Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000839
(load all 67 compositions to match this statistic)
Mapping
Mp00151: Permutations —to cycle type⟶ Set partitions
St000839: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => {{1}}
 => 1
[1,2] => {{1},{2}}
 => 2
[2,1] => {{1,2}}
 => 1
[1,2,3] => {{1},{2},{3}}
 => 3
[1,3,2] => {{1},{2,3}}
 => 2
[2,1,3] => {{1,2},{3}}
 => 3
[2,3,1] => {{1,2,3}}
 => 1
[3,1,2] => {{1,2,3}}
 => 1
[3,2,1] => {{1,3},{2}}
 => 2
[1,2,3,4] => {{1},{2},{3},{4}}
 => 4
[1,2,4,3] => {{1},{2},{3,4}}
 => 3
[1,3,2,4] => {{1},{2,3},{4}}
 => 4
[1,3,4,2] => {{1},{2,3,4}}
 => 2
[1,4,2,3] => {{1},{2,3,4}}
 => 2
[1,4,3,2] => {{1},{2,4},{3}}
 => 3
[2,1,3,4] => {{1,2},{3},{4}}
 => 4
[2,1,4,3] => {{1,2},{3,4}}
 => 3
[2,3,1,4] => {{1,2,3},{4}}
 => 4
[2,3,4,1] => {{1,2,3,4}}
 => 1
[2,4,1,3] => {{1,2,3,4}}
 => 1
[2,4,3,1] => {{1,2,4},{3}}
 => 3
[3,1,2,4] => {{1,2,3},{4}}
 => 4
[3,1,4,2] => {{1,2,3,4}}
 => 1
[3,2,1,4] => {{1,3},{2},{4}}
 => 4
[3,2,4,1] => {{1,3,4},{2}}
 => 2
[3,4,1,2] => {{1,3},{2,4}}
 => 2
[3,4,2,1] => {{1,2,3,4}}
 => 1
[4,1,2,3] => {{1,2,3,4}}
 => 1
[4,1,3,2] => {{1,2,4},{3}}
 => 3
[4,2,1,3] => {{1,3,4},{2}}
 => 2
[4,2,3,1] => {{1,4},{2},{3}}
 => 3
[4,3,1,2] => {{1,2,3,4}}
 => 1
[4,3,2,1] => {{1,4},{2,3}}
 => 2
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
 => 5
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
 => 4
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
 => 5
[1,2,4,5,3] => {{1},{2},{3,4,5}}
 => 3
[1,2,5,3,4] => {{1},{2},{3,4,5}}
 => 3
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
 => 4
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
 => 5
[1,3,2,5,4] => {{1},{2,3},{4,5}}
 => 4
[1,3,4,2,5] => {{1},{2,3,4},{5}}
 => 5
[1,3,4,5,2] => {{1},{2,3,4,5}}
 => 2
[1,3,5,2,4] => {{1},{2,3,4,5}}
 => 2
[1,3,5,4,2] => {{1},{2,3,5},{4}}
 => 4
[1,4,2,3,5] => {{1},{2,3,4},{5}}
 => 5
[1,4,2,5,3] => {{1},{2,3,4,5}}
 => 2
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
 => 5
[1,4,3,5,2] => {{1},{2,4,5},{3}}
 => 3
[1,4,5,2,3] => {{1},{2,4},{3,5}}
 => 3
Description
The largest opener of a set partition. An opener (or left hand endpoint) of a set partition is a number that is minimal in its block. For this statistic, singletons are considered as openers.
