Identifier
- St000021: Permutations ⟶ ℤ (values match St000325The width of the tree associated to a permutation., St000470The number of runs in a permutation.)
Values
=>
[]=>0
[1]=>0
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>1
[3,1,2]=>1
[3,2,1]=>2
[1,2,3,4]=>0
[1,2,4,3]=>1
[1,3,2,4]=>1
[1,3,4,2]=>1
[1,4,2,3]=>1
[1,4,3,2]=>2
[2,1,3,4]=>1
[2,1,4,3]=>2
[2,3,1,4]=>1
[2,3,4,1]=>1
[2,4,1,3]=>1
[2,4,3,1]=>2
[3,1,2,4]=>1
[3,1,4,2]=>2
[3,2,1,4]=>2
[3,2,4,1]=>2
[3,4,1,2]=>1
[3,4,2,1]=>2
[4,1,2,3]=>1
[4,1,3,2]=>2
[4,2,1,3]=>2
[4,2,3,1]=>2
[4,3,1,2]=>2
[4,3,2,1]=>3
[1,2,3,4,5]=>0
[1,2,3,5,4]=>1
[1,2,4,3,5]=>1
[1,2,4,5,3]=>1
[1,2,5,3,4]=>1
[1,2,5,4,3]=>2
[1,3,2,4,5]=>1
[1,3,2,5,4]=>2
[1,3,4,2,5]=>1
[1,3,4,5,2]=>1
[1,3,5,2,4]=>1
[1,3,5,4,2]=>2
[1,4,2,3,5]=>1
[1,4,2,5,3]=>2
[1,4,3,2,5]=>2
[1,4,3,5,2]=>2
[1,4,5,2,3]=>1
[1,4,5,3,2]=>2
[1,5,2,3,4]=>1
[1,5,2,4,3]=>2
[1,5,3,2,4]=>2
[1,5,3,4,2]=>2
[1,5,4,2,3]=>2
[1,5,4,3,2]=>3
[2,1,3,4,5]=>1
[2,1,3,5,4]=>2
[2,1,4,3,5]=>2
[2,1,4,5,3]=>2
[2,1,5,3,4]=>2
[2,1,5,4,3]=>3
[2,3,1,4,5]=>1
[2,3,1,5,4]=>2
[2,3,4,1,5]=>1
[2,3,4,5,1]=>1
[2,3,5,1,4]=>1
[2,3,5,4,1]=>2
[2,4,1,3,5]=>1
[2,4,1,5,3]=>2
[2,4,3,1,5]=>2
[2,4,3,5,1]=>2
[2,4,5,1,3]=>1
[2,4,5,3,1]=>2
[2,5,1,3,4]=>1
[2,5,1,4,3]=>2
[2,5,3,1,4]=>2
[2,5,3,4,1]=>2
[2,5,4,1,3]=>2
[2,5,4,3,1]=>3
[3,1,2,4,5]=>1
[3,1,2,5,4]=>2
[3,1,4,2,5]=>2
[3,1,4,5,2]=>2
[3,1,5,2,4]=>2
[3,1,5,4,2]=>3
[3,2,1,4,5]=>2
[3,2,1,5,4]=>3
[3,2,4,1,5]=>2
[3,2,4,5,1]=>2
[3,2,5,1,4]=>2
[3,2,5,4,1]=>3
[3,4,1,2,5]=>1
[3,4,1,5,2]=>2
[3,4,2,1,5]=>2
[3,4,2,5,1]=>2
[3,4,5,1,2]=>1
[3,4,5,2,1]=>2
[3,5,1,2,4]=>1
[3,5,1,4,2]=>2
[3,5,2,1,4]=>2
[3,5,2,4,1]=>2
[3,5,4,1,2]=>2
[3,5,4,2,1]=>3
[4,1,2,3,5]=>1
[4,1,2,5,3]=>2
[4,1,3,2,5]=>2
[4,1,3,5,2]=>2
[4,1,5,2,3]=>2
[4,1,5,3,2]=>3
[4,2,1,3,5]=>2
[4,2,1,5,3]=>3
[4,2,3,1,5]=>2
[4,2,3,5,1]=>2
[4,2,5,1,3]=>2
[4,2,5,3,1]=>3
[4,3,1,2,5]=>2
[4,3,1,5,2]=>3
[4,3,2,1,5]=>3
[4,3,2,5,1]=>3
[4,3,5,1,2]=>2
[4,3,5,2,1]=>3
[4,5,1,2,3]=>1
[4,5,1,3,2]=>2
[4,5,2,1,3]=>2
[4,5,2,3,1]=>2
