Identifier
Values
[1,0] => [1,0] => 1
[1,0,1,0] => [1,0,1,0] => 1
[1,1,0,0] => [1,1,0,0] => 1
[1,0,1,0,1,0] => [1,0,1,0,1,0] => 1
[1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => [1,0,1,1,0,0] => 1
[1,1,1,0,0,0] => [1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0] => 5
[1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 14
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 35
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => 21
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 21
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 42
[1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => 14
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => 14
[1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 14
[1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 35
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 14
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 21
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => 35
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 21
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 42
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 42
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 14
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 14
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 219
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 119
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 119
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 35
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 35
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 387
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 65
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 65
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 68
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 21
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 21
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 282
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 65
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 21
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 21
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 147
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 282
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 147
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 42
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 42
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 429
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 65
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 42
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 42
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 14
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 14
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 219
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 42
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 42
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 42
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 14
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 14
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 219
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 42
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 14
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 14
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 119
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 219
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 119
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 35
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 35
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 387
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 42
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 14
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 65
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 14
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 65
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 119
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 68
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 21
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 282
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 219
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 65
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 119
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 65
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 35
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 21
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 35
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 147
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 387
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 282
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 147
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 42
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 42
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 429
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Description
The number of alternating sign matrices for a given Dyck path.
The Dyck path is given by the last diagonal of the monotone triangle corresponding to an alternating sign matrix.
Map
Cori-Le Borgne involution
Description
The Cori-Le Borgne involution on Dyck paths.
Append an additional down step to the Dyck path and consider its (literal) reversal. The image of the involution is then the unique rotation of this word which is a Dyck word followed by an additional down step. Alternatively, it is the composite $\zeta\circ\mathrm{rev}\circ\zeta^{(-1)}$, where $\zeta$ is Mp00030zeta map.