Identifier
Mp00033:
Dyck paths
—to two-row standard tableau⟶
Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
[1,0] => [[1],[2]] => [2,1] => [2,1] => 0
[1,0,1,0] => [[1,3],[2,4]] => [2,4,1,3] => [4,2,1,3] => 000
[1,1,0,0] => [[1,2],[3,4]] => [3,4,1,2] => [3,1,4,2] => 000
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [6,4,2,1,3,5] => 00000
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [5,2,1,6,3,4] => 00000
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [6,3,1,4,2,5] => 00000
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [5,1,6,3,2,4] => 00000
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => 00000
[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => [2,4,6,8,1,3,5,7] => [8,6,4,2,1,3,5,7] => 0000000
[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => [2,4,7,8,1,3,5,6] => [2,7,1,8,4,3,5,6] => 0000000
[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => [2,5,6,8,1,3,4,7] => [8,5,2,1,6,3,4,7] => 0000000
[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => [2,5,7,8,1,3,4,6] => [7,2,1,8,5,3,4,6] => 0000000
[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => [2,6,7,8,1,3,4,5] => [6,2,1,7,3,8,4,5] => 0000000
[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => [3,4,6,8,1,2,5,7] => [8,6,3,1,4,2,5,7] => 0000000
[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => [3,4,7,8,1,2,5,6] => [7,3,1,8,4,2,5,6] => 0000000
[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => [3,5,6,8,1,2,4,7] => [8,5,1,6,3,2,4,7] => 0000000
[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => [3,5,7,8,1,2,4,6] => [7,1,8,5,3,2,4,6] => 0000000
[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => [3,6,7,8,1,2,4,5] => [6,1,7,3,2,8,4,5] => 0000000
[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => [4,5,6,8,1,2,3,7] => [8,4,1,5,2,6,3,7] => 0000000
[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => [4,5,7,8,1,2,3,6] => [7,1,8,4,2,5,3,6] => 0000000
[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => [4,6,7,8,1,2,3,5] => [6,1,7,2,8,4,3,5] => 0000000
[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [5,1,6,2,7,3,8,4] => 0000000
[1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => [2,4,6,8,10,1,3,5,7,9] => [10,8,6,4,2,1,3,5,7,9] => 000000000
[1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => [2,4,6,9,10,1,3,5,7,8] => [9,10,2,1,6,4,3,5,7,8] => 000000000
[1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => [2,4,7,8,10,1,3,5,6,9] => [7,10,2,1,8,4,3,5,6,9] => 000000000
[1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => [2,4,7,9,10,1,3,5,6,8] => [2,9,1,10,7,4,3,5,6,8] => 000000000
[1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => [2,4,8,9,10,1,3,5,6,7] => [2,8,1,9,4,3,10,5,6,7] => 000000000
[1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => [2,5,6,8,10,1,3,4,7,9] => [10,8,5,2,1,6,3,4,7,9] => 000000000
[1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => [2,5,6,9,10,1,3,4,7,8] => [9,5,2,1,10,6,3,4,7,8] => 000000000
[1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => [2,5,7,8,10,1,3,4,6,9] => [10,7,2,1,8,5,3,4,6,9] => 000000000
[1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => [2,5,7,9,10,1,3,4,6,8] => [9,2,1,10,7,5,3,4,6,8] => 000000000
[1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => [2,5,8,9,10,1,3,4,6,7] => [2,8,1,9,3,10,5,4,6,7] => 000000000
