Identifier
Values
[1,0] => [1,0] => 2
[1,0,1,0] => [1,1,0,0] => 3
[1,1,0,0] => [1,0,1,0] => 3
[1,0,1,0,1,0] => [1,1,1,0,0,0] => 4
[1,0,1,1,0,0] => [1,1,0,1,0,0] => 4
[1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[1,1,0,1,0,0] => [1,1,0,0,1,0] => 3
[1,1,1,0,0,0] => [1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => 5
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 7
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 7
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 6
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 7
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 7
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 6
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 6
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 6
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 7
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Description
The number of simple modules with injective dimension at most one or dominant dimension at least one.
Map
inverse Kreweras complement
Description
Return the inverse of the Kreweras complement of a Dyck path, regarded as a noncrossing set partition.
To identify Dyck paths and noncrossing set partitions, this maps uses the following classical bijection. The number of down steps after the $i$-th up step of the Dyck path is the size of the block of the set partition whose maximal element is $i$. If $i$ is not a maximal element of a block, the $(i+1)$-st step is also an up step.