Matching statistic: St000738
(load all 7 compositions to match this statistic)
Mapping
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
St000738: Standard tableaux ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 73%
Values
[1] => {{1}}
 => [[1]]
 => 1
[1,2] => {{1},{2}}
 => [[1],[2]]
 => 2
[2,1] => {{1,2}}
 => [[1,2]]
 => 1
[1,2,3] => {{1},{2},{3}}
 => [[1],[2],[3]]
 => 3
[1,3,2] => {{1},{2,3}}
 => [[1,3],[2]]
 => 2
[2,1,3] => {{1,2},{3}}
 => [[1,2],[3]]
 => 3
[2,3,1] => {{1,2,3}}
 => [[1,2,3]]
 => 1
[3,1,2] => {{1,2,3}}
 => [[1,2,3]]
 => 1
[3,2,1] => {{1,3},{2}}
 => [[1,3],[2]]
 => 2
[1,2,3,4] => {{1},{2},{3},{4}}
 => [[1],[2],[3],[4]]
 => 4
[1,2,4,3] => {{1},{2},{3,4}}
 => [[1,4],[2],[3]]
 => 3
[1,3,2,4] => {{1},{2,3},{4}}
 => [[1,3],[2],[4]]
 => 4
[1,3,4,2] => {{1},{2,3,4}}
 => [[1,3,4],[2]]
 => 2
[1,4,2,3] => {{1},{2,3,4}}
 => [[1,3,4],[2]]
 => 2
[1,4,3,2] => {{1},{2,4},{3}}
 => [[1,4],[2],[3]]
 => 3
[2,1,3,4] => {{1,2},{3},{4}}
 => [[1,2],[3],[4]]
 => 4
[2,1,4,3] => {{1,2},{3,4}}
 => [[1,2],[3,4]]
 => 3
[2,3,1,4] => {{1,2,3},{4}}
 => [[1,2,3],[4]]
 => 4
[2,3,4,1] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => 1
[2,4,1,3] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => 1
[2,4,3,1] => {{1,2,4},{3}}
 => [[1,2,4],[3]]
 => 3
[3,1,2,4] => {{1,2,3},{4}}
 => [[1,2,3],[4]]
 => 4
[3,1,4,2] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => 1
[3,2,1,4] => {{1,3},{2},{4}}
 => [[1,3],[2],[4]]
 => 4
[3,2,4,1] => {{1,3,4},{2}}
 => [[1,3,4],[2]]
 => 2
[3,4,1,2] => {{1,3},{2,4}}
 => [[1,3],[2,4]]
 => 2
[3,4,2,1] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => 1
[4,1,2,3] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => 1
[4,1,3,2] => {{1,2,4},{3}}
 => [[1,2,4],[3]]
 => 3
[4,2,1,3] => {{1,3,4},{2}}
 => [[1,3,4],[2]]
 => 2
[4,2,3,1] => {{1,4},{2},{3}}
 => [[1,4],[2],[3]]
 => 3
[4,3,1,2] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => 1
[4,3,2,1] => {{1,4},{2,3}}
 => [[1,3],[2,4]]
 => 2
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
 => [[1],[2],[3],[4],[5]]
 => 5
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
 => [[1,5],[2],[3],[4]]
 => 4
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
 => [[1,4],[2],[3],[5]]
 => 5
[1,2,4,5,3] => {{1},{2},{3,4,5}}
 => [[1,4,5],[2],[3]]
 => 3
[1,2,5,3,4] => {{1},{2},{3,4,5}}
 => [[1,4,5],[2],[3]]
 => 3
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
 => [[1,5],[2],[3],[4]]
 => 4
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
 => [[1,3],[2],[4],[5]]
 => 5
[1,3,2,5,4] => {{1},{2,3},{4,5}}
 => [[1,3],[2,5],[4]]
 => 4
[1,3,4,2,5] => {{1},{2,3,4},{5}}
 => [[1,3,4],[2],[5]]
 => 5
[1,3,4,5,2] => {{1},{2,3,4,5}}
 => [[1,3,4,5],[2]]
 => 2
[1,3,5,2,4] => {{1},{2,3,4,5}}
 => [[1,3,4,5],[2]]
 => 2
[1,3,5,4,2] => {{1},{2,3,5},{4}}
 => [[1,3,5],[2],[4]]
 => 4
[1,4,2,3,5] => {{1},{2,3,4},{5}}
 => [[1,3,4],[2],[5]]
 => 5
[1,4,2,5,3] => {{1},{2,3,4,5}}
 => [[1,3,4,5],[2]]
 => 2
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
 => [[1,4],[2],[3],[5]]
 => 5
[1,4,3,5,2] => {{1},{2,4,5},{3}}
 => [[1,4,5],[2],[3]]
 => 3
[1,4,5,2,3] => {{1},{2,4},{3,5}}
 => [[1,4],[2,5],[3]]
 => 3
[7,6,8,5,4,3,2,1] => {{1,2,3,6,7,8},{4,5}}
 => ?