[4,5,3,1,2]=>2
[4,5,3,2,1]=>3
[5,1,2,3,4]=>1
[5,1,2,4,3]=>2
[5,1,3,2,4]=>2
[5,1,3,4,2]=>2
[5,1,4,2,3]=>2
[5,1,4,3,2]=>3
[5,2,1,3,4]=>2
[5,2,1,4,3]=>3
[5,2,3,1,4]=>2
[5,2,3,4,1]=>2
[5,2,4,1,3]=>2
[5,2,4,3,1]=>3
[5,3,1,2,4]=>2
[5,3,1,4,2]=>3
[5,3,2,1,4]=>3
[5,3,2,4,1]=>3
[5,3,4,1,2]=>2
[5,3,4,2,1]=>3
[5,4,1,2,3]=>2
[5,4,1,3,2]=>3
[5,4,2,1,3]=>3
[5,4,2,3,1]=>3
[5,4,3,1,2]=>3
[5,4,3,2,1]=>4
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>1
[1,2,3,6,4,5]=>1
[1,2,3,6,5,4]=>2
[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>1
[1,2,4,5,6,3]=>1
[1,2,4,6,3,5]=>1
[1,2,4,6,5,3]=>2
[1,2,5,3,4,6]=>1
[1,2,5,3,6,4]=>2
[1,2,5,4,3,6]=>2
[1,2,5,4,6,3]=>2
[1,2,5,6,3,4]=>1
[1,2,5,6,4,3]=>2
[1,2,6,3,4,5]=>1
[1,2,6,3,5,4]=>2
[1,2,6,4,3,5]=>2
[1,2,6,4,5,3]=>2
[1,2,6,5,3,4]=>2
[1,2,6,5,4,3]=>3
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>2
[1,3,2,5,6,4]=>2
[1,3,2,6,4,5]=>2
[1,3,2,6,5,4]=>3
[1,3,4,2,5,6]=>1
[1,3,4,2,6,5]=>2
[1,3,4,5,2,6]=>1
[1,3,4,5,6,2]=>1
[1,3,4,6,2,5]=>1
[1,3,4,6,5,2]=>2
[1,3,5,2,4,6]=>1
[1,3,5,2,6,4]=>2
[1,3,5,4,2,6]=>2
[1,3,5,4,6,2]=>2
[1,3,5,6,2,4]=>1
[1,3,5,6,4,2]=>2
[1,3,6,2,4,5]=>1
[1,3,6,2,5,4]=>2
[1,3,6,4,2,5]=>2
[1,3,6,4,5,2]=>2
[1,3,6,5,2,4]=>2
[1,3,6,5,4,2]=>3
[1,4,2,3,5,6]=>1
[1,4,2,3,6,5]=>2
[1,4,2,5,3,6]=>2
[1,4,2,5,6,3]=>2
[1,4,2,6,3,5]=>2
[1,4,2,6,5,3]=>3
[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>3
[1,4,3,5,2,6]=>2
[1,4,3,5,6,2]=>2
[1,4,3,6,2,5]=>2
[1,4,3,6,5,2]=>3
[1,4,5,2,3,6]=>1
[1,4,5,2,6,3]=>2
[1,4,5,3,2,6]=>2
[1,4,5,3,6,2]=>2
[1,4,5,6,2,3]=>1
[1,4,5,6,3,2]=>2
[1,4,6,2,3,5]=>1
[1,4,6,2,5,3]=>2
[1,4,6,3,2,5]=>2
[1,4,6,3,5,2]=>2
[1,4,6,5,2,3]=>2
[1,4,6,5,3,2]=>3
[1,5,2,3,4,6]=>1
[1,5,2,3,6,4]=>2
[1,5,2,4,3,6]=>2
[1,5,2,4,6,3]=>2
[1,5,2,6,3,4]=>2
[1,5,2,6,4,3]=>3
[1,5,3,2,4,6]=>2
[1,5,3,2,6,4]=>3
[1,5,3,4,2,6]=>2
[1,5,3,4,6,2]=>2
[1,5,3,6,2,4]=>2
[1,5,3,6,4,2]=>3
[1,5,4,2,3,6]=>2
[1,5,4,2,6,3]=>3
[1,5,4,3,2,6]=>3
[1,5,4,3,6,2]=>3
[1,5,4,6,2,3]=>2
[1,5,4,6,3,2]=>3
[1,5,6,2,3,4]=>1
[1,5,6,2,4,3]=>2
[1,5,6,3,2,4]=>2
