5,4,6,2]=>648 [1,3,5,6,2,4]=>324 [1,3,5,6,4,2]=>648 [1,3,6,2,4,5]=>324 [1,3,6,2,5,4]=>216 [1,3,6,4,2,5]=>216 [1,3,6,4,5,2]=>648 [1,3,6,5,2,4]=>216 [1,3,6,5,4,2]=>432 [1,4,2,3,5,6]=>972 [1,4,2,3,6,5]=>648 [1,4,2,5,3,6]=>648 [1,4,2,5,6,3]=>648 [1,4,2,6,3,5]=>648 [1,4,2,6,5,3]=>432 [1,4,3,2,5,6]=>648 [1,4,3,2,6,5]=>432 [1,4,3,5,2,6]=>216 [1,4,3,5,6,2]=>648 [1,4,3,6,2,5]=>216 [1,4,3,6,5,2]=>432 [1,4,5,2,3,6]=>324 [1,4,5,2,6,3]=>216 [1,4,5,3,2,6]=>216 [1,4,5,3,6,2]=>216 [1,4,5,6,2,3]=>324 [1,4,5,6,3,2]=>648 [1,4,6,2,3,5]=>324 [1,4,6,2,5,3]=>216 [1,4,6,3,2,5]=>216 [1,4,6,3,5,2]=>216 [1,4,6,5,2,3]=>216 [1,4,6,5,3,2]=>432 [1,5,2,3,4,6]=>972 [1,5,2,3,6,4]=>648 [1,5,2,4,3,6]=>648 [1,5,2,4,6,3]=>648 [1,5,2,6,3,4]=>648 [1,5,2,6,4,3]=>432 [1,5,3,2,4,6]=>648 [1,5,3,2,6,4]=>432 [1,5,3,4,2,6]=>216 [1,5,3,4,6,2]=>648 [1,5,3,6,2,4]=>216 [1,5,3,6,4,2]=>432 [1,5,4,2,3,6]=>648 [1,5,4,2,6,3]=>432 [1,5,4,3,2,6]=>432 [1,5,4,3,6,2]=>432 [1,5,4,6,2,3]=>216 [1,5,4,6,3,2]=>432 [1,5,6,2,3,4]=>324 [1,5,6,2,4,3]=>216 [1,5,6,3,2,4]=>216 [1,5,6,3,4,2]=>216 [1,5,6,4,2,3]=>216 [1,5,6,4,3,2]=>432 [1,6,2,3,4,5]=>972 [1,6,2,3,5,4]=>648 [1,6,2,4,3,5]=>648 [1,6,2,4,5,3]=>648 [1,6,2,5,3,4]=>648 [1,6,2,5,4,3]=>432 [1,6,3,2,4,5]=>648 [1,6,3,2,5,4]=>432 [1,6,3,4,2,5]=>216 [1,6,3,4,5,2]=>648 [1,6,3,5,2,4]=>216 [1,6,3,5,4,2]=>432 [1,6,4,2,3,5]=>648 [1,6,4,2,5,3]=>432 [1,6,4,3,2,5]=>432 [1,6,4,3,5,2]=>432 [1,6,4,5,2,3]=>216 [1,6,4,5,3,2]=>432 [1,6,5,2,3,4]=>648 [1,6,5,2,4,3]=>432 [1,6,5,3,2,4]=>432 [1,6,5,3,4,2]=>432 [1,6,5,4,2,3]=>432 [1,6,5,4,3,2]=>288 [2,1,3,4,5,6]=>972 [2,1,3,4,6,5]=>648 [2,1,3,5,4,6]=>648 [2,1,3,5,6,4]=>648 [2,1,3,6,4,5]=>648 [2,1,3,6,5,4]=>432 [2,1,4,3,5,6]=>648 [2,1,4,3,6,5]=>432 [2,1,4,5,3,6]=>216 [2,1,4,5,6,3]=>648 [2,1,4,6,3,5]=>216 [2,1,4,6,5,3]=>432 [2,1,5,3,4,6]=>648 [2,1,5,3,6,4]=>432 [2,1,5,4,3,6]=>432 [2,1,5,4,6,3]=>432 [2,1,5,6,3,4]=>216 [2,1,5,6,4,3]=>432 [2,1,6,3,4,5]=>648 [2,1,6,3,5,4]=>432 [2,1,6,4,3,5]=>432 [2,1,6,4,5,3]=>432 [2,1,6,5,3,4]=>432 [2,1,6,5,4,3]=>288 [2,3,1,4,5,6]=>324 [2,3,1,4,6,5]=>216 [2,3,1,5,4,6]=>216 [2,3,1,5,6,4]=>216 [2,3,1,6,4,5]=>216 [2,3,1,6,5,4]=>144 [2,3,4,1,5,6]=>108 [2,3,4,1,6,5]=>216 [2,3,4,5,1,6]=>324 [2,3,4,5,6,1]=>972 [2,3,4,6,1,5]=>324 [2,3,4,6,5,1]=>648 [2,3,5,1,4,6]=>108 [2,3,5,1,6,4]=>216 [2,3,5,4,1,6]=>216 [2,3,5,4,6,1]=>648 [2,3,5,6,1,4]=>324 [2,3,5,6,4,1]=>648 [2,3,6,1,4,5]=>108 [2,3,6,1,5,4]=>216 [2,3,6,4,1,5]=>216 [2,3,6,4,5,1]=>648 [2,3,6,5,1,4]=>216 [2,3,6,5,4,1]=>432 [2,4,1,3,5,6]=>324 [2,4,1,3,6,5]=>216 [2,4,1,5,3,6]=>216 [2,4,1,5,6,3]=>216 [2,4,1,6,3,5]=>216 [2,4,1,6,5,3]=>144 [2,4,3,1,5,6]=>216 [2,4,3,1,6,5]=>144 [2,4,3,5,1,6]=>216 [2,4,3,5,6,1]=>648 [2,4,3,6,1,5]=>216 [2,4,3,6,5,1]=>432 [2,4,5,1,3,6]=>108 [2,4,5,1,6,3]=>216 [2,4,5,3,1,6]=>216 [2,4,5,3,6,1]=>216 [2,4,5,6,1,3]=>324 [2,4,5,6,3,1]=>648 [2,4,6,1,3,5]=>108 [2,4,6,1,5,3]=>216 [2,4,6,3,1,5]=>216 [2,4,6,3,5,1]=>216 [2,4,6,5,1,3]=>216 [2,4,6,5,3,1]=>432 [2,5,1,3,4,6]=>324 [2,5,1,3,6,4]=>216 [2,5,1,4,3,6]=>216 [2,5,1,4,6,3]=>216 [2,5,1,6,3,4]=>216 [2,5,1,6,4,3]=>144 [2,5,3,1,4,6]=>216 [2,5,3,1,6,4]=>144 [2,5,3,4,1,6]=>216 [2,5,3,4,6,1]=>648 [2,5,3,6,1,4]=>216 [2,5,3,6,4,1]=>432 [2,5,4,1,3,6]=>216 [2,5,4,1,6,3]=>144 [2,5,4,3,1,6]=>144 [2,5,4,3,6,1]=>432 [2,5,4,6,1,3]=>216 [2,5,4,6,3,1]=>432 [2,5,6,1,3,4]=>108 [2,5,6,1,4,3]=>216 [2,5,6,3,1,4]=>216 [2,5,6,3,4,1]=>216 [2,5,6,4,1,3]=>216 [2,5,6,4,3,1]=>432 [2,6,1,3,4,5]=>324 [2,6,1,3,5,4]=>216 [2,6,1,4,3,5]=>216 [2,6,1,4,5,3]=>216 [2,6,1,5,3,4]=>216 [2,6,1,5,4,3]=>144 [2,6,3,1,4,5]=>216 [2,6,3,1,5,4]=>144 [2,6,3,4,1,5]=>216 [2,6,3,4,5,1]=>648 [2,6,3,5,1,4]=>216 [2,6,3,5,4,1]=>432 [2,6,4,1,3,5]=>216 [2,6,4,1,5,3]=>144 [2,6,4,3,1,5]=>144 [2,6,4,3,5,1]=>432 [2,6,4,5,1,3]=>216 [2,6,4,5,3,1]=>432 [2,6,5,1,3,4]=>216 [2,6,5,1,4,3]=>144 [2,6,5,3,1,4]=>144 [2,6,5,3,4,1]=>432 [2,6,5,4,1,3]=>144 [2,6,5,4,3,1]=>288 [3,1,2,4,5,6]=>972 [3,1,2,4,6,5]=>648 [3,1,2,5,4,6]=>648 [3,1,2,5,6,4]=>648 [3,1,2,6,4,5]=>648 [3,1,2,6,5,4]=>432 [3,1,4,2,5,6]=>648 [3,1,4,2,6,5]=>432 [3,1,4,5,2,6]=>216 [3,1,4,5,6,2]=>648 [3,1,4,6,2,5]=>216 [3,1,4,6,5,2]=>432 [3,1,5,2,4,6]=>648 [3,1,5,2,6,4]=>432 [3,1,5,4,2,6]=>432 [3,1,5,4,6,2]=>432 [3,1,5,6,2,4]=>216 [3,1,5,6,4,2]=>432 [3,1,6,2,4,5]=>648 [3,1,6,2,5,4]=>432 [3,1,6,4,2,5]=>432 [3,1,6,4,5,2]=>432 [3,1,6,5,2,4]=>432 [3,1,6,5,4,2]=>288 [3,2,1,4,5,6]=>648 [3,2,1,4,6,5]=>432 [3,2,1,5,4,6]=>432 [3,2,1,5,6,4]=>432 [3,2,1,6,4,5]=>432 [3,2,1,6,5,4]=>288 [3,2,4,1,5,6]=>216 [3,2,4,1,6,5]=>144 [3,2,4,5,1,6]=>216 [3,2,4,5,6,1]=>648 [3,2,4,6,1,5]=>216 [3,2,4,6,5,1]=>432 [3,2,5,1,4,6]=>216 [3,2,5,1,6,4]=>144 [3,2,5,4,1,6]=>144 [3,2,5,4,6,1]=>432 [3,2,5,6,1,4]=>216 [3,2,5,6,4,1]=>432 [3,2,6,1,4,5]=>216 [3,2,6,1,5,4]=>144 [3,2,6,4,1,5]=>144 [3,2,6,4,5,1]=>432 [3,2,6,5,1,4]=>144 [3,2,6,5,4,1]=>288 [3,4,1,2,5,6]=>324 [3,4,1,2,6,5]=>216 [3,4,1,5,2,6]=>216 [3,4,1,5,6,2]=>216 [3,4,1,6,2,5]=>216 [3,4,1,6,5,2]=>144 [3,4,2,1,5,6]=>216 [3,4,2,1,6,5]=>144 [3,4,2,5,1,6]=>72 [3,4,2,5,6,1]=>216 [3,4,2,6,1,5]=>72 [3,4,2,6,5,1]=>144 [3,4,5,1,2,6]=>108 [3,4,5,1,6,2]=>216 [3,4,5,2,1,6]=>216 [3,4,5,2,6,1]=>216 [3,4,5,6,1,2]=>324 [3,4,5,6,2,1]=>648 [3,4,6,1,2,5]=>108 [3,4,6,1,5,2]=>216 [3,4,6,2,1,5]=>216 [3,4,6,2,5,1]=>216 [3,4,6,5,1,2]=>216 [3,4,6,5,2,1]=>432 [3,5,1,2,4,6]=>324 [3,5,1,2,6,4]=>216 [3,5,1,4,2,6]=>216 [3,5,1,4,6,2]=>216 [3,5,1,6,2,4]=>216 [3,5,1,6,4,2]=>144 [3,5,2,1,4,6]=>216 [3,5,2,1,6,4]=>144 [3,5,2,4,1,6]=>72 [3,5,2,4,6,1]=>216 [3,5,2,6,1,4]=>72 [3,5,2,6,4,1]=>144 [3,5,4,1,2,6]=>216 [3,5,4,1,6,2]=>144 [3,5,4,2,1,6]=>144 [3,5,4,2,6,1]=>144 [3,5,4,6,1,2]=>216 [3,5,4,6,2,1]=>432 [3,5,6,1,2,4]=>108 [3,5,6,1,4,2]=>216 [3,5,6,2,1,4]=>216 [3,5,6,2,4,1]=>216 [3,5,6,4,1,2]=>216 [3,5,6,4,2,1]=>432 [3,6,1,2,4,5]=>324 [3,6,1,2,5,4]=>216 [3,6,1,4,2,5]=>216 [3,6,1,4,5,2]=>216 [3,6,1,5,2,4]=>216 [3,6,1,5,4,2]=>144 [3,6,2,1,4,5]=>216 [3,6,2,1,5,4]=>144 [3,6,2,4,1,5]=>72 [3,6,2,4,5,1]=>216 [3,6,2,5,1,4]=>72 [3,6,2,5,4,1]=>144 [3,6,4,1,2,5]=>216 [3,6,4,1,5,2]=>144 [3,6,4,2,1,5]=>144 [3,6,4,2,5,1]=>144 [3,6,4,5,1,2]=>216 [3,6,4,5,2,1]=>432 [3,6,5,1,2,4]=>216 [3,6,5,1,4,2]=>144 [3,6,5,2,1,4]=>144 [3,6,5,2,4,1]=>144 [3,6,5,4,1,2]=>144 [3,6,5,4,2,1]=>288 [4,1,2,3,5,6]=>972 [4,1,2,3,6,5]=>648 [4,1,2,5,3,6]=>648 [4,1,2,5,6,3]=>648 [4,1,2,6,3,5]=>648 [4,1,2,6,5,3]=>432 [4,1,3,2,5,6]=>648 [4,1,3,2,6,5]=>432 [4,1,3,5,2,6]=>216 [4,1,3,5,6,2]=>648 [4,1,3,6,2,5]=>216 [4,1,3,6,5,2]=>432 [4,1,5,2,3,6]=>648 [4,1,5,2,6,3]=>432 [4,1,5,3,2,6]=>432 [4,1,5,3,6,2]=>432 [4,1,5,6,2,3]=>216 [4,1,5,6,3,2]=>432 [4,1,6,2,3,5]=>648 [4,1,6,2,5,3]=>432 [4,1,6,3,2,5]=>432 [4,1,6,3,5,2]=>432 [4,1,6,5,2,3]=>432 [4,1,6,5,3,2]=>288 [4,2,1,3,5,6]=>648 [4,2,1,3,6,5]=>432 [4,2,1,5,3,6]=>432 [4,2,1,5,6,3]=>432 [4,2,1,6,3,5]=>432 [4,2,1,6,5,3]=>288 [4,2,3,1,5,6]=>216 [4,2,3,1,6,5]=>144 [4,2,3,5,1,6]=>216 [4,2,3,5,6,1]=>648 [4,2,3,6,1,5]=>216 [4,2,3,6,5,1]=>432 [4,2,5,1,3,6]=>216 [4,2,5,1,6,3]=>144 [4,2,5,3,1,6]=>144 [4,2,5,3,6,1]=>432 [4,2,5,6,1,3]=>216 [4,2,5,6,3,1]=>432 [4,2,6,1,3,5]=>216 [4,2,6,1,5,3]=>144 [4,2,6,3,1,5]=>144 [4,2,6,3,5,1]=>432 [4,2,6,5,1,3]=>144 [4,2,6,5,3,1]=>288 [4,3,1,2,5,6]=>648 [4,3,1,2,6,5]=>432 [4,3,1,5,2,6]=>432 [4,3,1,5,6,2]=>432 [4,3,1,6,2,5]=>432 [4,3,1,6,5,2]=>288 [4,3,2,1,5,6]=>432 [4,3,2,1,6,5]=>288 [4,3,2,5,1,6]=>144 [4,3,2,5,6,1]=>432 [4,3,2,6,1,5]=>144 [4,3,2,6,5,1]=>288 [4,3,5,1,2,6]=>216 [4,3,5,1,6,2]=>144 [4,3,5,2,1,6]=>144 [4,3,5,2,6,1]=>144 [4,3,5,6,1,2]=>216 [4,3,5,6,2,1]=>432 [4,3,6,1,2,5]=>216 [4,3,6,1,5,2]=>144 [4,3,6,2,1,5]=>144 [4,3,6,2,5,1]=>144 [4,3,6,5,1,2]=>144 [4,3,6,5,2,1]=>288 [4,5,1,2,3,6]=>324 [4,5,1,2,6,3]=>216 [4,5,1,3,2,6]=>216 [4,5,1,3,6,2]=>216 [4,5,1,6,2,3]=>216 [4,5,1,6,3,2]=>144 [4,5,2,1,3,6]=>216 [4,5,2,1,6,3]=>144 [4,5,2,3,1,6]=>72 [4,5,2,3,6,1]=>216 [4,5,2,6,1,3]=>72 [4,5,2,6,3,1]=>144 [4,5,3,1,2,6]=>216 [4,5,3,1,6,2]=>144 [4,5,3,2,1,6]=>144 [4,5,3,2,6,1]=>144 [4,5,3,6,1,2]=>72 [4,5,3,6,2,1]=>144 [4,5,6,1,2,3]=>108 [4,5,6,1,3,2]=>216 [4,5,6,2,1,3]=>216 [4,5,6,2,3,1]=>216 [4,5,6,3,1,2]=>216 [4,5,6,3,2,1]=>432 [4,6,1,2,3,5]=>324 [4,6,1,2,5,3]=>216 [4,6,1,3,2,5]=>216 [4,6,1,3,5,2]=>216 [4,6,1,5,2,3]=>216 [4,6,1,5,3,2]=>144 [4,6,2,1,3,5]=>216 [4,6,2,1,5,3]=>144 [4,6,2,3,1,5]=>72 [4,6,2,3,5,1]=>216 [4,6,2,5,1,3]=>72 [4,6,2,5,3,1]=>144 [4,6,3,1,2,5]=>216 [4,6,3,1,5,2]=>144 [4,6,3,2,1,5]=>144 [4,6,3,2,5,1]=>144 [4,6,3,5,1,2]=>72 [4,6,3,5,2,1]=>144 [4,6,5,1,2,3]=>216 [4,6,5,1,3,2]=>144 [4,6,5,2,1,3]=>144 [4,6,5,2,3,1]=>144 [4,6,5,3,1,2]=>144 [4,6,5,3,2,1]=>288 [5,1,2,3,4,6]=>972 [5,1,2,3,6,4]=>648 [5,1,2,4,3,6]=>648 [5,1,2,4,6,3]=>648 [5,1,2,6,3,4]=>648 [5,1,2,6,4,3]=>432 [5,1,3,2,4,6]=>648 [5,1,3,2,6,4]=>432 [5,1,3,4,2,6]=>216 [5,1,3,4,6,2]=>648 [5,1,3,6,2,4]=>216 [5,1,3,6,4,2]=>432 [5,1,4,2,3,6]=>648 [5,1,4,2,6,3]=>432 [5,1,4,3,2,6]=>432 [5,1,4,3,6,2]=>432 [5,1,4,6,2,3]=>216 [5,1,4,6,3,2]=>432 [5,1,6,2,3,4]=>648 [5,1,6,2,4,3]=>432 [5,1,6,3,2,4]=>432 [5,1,6,3,4,2]=>432 [5,1,6,4,2,3]=>432 [5,1,6,4,3,2]=>288 [5,2,1,3,4,6]=>648 [5,2,1,3,6,4]=>432 [5,2,1,4,3,6]=>432 [5,2,1,4,6,3]=>432 [5,2,1,6,3,4]=>432 [5,2,1,6,4,3]=>288 [5,2,3,1,4,6]=>216 [5,2,3,1,6,4]=>144 [5,2,3,4,1,6]=>216 [5,2,3,4,6,1]=>648 [5,2,3,6,1,4]=>216 [5,2,3,6,4,1]=>432 [5,2,4,1,3,6]=>216 [5,2,4,1,6,3]=>144 [5,2,4,3,1,6]=>144 [5,2,4,3,6,1]=>432 [5,2,4,6,1,3]=>216 [5,2,4,6,3,1]=>432 [5,2,6,1,3,4]=>216 [5,2,6,1,4,3]=>144 [5,2,6,3,1,4]=>144 [5,2,6,3,4,1]=>432 [5,2,6,4,1,3]=>144 [5,2,6,4,3,1]=>288 [5,3,1,2,4,6]=>648 [5,3,1,2,6,4]=>432 [5,3,1,4,2,6]=>432 [5,3,1,4,6,2]=>432 [5,3,1,6,2,4]=>432 [5,3,1,6,4,2]=>288 [5,3,2,1,4,6]=>432 [5,3,2,1,6,4]=>288 [5,3,2,4,1,6]=>144 [5,3,2,4,6,1]=>432 [5,3,2,6,1,4]=>144 [5,3,2,6,4,1]=>288 [5,3,4,1,2,6]=>216 [5,3,4,1,6,2]=>144 [5,3,4,2,1,6]=>144 [5,3,4,2,6,1]=>144 [5,3,4,6,1,2]=>216 [5,3,4,6,2,1]=>432 [5,3,6,1,2,4]=>216 [5,3,6,1,4,2]=>144 [5,3,6,2,1,4]=>144 [5,3,6,2,4,1]=>144 [5,3,6,4,1,2]=>144 [5,3,6,4,2,1]=>288 [5,4,1,2,3,6]=>648 [5,4,1,2,6,3]=>432 [5,4,1,3,2,6]=>432 [5,4,1,3,6,2]=>432 [5,4,1,6,2,3]=>432 [5,4,1,6,3,2]=>288 [5,4,2,1,3,6]=>432 [5,4,2,1,6,3]=>288 [5,4,2,3,1,6]=>144 [5,4,2,3,6,1]=>432 [5,4,2,6,1,3]=>144 [5,4,2,6,3,1]=>288 [5,4,3,1,2,6]=>432 [5,4,3,1,6,2]=>288 [5,4,3,2,1,6]=>288 [5,4,3,2,6,1]=>288 [5,4,3,6,1,2]=>144 [5,4,3,6,2,1]=>288 [5,4,6,1,2,3]=>216 [5,4,6,1,3,2]=>144 [5,4,6,2,1,3]=>144 [5,4,6,2,3,1]=>144 [5,4,6,3,1,2]=>144 [5,4,6,3,2,1]=>288 [5,6,1,2,3,4]=>324 [5,6,1,2,4,3]=>216 [5,6,1,3,2,4]=>216 [5,6,1,3,4,2]=>216 [5,6,1,4,2,3]=>216 [5,6,1,4,3,2]=>144 [5,6,2,1,3,4]=>216 [5,6,2,1,4,3]=>144 [5,6,2,3,1,4]=>72 [5,6,2,3,4,1]=>216 [5,6,2,4,1,3]=>72 [5,6,2,4,3,1]=>144 [5,6,3,1,2,4]=>216 [5,6,3,1,4,2]=>144 [5,6,3,2,1,4]=>144 [5,6,3,2,4,1]=>144 [5,6,3,4,1,2]=>72 [5,6,3,4,2,1]=>144 [5,6,4,1,2,3]=>216 [5,6,4,1,3,2]=>144 [5,6,4,2,1,3]=>144 [5,6,4,2,3,1]=>144 [5,6,4,3,1,2]=>144 [5,6,4,3,2,1]=>288 [6,1,2,3,4,5]=>972 [6,1,2,3,5,4]=>648 [6,1,2,4,3,5]=>648 [6,1,2,4,5,3]=>648 [6,1,2,5,3,4]=>648 [6,1,2,5,4,3]=>432 [6,1,3,2,4,5]=>648 [6,1,3,2,5,4]=>432 [6,1,3,4,2,5]=>216 [6,1,3,4,5,2]=>648 [6,1,3,5,2,4]=>216 [6,1,3,5,4,2]=>432 [6,1,4,2,3,5]=>648 [6,1,4,2,5,3]=>432 [6,1,4,3,2,5]=>432 [6,1,4,3,5,2]=>432 [6,1,4,5,2,3]=>216 [6,1,4,5,3,2]=>432 [6,1,5,2,3,4]=>648 [6,1,5,2,4,3]=>432 [6,1,5,3,2,4]=>432 [6,1,5,3,4,2]=>432 [6,1,5,4,2,3]=>432 [6,1,5,4,3,2]=>288 [6,2,1,3,4,5]=>648 [6,2,1,3,5,4]=>432 [6,2,1,4,3,5]=>432 [6,2,1,4,5,3]=>432 [6,2,1,5,3,4]=>432 [6,2,1,5,4,3]=>288 [6,2,3,1,4,5]=>216 [6,2,3,1,5,4]=>144 [6,2,3,4,1,5]=>216 [6,2,3,4,5,1]=>648 [6,2,3,5,1,4]=>216 [6,2,3,5,4,1]=>432 [6,2,4,1,3,5]=>216 [6,2,4,1,5,3]=>144 [6,2,4,3,1,5]=>144 [6,2,4,3,5,1]=>432 [6,2,4,5,1,3]=>216 [6,2,4,5,3,1]=>432 [6,2,5,1,3,4]=>216 [6,2,5,1,4,3]=>144 [6,2,5,3,1,4]=>144 [6,2,5,3,4,1]=>432 [6,2,5,4,1,3]=>144 [6,2,5,4,3,1]=>288 [6,3,1,2,4,5]=>648 [6,3,1,2,5,4]=>432 [6,3,1,4,2,5]=>432 [6,3,1,4,5,2]=>432 [6,3,1,5,2,4]=>432 [6,3,1,5,4,2]=>288 [6,3,2,1,4,5]=>432 [6,3,2,1,5,4]=>288 [6,3,2,4,1,5]=>144 [6,3,2,4,5,1]=>432 [6,3,2,5,1,4]=>144 [6,3,2,5,4,1]=>288 [6,3,4,1,2,5]=>216 [6,3,4,1,5,2]=>144 [6,3,4,2,1,5]=>144 [6,3,4,2,5,1]=>144 [6,3,4,5,1,2]=>216 [6,3,4,5,2,1]=>432 [6,3,5,1,2,4]=>216 [6,3,5,1,4,2]=>144 [6,3,5,2,1,4]=>144 [6,3,5,2,4,1]=>144 [6,3,5,4,1,2]=>144 [6,3,5,4,2,1]=>288 [6,4,1,2,3,5]=>648 [6,4,1,2,5,3]=>432 [6,4,1,3,2,5]=>432 [6,4,1,3,5,2]=>432 [6,4,1,5,2,3]=>432 [6,4,1,5,3,2]=>288 [6,4,2,1,3,5]=>432 [6,4,2,1,5,3]=>288 [6,4,2,3,1,5]=>144 [6,4,2,3,5,1]=>432 [6,4,2,5,1,3]=>144 [6,4,2,5,3,1]=>288 [6,4,3,1,2,5]=>432 [6,4,3,1,5,2]=>288 [6,4,3,2,1,5]=>288 [6,4,3,2,5,1]=>288 [6,4,3,5,1,2]=>144 [6,4,3,5,2,1]=>288 [6,4,5,1,2,3]=>216 [6,4,5,1,3,2]=>144 [6,4,5,2,1,3]=>144 [6,4,5,2,3,1]=>144 [6,4,5,3,1,2]=>144 [6,4,5,3,2,1]=>288 [6,5,1,2,3,4]=>648 [6,5,1,2,4,3]=>432 [6,5,1,3,2,4]=>432 [6,5,1,3,4,2]=>432 [6,5,1,4,2,3]=>432 [6,5,1,4,3,2]=>288 [6,5,2,1,3,4]=>432 [6,5,2,1,4,3]=>288 [6,5,2,3,1,4]=>144 [6,5,2,3,4,1]=>432 [6,5,2,4,1,3]=>144 [6,5,2,4,3,1]=>288 [6,5,3,1,2,4]=>432 [6,5,3,1,4,2]=>288 [6,5,3,2,1,4]=>288 [6,5,3,2,4,1]=>288 [6,5,3,4,1,2]=>144 [6,5,3,4,2,1]=>288 [6,5,4,1,2,3]=>432 [6,5,4,1,3,2]=>288 [6,5,4,2,1,3]=>288 [6,5,4,2,3,1]=>288 [6,5,4,3,1,2]=>288 [6,5,4,3,2,1]=>192
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Description
The shape of the tree associated to a permutation.
A permutation can be mapped to a rooted tree with vertices {0,1,2,…,n} and root 0 in the following way. Entries of the permutations are inserted one after the other, each child is larger than its parent and the children are in strict order from left to right. Details of the construction are found in [1].
The statistic is given by $2^w 3^h$, where $w$ is the width St000325The width of the tree associated to a permutation. and $h$ is the height St000308The height of the tree associated to a permutation. of this tree.
References
[1] http://oeis.org/wiki/User:Peter_Luschny/PermutationTrees
Code
def statistic(pi):
    if pi == []: return (0, 0)
    h, w, i, branch, next = 0, 0, 0, [0], pi[0]

    while true:
        while next < branch[len(branch)-1]:
            branch.pop()

        current = 0
        w += 1
        while next > current:
            i += 1
            h = max(h, len(branch))
            if i == len(pi): return 2^w*3^h
            branch.append(next)
            current, next = next, pi[i]
Created
Dec 11, 2015 at 11:05 by Peter Luschny
Updated
Feb 25, 2022 at 16:54 by Nadia Lafreniere