 => ? = 4
[8,6,5,7,4,3,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ? = 2
[7,6,5,8,4,3,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[6,7,5,8,4,3,2,1] => {{1,3,4,5,6,8},{2,7}}
 => ?
 => ? = 2
[7,5,6,8,4,3,2,1] => {{1,2,4,5,7,8},{3,6}}
 => ?
 => ? = 3
[6,5,7,8,4,3,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[8,6,4,5,7,3,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ? = 2
[8,4,5,6,7,3,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ? = 2
[7,6,5,4,8,3,2,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ? = 4
[6,5,7,4,8,3,2,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ? = 4
[7,6,4,5,8,3,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[6,7,4,5,8,3,2,1] => {{1,3,4,5,6,8},{2,7}}
 => ?
 => ? = 2
[7,4,5,6,8,3,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[6,5,4,7,8,3,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[4,5,6,7,8,3,2,1] => {{1,2,4,5,7,8},{3,6}}
 => ?
 => ? = 3
[8,6,7,5,3,4,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ? = 2
[7,6,8,5,3,4,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[8,5,6,7,3,4,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ? = 2
[7,6,5,8,3,4,2,1] => {{1,2,4,6,7,8},{3,5}}
 => ?
 => ? = 3
[5,6,7,8,3,4,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[7,6,8,4,3,5,2,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ? = 4
[8,6,7,3,4,5,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ? = 2
[7,6,8,3,4,5,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[6,7,8,3,4,5,2,1] => {{1,3,4,5,6,8},{2,7}}
 => ?
 => ? = 2
[8,3,4,5,6,7,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ? = 2
[7,5,6,4,3,8,2,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ? = 4
[5,6,7,4,3,8,2,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ? = 4
[7,5,4,6,3,8,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[7,4,5,6,3,8,2,1] => {{1,2,4,6,7,8},{3,5}}
 => ?
 => ? = 3
[4,5,6,7,3,8,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[7,5,4,3,6,8,2,1] => {{1,2,5,6,7,8},{3,4}}
 => ?
 => ? = 3
[7,3,4,5,6,8,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[5,4,3,6,7,8,2,1] => {{1,2,4,5,6,7,8},{3}}
 => ?
 => ? = 3
[5,3,4,6,7,8,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[3,4,5,6,7,8,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[7,8,6,5,4,2,3,1] => {{1,2,3,6,7,8},{4,5}}
 => ?
 => ? = 4
[8,7,5,6,4,2,3,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ? = 2
[7,6,5,8,4,2,3,1] => {{1,3,4,5,7,8},{2,6}}
 => ?
 => ? = 2
[6,7,5,8,4,2,3,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[7,5,6,8,4,2,3,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[8,7,4,5,6,2,3,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ? = 2
[7,8,4,5,6,2,3,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[7,5,6,4,8,2,3,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ? = 4
[6,7,4,5,8,2,3,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[4,5,6,7,8,2,3,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[8,7,6,5,3,2,4,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ? = 2
[7,8,6,5,3,2,4,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[7,6,8,5,3,2,4,1] => {{1,3,4,5,7,8},{2,6}}
 => ?
 => ? = 2
[6,7,8,5,3,2,4,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ? = 1
[6,7,5,8,3,2,4,1] => {{1,2,4,6,7,8},{3,5}}
 => ?
 => ? = 3
Description
The first entry in the last row of a standard tableau. For the last entry in the first row, see [[St000734]].