[1,5,6,3,4,2]=>2
[1,5,6,4,2,3]=>2
[1,5,6,4,3,2]=>3
[1,6,2,3,4,5]=>1
[1,6,2,3,5,4]=>2
[1,6,2,4,3,5]=>2
[1,6,2,4,5,3]=>2
[1,6,2,5,3,4]=>2
[1,6,2,5,4,3]=>3
[1,6,3,2,4,5]=>2
[1,6,3,2,5,4]=>3
[1,6,3,4,2,5]=>2
[1,6,3,4,5,2]=>2
[1,6,3,5,2,4]=>2
[1,6,3,5,4,2]=>3
[1,6,4,2,3,5]=>2
[1,6,4,2,5,3]=>3
[1,6,4,3,2,5]=>3
[1,6,4,3,5,2]=>3
[1,6,4,5,2,3]=>2
[1,6,4,5,3,2]=>3
[1,6,5,2,3,4]=>2
[1,6,5,2,4,3]=>3
[1,6,5,3,2,4]=>3
[1,6,5,3,4,2]=>3
[1,6,5,4,2,3]=>3
[1,6,5,4,3,2]=>4
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>2
[2,1,3,5,6,4]=>2
[2,1,3,6,4,5]=>2
[2,1,3,6,5,4]=>3
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>2
[2,1,4,5,6,3]=>2
[2,1,4,6,3,5]=>2
[2,1,4,6,5,3]=>3
[2,1,5,3,4,6]=>2
[2,1,5,3,6,4]=>3
[2,1,5,4,3,6]=>3
[2,1,5,4,6,3]=>3
[2,1,5,6,3,4]=>2
[2,1,5,6,4,3]=>3
[2,1,6,3,4,5]=>2
[2,1,6,3,5,4]=>3
[2,1,6,4,3,5]=>3
[2,1,6,4,5,3]=>3
[2,1,6,5,3,4]=>3
[2,1,6,5,4,3]=>4
[2,3,1,4,5,6]=>1
[2,3,1,4,6,5]=>2
[2,3,1,5,4,6]=>2
[2,3,1,5,6,4]=>2
[2,3,1,6,4,5]=>2
[2,3,1,6,5,4]=>3
[2,3,4,1,5,6]=>1
[2,3,4,1,6,5]=>2
[2,3,4,5,1,6]=>1
[2,3,4,5,6,1]=>1
[2,3,4,6,1,5]=>1
[2,3,4,6,5,1]=>2
[2,3,5,1,4,6]=>1
[2,3,5,1,6,4]=>2
[2,3,5,4,1,6]=>2
[2,3,5,4,6,1]=>2
[2,3,5,6,1,4]=>1
[2,3,5,6,4,1]=>2
[2,3,6,1,4,5]=>1
[2,3,6,1,5,4]=>2
[2,3,6,4,1,5]=>2
[2,3,6,4,5,1]=>2
[2,3,6,5,1,4]=>2
[2,3,6,5,4,1]=>3
[2,4,1,3,5,6]=>1
[2,4,1,3,6,5]=>2
[2,4,1,5,3,6]=>2
[2,4,1,5,6,3]=>2
[2,4,1,6,3,5]=>2
[2,4,1,6,5,3]=>3
[2,4,3,1,5,6]=>2
[2,4,3,1,6,5]=>3
[2,4,3,5,1,6]=>2
[2,4,3,5,6,1]=>2
[2,4,3,6,1,5]=>2
[2,4,3,6,5,1]=>3
[2,4,5,1,3,6]=>1
[2,4,5,1,6,3]=>2
[2,4,5,3,1,6]=>2
[2,4,5,3,6,1]=>2
[2,4,5,6,1,3]=>1
[2,4,5,6,3,1]=>2
[2,4,6,1,3,5]=>1
[2,4,6,1,5,3]=>2
[2,4,6,3,1,5]=>2
[2,4,6,3,5,1]=>2
[2,4,6,5,1,3]=>2
[2,4,6,5,3,1]=>3
[2,5,1,3,4,6]=>1
[2,5,1,3,6,4]=>2
[2,5,1,4,3,6]=>2
[2,5,1,4,6,3]=>2
[2,5,1,6,3,4]=>2
[2,5,1,6,4,3]=>3
[2,5,3,1,4,6]=>2
[2,5,3,1,6,4]=>3
[2,5,3,4,1,6]=>2
[2,5,3,4,6,1]=>2
[2,5,3,6,1,4]=>2
[2,5,3,6,4,1]=>3
[2,5,4,1,3,6]=>2
[2,5,4,1,6,3]=>3
[2,5,4,3,1,6]=>3
[2,5,4,3,6,1]=>3
[2,5,4,6,1,3]=>2
[2,5,4,6,3,1]=>3