[1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => [2,6,7,8,10,1,3,4,5,9] => [10,6,2,1,7,3,8,4,5,9] => 000000000
[1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => [2,6,7,9,10,1,3,4,5,8] => [9,2,1,10,6,3,7,4,5,8] => 000000000
[1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => [2,6,8,9,10,1,3,4,5,7] => [8,2,1,9,3,10,6,4,5,7] => 000000000
[1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => [2,7,8,9,10,1,3,4,5,6] => [7,2,1,8,3,9,4,10,5,6] => 000000000
[1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => [3,4,6,8,10,1,2,5,7,9] => [10,8,6,3,1,4,2,5,7,9] => 000000000
[1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => [3,4,6,9,10,1,2,5,7,8] => [3,9,1,10,6,4,2,5,7,8] => 000000000
[1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => [3,4,7,8,10,1,2,5,6,9] => [10,7,3,1,8,4,2,5,6,9] => 000000000
[1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => [3,4,7,9,10,1,2,5,6,8] => [9,3,1,10,7,4,2,5,6,8] => 000000000
[1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,7],[3,4,8,9,10]] => [3,4,8,9,10,1,2,5,6,7] => [8,3,1,9,4,2,10,5,6,7] => 000000000
[1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => [3,5,6,8,10,1,2,4,7,9] => [10,8,5,1,6,3,2,4,7,9] => 000000000
[1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => [3,5,6,9,10,1,2,4,7,8] => [9,5,1,10,6,3,2,4,7,8] => 000000000
[1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => [3,5,7,8,10,1,2,4,6,9] => [10,7,1,8,5,3,2,4,6,9] => 000000000
[1,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8],[3,5,7,9,10]] => [3,5,7,9,10,1,2,4,6,8] => [9,1,10,7,5,3,2,4,6,8] => 000000000
[1,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,7],[3,5,8,9,10]] => [3,5,8,9,10,1,2,4,6,7] => [8,3,1,9,2,10,5,4,6,7] => 000000000
[1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => [3,6,7,8,10,1,2,4,5,9] => [10,6,1,7,3,2,8,4,5,9] => 000000000
[1,1,0,1,1,0,0,1,0,0] => [[1,2,4,5,8],[3,6,7,9,10]] => [3,6,7,9,10,1,2,4,5,8] => [9,1,10,6,3,2,7,4,5,8] => 000000000
[1,1,0,1,1,0,1,0,0,0] => [[1,2,4,5,7],[3,6,8,9,10]] => [3,6,8,9,10,1,2,4,5,7] => [8,1,9,3,2,10,6,4,5,7] => 000000000
[1,1,0,1,1,1,0,0,0,0] => [[1,2,4,5,6],[3,7,8,9,10]] => [3,7,8,9,10,1,2,4,5,6] => [7,1,8,3,2,9,4,10,5,6] => 000000000
[1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => [4,5,6,8,10,1,2,3,7,9] => [10,8,4,1,5,2,6,3,7,9] => 000000000
[1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => [4,5,6,9,10,1,2,3,7,8] => [9,4,1,10,5,2,6,3,7,8] => 000000000
[1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => [4,5,7,8,10,1,2,3,6,9] => [10,7,1,8,4,2,5,3,6,9] => 000000000
[1,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,8],[4,5,7,9,10]] => [4,5,7,9,10,1,2,3,6,8] => [9,1,10,7,4,2,5,3,6,8] => 000000000
[1,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7],[4,5,8,9,10]] => [4,5,8,9,10,1,2,3,6,7] => [8,1,9,4,2,10,5,3,6,7] => 000000000
[1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => [4,6,7,8,10,1,2,3,5,9] => [10,6,1,7,2,8,4,3,5,9] => 000000000
[1,1,1,0,1,0,0,1,0,0] => [[1,2,3,5,8],[4,6,7,9,10]] => [4,6,7,9,10,1,2,3,5,8] => [9,1,10,6,2,7,4,3,5,8] => 000000000
[1,1,1,0,1,0,1,0,0,0] => [[1,2,3,5,7],[4,6,8,9,10]] => [4,6,8,9,10,1,2,3,5,7] => [8,1,9,2,10,6,4,3,5,7] => 000000000
[1,1,1,0,1,1,0,0,0,0] => [[1,2,3,5,6],[4,7,8,9,10]] => [4,7,8,9,10,1,2,3,5,6] => [7,1,8,2,9,4,3,10,5,6] => 000000000