Matching statistic: St000734
Mapping
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
St000734: Standard tableaux ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 73%
Values
[1] => {{1}}
 => [[1]]
 => [[1]]
 => 1
[1,2] => {{1},{2}}
 => [[1],[2]]
 => [[1,2]]
 => 2
[2,1] => {{1,2}}
 => [[1,2]]
 => [[1],[2]]
 => 1
[1,2,3] => {{1},{2},{3}}
 => [[1],[2],[3]]
 => [[1,2,3]]
 => 3
[1,3,2] => {{1},{2,3}}
 => [[1,3],[2]]
 => [[1,2],[3]]
 => 2
[2,1,3] => {{1,2},{3}}
 => [[1,2],[3]]
 => [[1,3],[2]]
 => 3
[2,3,1] => {{1,2,3}}
 => [[1,2,3]]
 => [[1],[2],[3]]
 => 1
[3,1,2] => {{1,2,3}}
 => [[1,2,3]]
 => [[1],[2],[3]]
 => 1
[3,2,1] => {{1,3},{2}}
 => [[1,3],[2]]
 => [[1,2],[3]]
 => 2
[1,2,3,4] => {{1},{2},{3},{4}}
 => [[1],[2],[3],[4]]
 => [[1,2,3,4]]
 => 4
[1,2,4,3] => {{1},{2},{3,4}}
 => [[1,4],[2],[3]]
 => [[1,2,3],[4]]
 => 3
[1,3,2,4] => {{1},{2,3},{4}}
 => [[1,3],[2],[4]]
 => [[1,2,4],[3]]
 => 4
[1,3,4,2] => {{1},{2,3,4}}
 => [[1,3,4],[2]]
 => [[1,2],[3],[4]]
 => 2
[1,4,2,3] => {{1},{2,3,4}}
 => [[1,3,4],[2]]
 => [[1,2],[3],[4]]
 => 2
[1,4,3,2] => {{1},{2,4},{3}}
 => [[1,4],[2],[3]]
 => [[1,2,3],[4]]
 => 3
[2,1,3,4] => {{1,2},{3},{4}}
 => [[1,2],[3],[4]]
 => [[1,3,4],[2]]
 => 4
[2,1,4,3] => {{1,2},{3,4}}
 => [[1,2],[3,4]]
 => [[1,3],[2,4]]
 => 3
[2,3,1,4] => {{1,2,3},{4}}
 => [[1,2,3],[4]]
 => [[1,4],[2],[3]]
 => 4
[2,3,4,1] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => 1
[2,4,1,3] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => 1
[2,4,3,1] => {{1,2,4},{3}}
 => [[1,2,4],[3]]
 => [[1,3],[2],[4]]
 => 3
[3,1,2,4] => {{1,2,3},{4}}
 => [[1,2,3],[4]]
 => [[1,4],[2],[3]]
 => 4
[3,1,4,2] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => 1
[3,2,1,4] => {{1,3},{2},{4}}
 => [[1,3],[2],[4]]
 => [[1,2,4],[3]]
 => 4
[3,2,4,1] => {{1,3,4},{2}}
 => [[1,3,4],[2]]
 => [[1,2],[3],[4]]
 => 2
[3,4,1,2] => {{1,3},{2,4}}
 => [[1,3],[2,4]]
 => [[1,2],[3,4]]
 => 2
[3,4,2,1] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => 1
[4,1,2,3] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => 1
[4,1,3,2] => {{1,2,4},{3}}
 => [[1,2,4],[3]]
 => [[1,3],[2],[4]]
 => 3
[4,2,1,3] => {{1,3,4},{2}}
 => [[1,3,4],[2]]
 => [[1,2],[3],[4]]
 => 2
[4,2,3,1] => {{1,4},{2},{3}}
 => [[1,4],[2],[3]]
 => [[1,2,3],[4]]
 => 3
[4,3,1,2] => {{1,2,3,4}}
 => [[1,2,3,4]]
 => [[1],[2],[3],[4]]
 => 1
[4,3,2,1] => {{1,4},{2,3}}
 => [[1,3],[2,4]]
 => [[1,2],[3,4]]
 => 2
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
 => [[1],[2],[3],[4],[5]]
 => [[1,2,3,4,5]]
 => 5
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
 => [[1,5],[2],[3],[4]]
 => [[1,2,3,4],[5]]
 => 4
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
 => [[1,4],[2],[3],[5]]
 => [[1,2,3,5],[4]]
 => 5
[1,2,4,5,3] => {{1},{2},{3,4,5}}
 => [[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 3
[1,2,5,3,4] => {{1},{2},{3,4,5}}
 => [[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 3
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
 => [[1,5],[2],[3],[4]]
 => [[1,2,3,4],[5]]
 => 4
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
 => [[1,3],[2],[4],[5]]