[2,5,6,1,3,4]=>1
[2,5,6,1,4,3]=>2
[2,5,6,3,1,4]=>2
[2,5,6,3,4,1]=>2
[2,5,6,4,1,3]=>2
[2,5,6,4,3,1]=>3
[2,6,1,3,4,5]=>1
[2,6,1,3,5,4]=>2
[2,6,1,4,3,5]=>2
[2,6,1,4,5,3]=>2
[2,6,1,5,3,4]=>2
[2,6,1,5,4,3]=>3
[2,6,3,1,4,5]=>2
[2,6,3,1,5,4]=>3
[2,6,3,4,1,5]=>2
[2,6,3,4,5,1]=>2
[2,6,3,5,1,4]=>2
[2,6,3,5,4,1]=>3
[2,6,4,1,3,5]=>2
[2,6,4,1,5,3]=>3
[2,6,4,3,1,5]=>3
[2,6,4,3,5,1]=>3
[2,6,4,5,1,3]=>2
[2,6,4,5,3,1]=>3
[2,6,5,1,3,4]=>2
[2,6,5,1,4,3]=>3
[2,6,5,3,1,4]=>3
[2,6,5,3,4,1]=>3
[2,6,5,4,1,3]=>3
[2,6,5,4,3,1]=>4
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>2
[3,1,2,5,4,6]=>2
[3,1,2,5,6,4]=>2
[3,1,2,6,4,5]=>2
[3,1,2,6,5,4]=>3
[3,1,4,2,5,6]=>2
[3,1,4,2,6,5]=>3
[3,1,4,5,2,6]=>2
[3,1,4,5,6,2]=>2
[3,1,4,6,2,5]=>2
[3,1,4,6,5,2]=>3
[3,1,5,2,4,6]=>2
[3,1,5,2,6,4]=>3
[3,1,5,4,2,6]=>3
[3,1,5,4,6,2]=>3
[3,1,5,6,2,4]=>2
[3,1,5,6,4,2]=>3
[3,1,6,2,4,5]=>2
[3,1,6,2,5,4]=>3
[3,1,6,4,2,5]=>3
[3,1,6,4,5,2]=>3
[3,1,6,5,2,4]=>3
[3,1,6,5,4,2]=>4
[3,2,1,4,5,6]=>2
[3,2,1,4,6,5]=>3
[3,2,1,5,4,6]=>3
[3,2,1,5,6,4]=>3
[3,2,1,6,4,5]=>3
[3,2,1,6,5,4]=>4
[3,2,4,1,5,6]=>2
[3,2,4,1,6,5]=>3
[3,2,4,5,1,6]=>2
[3,2,4,5,6,1]=>2
[3,2,4,6,1,5]=>2
[3,2,4,6,5,1]=>3
[3,2,5,1,4,6]=>2
[3,2,5,1,6,4]=>3
[3,2,5,4,1,6]=>3
[3,2,5,4,6,1]=>3
[3,2,5,6,1,4]=>2
[3,2,5,6,4,1]=>3
[3,2,6,1,4,5]=>2
[3,2,6,1,5,4]=>3
[3,2,6,4,1,5]=>3
[3,2,6,4,5,1]=>3
[3,2,6,5,1,4]=>3
[3,2,6,5,4,1]=>4
[3,4,1,2,5,6]=>1
[3,4,1,2,6,5]=>2
[3,4,1,5,2,6]=>2
[3,4,1,5,6,2]=>2
[3,4,1,6,2,5]=>2
[3,4,1,6,5,2]=>3
[3,4,2,1,5,6]=>2
[3,4,2,1,6,5]=>3
[3,4,2,5,1,6]=>2
[3,4,2,5,6,1]=>2
[3,4,2,6,1,5]=>2
[3,4,2,6,5,1]=>3
[3,4,5,1,2,6]=>1
[3,4,5,1,6,2]=>2
[3,4,5,2,1,6]=>2
[3,4,5,2,6,1]=>2
[3,4,5,6,1,2]=>1
[3,4,5,6,2,1]=>2
[3,4,6,1,2,5]=>1
[3,4,6,1,5,2]=>2
[3,4,6,2,1,5]=>2
[3,4,6,2,5,1]=>2
[3,4,6,5,1,2]=>2
[3,4,6,5,2,1]=>3
[3,5,1,2,4,6]=>1
[3,5,1,2,6,4]=>2
[3,5,1,4,2,6]=>2
[3,5,1,4,6,2]=>2
[3,5,1,6,2,4]=>2
[3,5,1,6,4,2]=>3
[3,5,2,1,4,6]=>2
[3,5,2,1,6,4]=>3
[3,5,2,4,1,6]=>2
[3,5,2,4,6,1]=>2
[3,5,2,6,1,4]=>2
[3,5,2,6,4,1]=>3
[3,5,4,1,2,6]=>2
[3,5,4,1,6,2]=>3