[1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => [5,6,7,8,10,1,2,3,4,9] => [10,5,1,6,2,7,3,8,4,9] => 000000000
[1,1,1,1,0,0,0,1,0,0] => [[1,2,3,4,8],[5,6,7,9,10]] => [5,6,7,9,10,1,2,3,4,8] => [9,1,10,5,2,6,3,7,4,8] => 000000000
[1,1,1,1,0,0,1,0,0,0] => [[1,2,3,4,7],[5,6,8,9,10]] => [5,6,8,9,10,1,2,3,4,7] => [8,1,9,2,10,5,3,6,4,7] => 000000000
[1,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,6],[5,7,8,9,10]] => [5,7,8,9,10,1,2,3,4,6] => [7,1,8,2,9,3,10,5,4,6] => 000000000
[1,1,1,1,1,0,0,0,0,0] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => [6,1,7,2,8,3,9,4,10,5] => 000000000
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [2,4,6,8,10,12,1,3,5,7,9,11] => [12,10,8,6,4,2,1,3,5,7,9,11] => 00000000000
[1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => [2,4,6,8,11,12,1,3,5,7,9,10] => [11,12,8,2,1,6,4,3,5,7,9,10] => 00000000000
[1,0,1,0,1,0,1,1,0,0,1,0] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => [2,4,6,9,10,12,1,3,5,7,8,11] => [12,2,9,1,10,6,4,3,5,7,8,11] => 00000000000
[1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => [2,4,6,9,11,12,1,3,5,7,8,10] => [11,12,2,1,9,6,4,3,5,7,8,10] => 00000000000
[1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => [2,4,6,10,11,12,1,3,5,7,8,9] => [10,2,4,1,11,3,12,6,5,7,8,9] => 00000000000
[1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => [2,4,7,8,10,12,1,3,5,6,9,11] => [7,12,10,2,1,8,4,3,5,6,9,11] => 00000000000
[1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => [2,4,7,8,11,12,1,3,5,6,9,10] => [2,11,7,1,12,8,4,3,5,6,9,10] => 00000000000
[1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => [2,4,7,9,10,12,1,3,5,6,8,11] => [9,12,2,1,10,7,4,3,5,6,8,11] => 00000000000
[1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => [2,4,7,9,11,12,1,3,5,6,8,10] => [2,11,1,12,9,7,4,3,5,6,8,10] => 00000000000
[1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => [2,4,7,10,11,12,1,3,5,6,8,9] => [10,11,2,1,4,3,12,7,5,6,8,9] => 00000000000
[1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => [2,4,8,9,10,12,1,3,5,6,7,11] => [8,12,2,1,9,4,3,10,5,6,7,11] => 00000000000
[1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => [2,4,8,9,11,12,1,3,5,6,7,10] => [2,11,1,12,8,4,3,9,5,6,7,10] => 00000000000
[1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => [2,4,8,10,11,12,1,3,5,6,7,9] => [2,10,1,11,4,3,12,8,5,6,7,9] => 00000000000
[1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => [2,4,9,10,11,12,1,3,5,6,7,8] => [2,9,1,10,4,3,11,5,12,6,7,8] => 00000000000
[1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => [2,5,6,8,10,12,1,3,4,7,9,11] => [12,10,8,5,2,1,6,3,4,7,9,11] => 00000000000
[1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => [2,5,6,8,11,12,1,3,4,7,9,10] => [5,11,2,1,12,8,6,3,4,7,9,10] => 00000000000
[1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => [2,5,6,9,10,12,1,3,4,7,8,11] => [12,9,5,2,1,10,6,3,4,7,8,11] => 00000000000
[1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => [2,5,6,9,11,12,1,3,4,7,8,10] => [11,5,2,1,12,9,6,3,4,7,8,10] => 00000000000
[1,0,1,1,0,0,1,1,1,0,0,0] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => [2,5,6,10,11,12,1,3,4,7,8,9] => [10,11,2,1,5,3,12,6,4,7,8,9] => 00000000000
[1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => [2,5,7,8,10,12,1,3,4,6,9,11] => [12,10,7,2,1,8,5,3,4,6,9,11] => 00000000000