 => [[1,2,4,5],[3]]
 => 5
[1,3,2,5,4] => {{1},{2,3},{4,5}}
 => [[1,3],[2,5],[4]]
 => [[1,2,4],[3,5]]
 => 4
[1,3,4,2,5] => {{1},{2,3,4},{5}}
 => [[1,3,4],[2],[5]]
 => [[1,2,5],[3],[4]]
 => 5
[1,3,4,5,2] => {{1},{2,3,4,5}}
 => [[1,3,4,5],[2]]
 => [[1,2],[3],[4],[5]]
 => 2
[1,3,5,2,4] => {{1},{2,3,4,5}}
 => [[1,3,4,5],[2]]
 => [[1,2],[3],[4],[5]]
 => 2
[1,3,5,4,2] => {{1},{2,3,5},{4}}
 => [[1,3,5],[2],[4]]
 => [[1,2,4],[3],[5]]
 => 4
[1,4,2,3,5] => {{1},{2,3,4},{5}}
 => [[1,3,4],[2],[5]]
 => [[1,2,5],[3],[4]]
 => 5
[1,4,2,5,3] => {{1},{2,3,4,5}}
 => [[1,3,4,5],[2]]
 => [[1,2],[3],[4],[5]]
 => 2
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
 => [[1,4],[2],[3],[5]]
 => [[1,2,3,5],[4]]
 => 5
[1,4,3,5,2] => {{1},{2,4,5},{3}}
 => [[1,4,5],[2],[3]]
 => [[1,2,3],[4],[5]]
 => 3
[1,4,5,2,3] => {{1},{2,4},{3,5}}
 => [[1,4],[2,5],[3]]
 => [[1,2,3],[4,5]]
 => 3
[7,6,8,5,4,3,2,1] => {{1,2,3,6,7,8},{4,5}}
 => ?
 => ?
 => ? = 4
[8,6,5,7,4,3,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ?
 => ? = 2
[7,6,5,8,4,3,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[6,7,5,8,4,3,2,1] => {{1,3,4,5,6,8},{2,7}}
 => ?
 => ?
 => ? = 2
[7,5,6,8,4,3,2,1] => {{1,2,4,5,7,8},{3,6}}
 => ?
 => ?
 => ? = 3
[6,5,7,8,4,3,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[8,6,4,5,7,3,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ?
 => ? = 2
[8,4,5,6,7,3,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ?
 => ? = 2
[7,6,5,4,8,3,2,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ?
 => ? = 4
[6,5,7,4,8,3,2,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ?
 => ? = 4
[7,6,4,5,8,3,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[6,7,4,5,8,3,2,1] => {{1,3,4,5,6,8},{2,7}}
 => ?
 => ?
 => ? = 2
[7,4,5,6,8,3,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[6,5,4,7,8,3,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[4,5,6,7,8,3,2,1] => {{1,2,4,5,7,8},{3,6}}
 => ?
 => ?
 => ? = 3
[8,6,7,5,3,4,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ?
 => ? = 2
[7,6,8,5,3,4,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[8,5,6,7,3,4,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ?
 => ? = 2
[7,6,5,8,3,4,2,1] => {{1,2,4,6,7,8},{3,5}}
 => ?
 => ?
 => ? = 3
[5,6,7,8,3,4,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[7,6,8,4,3,5,2,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ?
 => ? = 4
[8,6,7,3,4,5,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ?
 => ? = 2
[7,6,8,3,4,5,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[6,7,8,3,4,5,2,1] => {{1,3,4,5,6,8},{2,7}}
 => ?
 => ?
 => ? = 2
[8,3,4,5,6,7,2,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ?
 => ? = 2
[7,5,6,4,3,8,2,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ?
 => ? = 4
[5,6,7,4,3,8,2,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ?
 => ? = 4
[7,5,4,6,3,8,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[7,4,5,6,3,8,2,1] => {{1,2,4,6,7,8},{3,5}}
 => ?
 => ?
 => ? = 3
[4,5,6,7,3,8,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[7,5,4,3,6,8,2,1] => {{1,2,5,6,7,8},{3,4}}
 => ?