[3,5,4,2,1,6]=>3
[3,5,4,2,6,1]=>3
[3,5,4,6,1,2]=>2
[3,5,4,6,2,1]=>3
[3,5,6,1,2,4]=>1
[3,5,6,1,4,2]=>2
[3,5,6,2,1,4]=>2
[3,5,6,2,4,1]=>2
[3,5,6,4,1,2]=>2
[3,5,6,4,2,1]=>3
[3,6,1,2,4,5]=>1
[3,6,1,2,5,4]=>2
[3,6,1,4,2,5]=>2
[3,6,1,4,5,2]=>2
[3,6,1,5,2,4]=>2
[3,6,1,5,4,2]=>3
[3,6,2,1,4,5]=>2
[3,6,2,1,5,4]=>3
[3,6,2,4,1,5]=>2
[3,6,2,4,5,1]=>2
[3,6,2,5,1,4]=>2
[3,6,2,5,4,1]=>3
[3,6,4,1,2,5]=>2
[3,6,4,1,5,2]=>3
[3,6,4,2,1,5]=>3
[3,6,4,2,5,1]=>3
[3,6,4,5,1,2]=>2
[3,6,4,5,2,1]=>3
[3,6,5,1,2,4]=>2
[3,6,5,1,4,2]=>3
[3,6,5,2,1,4]=>3
[3,6,5,2,4,1]=>3
[3,6,5,4,1,2]=>3
[3,6,5,4,2,1]=>4
[4,1,2,3,5,6]=>1
[4,1,2,3,6,5]=>2
[4,1,2,5,3,6]=>2
[4,1,2,5,6,3]=>2
[4,1,2,6,3,5]=>2
[4,1,2,6,5,3]=>3
[4,1,3,2,5,6]=>2
[4,1,3,2,6,5]=>3
[4,1,3,5,2,6]=>2
[4,1,3,5,6,2]=>2
[4,1,3,6,2,5]=>2
[4,1,3,6,5,2]=>3
[4,1,5,2,3,6]=>2
[4,1,5,2,6,3]=>3
[4,1,5,3,2,6]=>3
[4,1,5,3,6,2]=>3
[4,1,5,6,2,3]=>2
[4,1,5,6,3,2]=>3
[4,1,6,2,3,5]=>2
[4,1,6,2,5,3]=>3
[4,1,6,3,2,5]=>3
[4,1,6,3,5,2]=>3
[4,1,6,5,2,3]=>3
[4,1,6,5,3,2]=>4
[4,2,1,3,5,6]=>2
[4,2,1,3,6,5]=>3
[4,2,1,5,3,6]=>3
[4,2,1,5,6,3]=>3
[4,2,1,6,3,5]=>3
[4,2,1,6,5,3]=>4
[4,2,3,1,5,6]=>2
[4,2,3,1,6,5]=>3
[4,2,3,5,1,6]=>2
[4,2,3,5,6,1]=>2
[4,2,3,6,1,5]=>2
[4,2,3,6,5,1]=>3
[4,2,5,1,3,6]=>2
[4,2,5,1,6,3]=>3
[4,2,5,3,1,6]=>3
[4,2,5,3,6,1]=>3
[4,2,5,6,1,3]=>2
[4,2,5,6,3,1]=>3
[4,2,6,1,3,5]=>2
[4,2,6,1,5,3]=>3
[4,2,6,3,1,5]=>3
[4,2,6,3,5,1]=>3
[4,2,6,5,1,3]=>3
[4,2,6,5,3,1]=>4
[4,3,1,2,5,6]=>2
[4,3,1,2,6,5]=>3
[4,3,1,5,2,6]=>3
[4,3,1,5,6,2]=>3
[4,3,1,6,2,5]=>3
[4,3,1,6,5,2]=>4
[4,3,2,1,5,6]=>3
[4,3,2,1,6,5]=>4
[4,3,2,5,1,6]=>3
[4,3,2,5,6,1]=>3
[4,3,2,6,1,5]=>3
[4,3,2,6,5,1]=>4
[4,3,5,1,2,6]=>2
[4,3,5,1,6,2]=>3
[4,3,5,2,1,6]=>3
[4,3,5,2,6,1]=>3
[4,3,5,6,1,2]=>2
[4,3,5,6,2,1]=>3
[4,3,6,1,2,5]=>2
[4,3,6,1,5,2]=>3
[4,3,6,2,1,5]=>3
[4,3,6,2,5,1]=>3
[4,3,6,5,1,2]=>3
[4,3,6,5,2,1]=>4
[4,5,1,2,3,6]=>1
[4,5,1,2,6,3]=>2
[4,5,1,3,2,6]=>2
[4,5,1,3,6,2]=>2
[4,5,1,6,2,3]=>2
[4,5,1,6,3,2]=>3
[4,5,2,1,3,6]=>2
[4,5,2,1,6,3]=>3
[4,5,2,3,1,6]=>2
[4,5,2,3,6,1]=>2