[1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => [2,5,7,8,11,12,1,3,4,6,9,10] => [11,7,2,1,12,8,5,3,4,6,9,10] => 00000000000
[1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => [2,5,7,9,10,12,1,3,4,6,8,11] => [12,9,2,1,10,7,5,3,4,6,8,11] => 00000000000
[1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => [2,5,7,9,11,12,1,3,4,6,8,10] => [11,2,1,12,9,7,5,3,4,6,8,10] => 00000000000
[1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => [2,5,7,10,11,12,1,3,4,6,8,9] => [10,11,2,1,3,12,7,5,4,6,8,9] => 00000000000
[1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => [2,5,8,9,10,12,1,3,4,6,7,11] => [8,9,2,1,12,3,10,5,4,6,7,11] => 00000000000
[1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => [2,5,8,9,11,12,1,3,4,6,7,10] => [11,8,2,1,12,3,9,5,4,6,7,10] => 00000000000
[1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => [2,5,8,10,11,12,1,3,4,6,7,9] => [2,10,1,11,3,12,8,5,4,6,7,9] => 00000000000
[1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => [2,5,9,10,11,12,1,3,4,6,7,8] => [2,9,1,10,3,11,5,4,12,6,7,8] => 00000000000
[1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => [2,6,7,8,10,12,1,3,4,5,9,11] => [12,10,6,2,1,7,3,8,4,5,9,11] => 00000000000
[1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => [2,6,7,8,11,12,1,3,4,5,9,10] => [11,6,2,1,12,7,3,8,4,5,9,10] => 00000000000
[1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => [2,6,7,9,10,12,1,3,4,5,8,11] => [12,9,2,1,10,6,3,7,4,5,8,11] => 00000000000
[1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => [2,6,7,9,11,12,1,3,4,5,8,10] => [11,2,1,12,9,6,3,7,4,5,8,10] => 00000000000
[1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => [2,6,7,10,11,12,1,3,4,5,8,9] => [10,2,1,11,6,3,12,7,4,5,8,9] => 00000000000
[1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => [2,6,8,9,10,12,1,3,4,5,7,11] => [12,8,2,1,9,3,10,6,4,5,7,11] => 00000000000
[1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => [2,6,8,9,11,12,1,3,4,5,7,10] => [11,2,1,12,8,3,9,6,4,5,7,10] => 00000000000
[1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => [2,6,8,10,11,12,1,3,4,5,7,9] => [10,2,1,11,3,12,8,6,4,5,7,9] => 00000000000
[1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => [2,6,9,10,11,12,1,3,4,5,7,8] => [2,9,1,10,3,11,4,12,6,5,7,8] => 00000000000
>>> Load all 196 entries. <<<Map
to two-row standard tableau
Description
Return a standard tableau of shape (n,n) where n is the semilength of the Dyck path.
Given a Dyck path D, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
Given a Dyck path D, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
See Mp00067Foata bijection.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
C(π)={i∈[n−1]|∀1≤j≤i<k≤n:π(j)<π(k)}.
For n>1 it can also be described as the set of occurrences of the mesh pattern
([1,2],{(0,2),(1,0),(1,1),(2,0),(2,1)})
or equivalently
([1,2],{(0,1),(0,2),(1,1),(1,2),(2,0)}),
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
C(π)={i∈[n−1]|∀1≤j≤i<k≤n:π(j)<π(k)}.
For n>1 it can also be described as the set of occurrences of the mesh pattern
([1,2],{(0,2),(1,0),(1,1),(2,0),(2,1)})
or equivalently
([1,2],{(0,1),(0,2),(1,1),(1,2),(2,0)}),
see [3].
The permutation is connected, when the connectivity set is empty.
searching the database
Sorry, this map was not found in the database.