 => ?
 => ? = 3
[7,3,4,5,6,8,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[5,4,3,6,7,8,2,1] => {{1,2,4,5,6,7,8},{3}}
 => ?
 => ?
 => ? = 3
[5,3,4,6,7,8,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[3,4,5,6,7,8,2,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[7,8,6,5,4,2,3,1] => {{1,2,3,6,7,8},{4,5}}
 => ?
 => ?
 => ? = 4
[8,7,5,6,4,2,3,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ?
 => ? = 2
[7,6,5,8,4,2,3,1] => {{1,3,4,5,7,8},{2,6}}
 => ?
 => ?
 => ? = 2
[6,7,5,8,4,2,3,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[7,5,6,8,4,2,3,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[8,7,4,5,6,2,3,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ?
 => ? = 2
[7,8,4,5,6,2,3,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[7,5,6,4,8,2,3,1] => {{1,2,3,5,6,7,8},{4}}
 => ?
 => ?
 => ? = 4
[6,7,4,5,8,2,3,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[4,5,6,7,8,2,3,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[8,7,6,5,3,2,4,1] => {{1,8},{2,3,4,5,6,7}}
 => ?
 => ?
 => ? = 2
[7,8,6,5,3,2,4,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[7,6,8,5,3,2,4,1] => {{1,3,4,5,7,8},{2,6}}
 => ?
 => ?
 => ? = 2
[6,7,8,5,3,2,4,1] => {{1,2,3,4,5,6,7,8}}
 => ?
 => ?
 => ? = 1
[6,7,5,8,3,2,4,1] => {{1,2,4,6,7,8},{3,5}}
 => ?
 => ?
 => ? = 3
Description
The last entry in the first row of a standard tableau.
Matching statistic: St001497
Mapping
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St001497: Permutations ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 64%
Values
[1] => {{1}}
 => [1] => [1] => 1
[1,2] => {{1},{2}}
 => [1,2] => [1,2] => 2
[2,1] => {{1,2}}
 => [2,1] => [2,1] => 1
[1,2,3] => {{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 3
[1,3,2] => {{1},{2,3}}
 => [1,3,2] => [1,3,2] => 2
[2,1,3] => {{1,2},{3}}
 => [2,1,3] => [2,1,3] => 3
[2,3,1] => {{1,2,3}}
 => [2,3,1] => [3,1,2] => 1
[3,1,2] => {{1,2,3}}
 => [2,3,1] => [3,1,2] => 1
[3,2,1] => {{1,3},{2}}
 => [3,2,1] => [3,2,1] => 2
[1,2,3,4] => {{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => 4
[1,2,4,3] => {{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => 3
[1,3,2,4] => {{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => 4
[1,3,4,2] => {{1},{2,3,4}}
 => [1,3,4,2] => [1,4,2,3] => 2
[1,4,2,3] => {{1},{2,3,4}}
 => [1,3,4,2] => [1,4,2,3] => 2
[1,4,3,2] => {{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => 3
[2,1,3,4] => {{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => 4
[2,1,4,3] => {{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => 3
[2,3,1,4] => {{1,2,3},{4}}
 => [2,3,1,4] => [3,1,2,4] => 4
[2,3,4,1] => {{1,2,3,4}}
 => [2,3,4,1] => [4,1,2,3] => 1
[2,4,1,3] => {{1,2,3,4}}
 => [2,3,4,1] => [4,1,2,3] => 1
[2,4,3,1] => {{1,2,4},{3}}
 => [2,4,3,1] => [4,1,3,2] => 3
[3,1,2,4] => {{1,2,3},{4}}
 => [2,3,1,4] => [3,1,2,4] => 4
[3,1,4,2] => {{1,2,3,4}}
 => [2,3,4,1] => [4,1,2,3] => 1
[3,2,1,4] => {{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => 4
[3,2,4,1] => {{1,3,4},{2}}
 => [3,2,4,1] => [4,2,1,3] => 2
[3,4,1,2] => {{1,3},{2,4}}
 => [3,4,1,2] => [3,4,1,2] => 2