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>3
[4,5,3,1,2,6]=>2
[4,5,3,1,6,2]=>3
[4,5,3,2,1,6]=>3
[4,5,3,2,6,1]=>3
[4,5,3,6,1,2]=>2
[4,5,3,6,2,1]=>3
[4,5,6,1,2,3]=>1
[4,5,6,1,3,2]=>2
[4,5,6,2,1,3]=>2
[4,5,6,2,3,1]=>2
[4,5,6,3,1,2]=>2
[4,5,6,3,2,1]=>3
[4,6,1,2,3,5]=>1
[4,6,1,2,5,3]=>2
[4,6,1,3,2,5]=>2
[4,6,1,3,5,2]=>2
[4,6,1,5,2,3]=>2
[4,6,1,5,3,2]=>3
[4,6,2,1,3,5]=>2
[4,6,2,1,5,3]=>3
[4,6,2,3,1,5]=>2
[4,6,2,3,5,1]=>2
[4,6,2,5,1,3]=>2
[4,6,2,5,3,1]=>3
[4,6,3,1,2,5]=>2
[4,6,3,1,5,2]=>3
[4,6,3,2,1,5]=>3
[4,6,3,2,5,1]=>3
[4,6,3,5,1,2]=>2
[4,6,3,5,2,1]=>3
[4,6,5,1,2,3]=>2
[4,6,5,1,3,2]=>3
[4,6,5,2,1,3]=>3
[4,6,5,2,3,1]=>3
[4,6,5,3,1,2]=>3
[4,6,5,3,2,1]=>4
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>2
[5,1,2,4,3,6]=>2
[5,1,2,4,6,3]=>2
[5,1,2,6,3,4]=>2
[5,1,2,6,4,3]=>3
[5,1,3,2,4,6]=>2
[5,1,3,2,6,4]=>3
[5,1,3,4,2,6]=>2
[5,1,3,4,6,2]=>2
[5,1,3,6,2,4]=>2
[5,1,3,6,4,2]=>3
[5,1,4,2,3,6]=>2
[5,1,4,2,6,3]=>3
[5,1,4,3,2,6]=>3
[5,1,4,3,6,2]=>3
[5,1,4,6,2,3]=>2
[5,1,4,6,3,2]=>3
[5,1,6,2,3,4]=>2
[5,1,6,2,4,3]=>3
[5,1,6,3,2,4]=>3
[5,1,6,3,4,2]=>3
[5,1,6,4,2,3]=>3
[5,1,6,4,3,2]=>4
[5,2,1,3,4,6]=>2
[5,2,1,3,6,4]=>3
[5,2,1,4,3,6]=>3
[5,2,1,4,6,3]=>3
[5,2,1,6,3,4]=>3
[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>2
[5,2,3,1,6,4]=>3
[5,2,3,4,1,6]=>2
[5,2,3,4,6,1]=>2
[5,2,3,6,1,4]=>2
[5,2,3,6,4,1]=>3
[5,2,4,1,3,6]=>2
[5,2,4,1,6,3]=>3
[5,2,4,3,1,6]=>3
[5,2,4,3,6,1]=>3
[5,2,4,6,1,3]=>2
[5,2,4,6,3,1]=>3
[5,2,6,1,3,4]=>2
[5,2,6,1,4,3]=>3
[5,2,6,3,1,4]=>3
[5,2,6,3,4,1]=>3
[5,2,6,4,1,3]=>3
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>2
[5,3,1,2,6,4]=>3
[5,3,1,4,2,6]=>3
[5,3,1,4,6,2]=>3
[5,3,1,6,2,4]=>3
[5,3,1,6,4,2]=>4
[5,3,2,1,4,6]=>3
[5,3,2,1,6,4]=>4
[5,3,2,4,1,6]=>3
[5,3,2,4,6,1]=>3
[5,3,2,6,1,4]=>3
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>2
[5,3,4,1,6,2]=>3
[5,3,4,2,1,6]=>3
[5,3,4,2,6,1]=>3
[5,3,4,6,1,2]=>2
[5,3,4,6,2,1]=>3
[5,3,6,1,2,4]=>2
[5,3,6,1,4,2]=>3
[5,3,6,2,1,4]=>3
[5,3,6,2,4,1]=>3
[5,3,6,4,1,2]=>3
[5,3,6,4,2,1]=>4
[5,4,1,2,3,6]=>2
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>3
[5,4,1,3,6,2]=>3
[5,4,1,6,2,3]=>3
[5,4,1,6,3,2]=>4
[5,4,2,1,3,6]=>3
[5,4,2,1,6,3]=>4
[5,4,2,3,1,6]=>3
[5,4,2,3,6,1]=>3
[5,4,2,6,1,3]=>3
[5,4,2,6,3,1]=>4
[5,4,3,1,2,6]=>3
[5,4,3,1,6,2]=>4
[5,4,3,2,1,6]=>4
[5,4,3,2,6,1]=>4
[5,4,3,6,1,2]=>3
[5,4,3,6,2,1]=>4
[5,4,6,1,2,3]=>2
[5,4,6,1,3,2]=>3
[5,4,6,2,1,3]=>3
[5,4,6,2,3,1]=>3
[5,4,6,3,1,2]=>3
[5,4,6,3,2,1]=>4
[5,6,1,2,3,4]=>1
[5,6,1,2,4,3]=>2
[5,6,1,3,2,4]=>2
[5,6,1,3,4,2]=>2
[5,6,1,4,2,3]=>2
[5,6,1,4,3,2]=>3
[5,6,2,1,3,4]=>2
[5,6,2,1,4,3]=>3
[5,6,2,3,1,4]=>2
[5,6,2,3,4,1]=>2
[5,6,2,4,1,3]=>2
[5,6,2,4,3,1]=>3
[5,6,3,1,2,4]=>2
[5,6,3,1,4,2]=>3
[5,6,3,2,1,4]=>3
[5,6,3,2,4,1]=>3
[5,6,3,4,1,2]=>2
[5,6,3,4,2,1]=>3
[5,6,4,1,2,3]=>2
[5,6,4,1,3,2]=>3
[5,6,4,2,1,3]=>3
[5,6,4,2,3,1]=>3
[5,6,4,3,1,2]=>3
[5,6,4,3,2,1]=>4
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>2
[6,1,2,4,3,5]=>2
[6,1,2,4,5,3]=>2
[6,1,2,5,3,4]=>2
[6,1,2,5,4,3]=>3
[6,1,3,2,4,5]=>2
[6,1,3,2,5,4]=>3
[6,1,3,4,2,5]=>2
[6,1,3,4,5,2]=>2
[6,1,3,5,2,4]=>2
[6,1,3,5,4,2]=>3
[6,1,4,2,3,5]=>2
[6,1,4,2,5,3]=>3
[6,1,4,3,2,5]=>3
[6,1,4,3,5,2]=>3
[6,1,4,5,2,3]=>2
[6,1,4,5,3,2]=>3
[6,1,5,2,3,4]=>2
[6,1,5,2,4,3]=>3
[6,1,5,3,2,4]=>3
[6,1,5,3,4,2]=>3
[6,1,5,4,2,3]=>3
[6,1,5,4,3,2]=>4
[6,2,1,3,4,5]=>2
[6,2,1,3,5,4]=>3
[6,2,1,4,3,5]=>3
[6,2,1,4,5,3]=>3
[6,2,1,5,3,4]=>3
[6,2,1,5,4,3]=>4
[6,2,3,1,4,5]=>2
[6,2,3,1,5,4]=>3
[6,2,3,4,1,5]=>2
[6,2,3,4,5,1]=>2
[6,2,3,5,1,4]=>2
[6,2,3,5,4,1]=>3
[6,2,4,1,3,5]=>2
[6,2,4,1,5,3]=>3
[6,2,4,3,1,5]=>3
[6,2,4,3,5,1]=>3
[6,2,4,5,1,3]=>2
[6,2,4,5,3,1]=>3
[6,2,5,1,3,4]=>2
[6,2,5,1,4,3]=>3
[6,2,5,3,1,4]=>3
[6,2,5,3,4,1]=>3
[6,2,5,4,1,3]=>3
[6,2,5,4,3,1]=>4
[6,3,1,2,4,5]=>2
[6,3,1,2,5,4]=>3
[6,3,1,4,2,5]=>3
[6,3,1,4,5,2]=>3
[6,3,1,5,2,4]=>3
[6,3,1,5,4,2]=>4
[6,3,2,1,4,5]=>3
[6,3,2,1,5,4]=>4
[6,3,2,4,1,5]=>3
[6,3,2,4,5,1]=>3
[6,3,2,5,1,4]=>3
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>2
[6,3,4,1,5,2]=>3
[6,3,4,2,1,5]=>3
[6,3,4,2,5,1]=>3
[6,3,4,5,1,2]=>2
[6,3,4,5,2,1]=>3