[3,4,2,1] => {{1,2,3,4}}
 => [2,3,4,1] => [4,1,2,3] => 1
[4,1,2,3] => {{1,2,3,4}}
 => [2,3,4,1] => [4,1,2,3] => 1
[4,1,3,2] => {{1,2,4},{3}}
 => [2,4,3,1] => [4,1,3,2] => 3
[4,2,1,3] => {{1,3,4},{2}}
 => [3,2,4,1] => [4,2,1,3] => 2
[4,2,3,1] => {{1,4},{2},{3}}
 => [4,2,3,1] => [4,2,3,1] => 3
[4,3,1,2] => {{1,2,3,4}}
 => [2,3,4,1] => [4,1,2,3] => 1
[4,3,2,1] => {{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => 2
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => 5
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [1,2,3,5,4] => 4
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,4,3,5] => 5
[1,2,4,5,3] => {{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,5,3,4] => 3
[1,2,5,3,4] => {{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,5,3,4] => 3
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [1,2,5,4,3] => 4
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,3,2,4,5] => 5
[1,3,2,5,4] => {{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,3,2,5,4] => 4
[1,3,4,2,5] => {{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,4,2,3,5] => 5
[1,3,4,5,2] => {{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,5,2,3,4] => 2
[1,3,5,2,4] => {{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,5,2,3,4] => 2
[1,3,5,4,2] => {{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,5,2,4,3] => 4
[1,4,2,3,5] => {{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,4,2,3,5] => 5
[1,4,2,5,3] => {{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,5,2,3,4] => 2
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,4,3,2,5] => 5
[1,4,3,5,2] => {{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,5,3,2,4] => 3
[1,4,5,2,3] => {{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,4,5,2,3] => 3
[1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}}
 => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => ? = 7
[1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}}
 => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => ? = 6
[1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}}
 => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => ? = 7
[1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,4,5,7,2,6] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,4,5,7,6,2] => {{1},{2,3,4,5,7},{6}}
 => [1,3,4,5,7,6,2] => [1,7,2,3,4,6,5] => ? = 6
[1,3,4,6,2,5,7] => {{1},{2,3,4,5,6},{7}}
 => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => ? = 7
[1,3,4,6,2,7,5] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,4,6,5,2,7] => {{1},{2,3,4,6},{5},{7}}
 => [1,3,4,6,5,2,7] => [1,6,2,3,5,4,7] => ? = 7
[1,3,4,6,5,7,2] => {{1},{2,3,4,6,7},{5}}
 => [1,3,4,6,5,7,2] => [1,7,2,3,5,4,6] => ? = 5
[1,3,4,6,7,2,5] => {{1},{2,3,4,6},{5,7}}
 => [1,3,4,6,7,2,5] => [1,6,2,3,7,4,5] => ? = 5
[1,3,4,6,7,5,2] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,4,7,2,5,6] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,4,7,2,6,5] => {{1},{2,3,4,5,7},{6}}
 => [1,3,4,5,7,6,2] => [1,7,2,3,4,6,5] => ? = 6
[1,3,4,7,5,2,6] => {{1},{2,3,4,6,7},{5}}
 => [1,3,4,6,5,7,2] => [1,7,2,3,5,4,6] => ? = 5
[1,3,4,7,5,6,2] => {{1},{2,3,4,7},{5},{6}}
 => [1,3,4,7,5,6,2] => [1,7,2,3,5,6,4] => ? = 6
[1,3,4,7,6,2,5] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,4,7,6,5,2] => {{1},{2,3,4,7},{5,6}}
 => [1,3,4,7,6,5,2] => [1,7,2,3,6,5,4] => ? = 5
[1,3,5,2,4,6,7] => {{1},{2,3,4,5},{6},{7}}
 => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => ? = 7
[1,3,5,2,4,7,6] => {{1},{2,3,4,5},{6,7}}
 => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => ? = 6
[1,3,5,2,6,4,7] => {{1},{2,3,4,5,6},{7}}
 => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => ? = 7
[1,3,5,2,6,7,4] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,5,2,7,4,6] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,5,2,7,6,4] => {{1},{2,3,4,5,7},{6}}
 => [1,3,4,5,7,6,2] => [1,7,2,3,4,6,5] => ? = 6
[1,3,5,4,2,6,7] => {{1},{2,3,5},{4},{6},{7}}
 => [1,3,5,4,2,6,7] => [1,5,2,4,3,6,7] => ? = 7
[1,3,5,4,2,7,6] => {{1},{2,3,5},{4},{6,7}}
 => [1,3,5,4,2,7,6] => [1,5,2,4,3,7,6] => ? = 6
[1,3,5,4,6,2,7] => {{1},{2,3,5,6},{4},{7}}
 => [1,3,5,4,6,2,7] => [1,6,2,4,3,5,7] => ? = 7
[1,3,5,4,6,7,2] => {{1},{2,3,5,6,7},{4}}
 => [1,3,5,4,6,7,2] => [1,7,2,4,3,5,6] => ? = 4
[1,3,5,4,7,2,6] => {{1},{2,3,5,6,7},{4}}
 => [1,3,5,4,6,7,2] => [1,7,2,4,3,5,6] => ? = 4
[1,3,5,4,7,6,2] => {{1},{2,3,5,7},{4},{6}}
 => [1,3,5,4,7,6,2] => [1,7,2,4,3,6,5] => ? = 6
[1,3,5,6,2,4,7] => {{1},{2,3,5},{4,6},{7}}
 => [1,3,5,6,2,4,7] => [1,5,2,6,3,4,7] => ? = 7
[1,3,5,6,2,7,4] => {{1},{2,3,5},{4,6,7}}
 => [1,3,5,6,2,7,4] => [1,5,2,7,3,4,6] => ? = 4
[1,3,5,6,4,2,7] => {{1},{2,3,4,5,6},{7}}
 => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => ? = 7
[1,3,5,6,4,7,2] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,5,6,7,2,4] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,5,6,7,4,2] => {{1},{2,3,5,7},{4,6}}
 => [1,3,5,6,7,4,2] => [1,7,2,6,3,4,5] => ? = 4
[1,3,5,7,2,4,6] => {{1},{2,3,5},{4,6,7}}
 => [1,3,5,6,2,7,4] => [1,5,2,7,3,4,6] => ? = 4
[1,3,5,7,2,6,4] => {{1},{2,3,5},{4,7},{6}}
 => [1,3,5,7,2,6,4] => [1,5,2,7,3,6,4] => ? = 6
[1,3,5,7,4,2,6] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,5,7,4,6,2] => {{1},{2,3,4,5,7},{6}}
 => [1,3,4,5,7,6,2] => [1,7,2,3,4,6,5] => ? = 6
[1,3,5,7,6,2,4] => {{1},{2,3,5,6},{4,7}}
 => [1,3,5,7,6,2,4] => [1,6,2,7,3,5,4] => ? = 4
[1,3,5,7,6,4,2] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,6,2,4,5,7] => {{1},{2,3,4,5,6},{7}}
 => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => ? = 7
[1,3,6,2,4,7,5] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,6,2,5,4,7] => {{1},{2,3,4,6},{5},{7}}
 => [1,3,4,6,5,2,7] => [1,6,2,3,5,4,7] => ? = 7
[1,3,6,2,5,7,4] => {{1},{2,3,4,6,7},{5}}
 => [1,3,4,6,5,7,2] => [1,7,2,3,5,4,6] => ? = 5
[1,3,6,2,7,4,5] => {{1},{2,3,4,6},{5,7}}
 => [1,3,4,6,7,2,5] => [1,6,2,3,7,4,5] => ? = 5
[1,3,6,2,7,5,4] => {{1},{2,3,4,5,6,7}}
 => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ? = 2
[1,3,6,4,2,5,7] => {{1},{2,3,5,6},{4},{7}}
 => [1,3,5,4,6,2,7] => [1,6,2,4,3,5,7] => ? = 7
[1,3,6,4,2,7,5] => {{1},{2,3,5,6,7},{4}}
 => [1,3,5,4,6,7,2] => [1,7,2,4,3,5,6] => ? = 4
Description
The position of the largest weak excedence of a permutation.