[6,3,5,1,2,4]=>2
[6,3,5,1,4,2]=>3
[6,3,5,2,1,4]=>3
[6,3,5,2,4,1]=>3
[6,3,5,4,1,2]=>3
[6,3,5,4,2,1]=>4
[6,4,1,2,3,5]=>2
[6,4,1,2,5,3]=>3
[6,4,1,3,2,5]=>3
[6,4,1,3,5,2]=>3
[6,4,1,5,2,3]=>3
[6,4,1,5,3,2]=>4
[6,4,2,1,3,5]=>3
[6,4,2,1,5,3]=>4
[6,4,2,3,1,5]=>3
[6,4,2,3,5,1]=>3
[6,4,2,5,1,3]=>3
[6,4,2,5,3,1]=>4
[6,4,3,1,2,5]=>3
[6,4,3,1,5,2]=>4
[6,4,3,2,1,5]=>4
[6,4,3,2,5,1]=>4
[6,4,3,5,1,2]=>3
[6,4,3,5,2,1]=>4
[6,4,5,1,2,3]=>2
[6,4,5,1,3,2]=>3
[6,4,5,2,1,3]=>3
[6,4,5,2,3,1]=>3
[6,4,5,3,1,2]=>3
[6,4,5,3,2,1]=>4
[6,5,1,2,3,4]=>2
[6,5,1,2,4,3]=>3
[6,5,1,3,2,4]=>3
[6,5,1,3,4,2]=>3
[6,5,1,4,2,3]=>3
[6,5,1,4,3,2]=>4
[6,5,2,1,3,4]=>3
[6,5,2,1,4,3]=>4
[6,5,2,3,1,4]=>3
[6,5,2,3,4,1]=>3
[6,5,2,4,1,3]=>3
[6,5,2,4,3,1]=>4
[6,5,3,1,2,4]=>3
[6,5,3,1,4,2]=>4
[6,5,3,2,1,4]=>4
[6,5,3,2,4,1]=>4
[6,5,3,4,1,2]=>3
[6,5,3,4,2,1]=>4
[6,5,4,1,2,3]=>3
[6,5,4,1,3,2]=>4
[6,5,4,2,1,3]=>4
[6,5,4,2,3,1]=>4
[6,5,4,3,1,2]=>4
[6,5,4,3,2,1]=>5
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Description
The number of descents of a permutation.
This can be described as an occurrence of the vincular mesh pattern ([2,1], {(1,0),(1,1),(1,2)}), i.e., the middle column is shaded, see [3].
This can be described as an occurrence of the vincular mesh pattern ([2,1], {(1,0),(1,1),(1,2)}), i.e., the middle column is shaded, see [3].
References
[1] /Permutations/Descents
[2] Triangle of Eulerian numbers T(n,k) (n>=1, 1 <= k <= n) read by rows. OEIS:A008292
[3] Brändén, P., Claesson, A. Mesh patterns and the expansion of permutation statistics as sums of permutation patterns arXiv:1102.4226
[2] Triangle of Eulerian numbers T(n,k) (n>=1, 1 <= k <= n) read by rows. OEIS:A008292
[3] Brändén, P., Claesson, A. Mesh patterns and the expansion of permutation statistics as sums of permutation patterns arXiv:1102.4226
Code
def statistic(x): return x.number_of_descents()
Created
Oct 11, 2011 at 19:06 by Christian Stump
Updated
May 10, 2019 at 17:11 by Henning Ulfarsson
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