Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000391
(load all 2 compositions to match this statistic)
Mapping
Mp00223: Permutations —runsort⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
St000391: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => 0 => 0
[2,1] => [1,2] => 0 => 0
[1,2,3] => [1,2,3] => 00 => 0
[1,3,2] => [1,3,2] => 01 => 2
[2,1,3] => [1,3,2] => 01 => 2
[2,3,1] => [1,2,3] => 00 => 0
[3,1,2] => [1,2,3] => 00 => 0
[3,2,1] => [1,2,3] => 00 => 0
[1,2,3,4] => [1,2,3,4] => 000 => 0
[1,2,4,3] => [1,2,4,3] => 001 => 3
[1,3,2,4] => [1,3,2,4] => 010 => 2
[1,3,4,2] => [1,3,4,2] => 001 => 3
[1,4,2,3] => [1,4,2,3] => 001 => 3
[1,4,3,2] => [1,4,2,3] => 001 => 3
[2,1,3,4] => [1,3,4,2] => 001 => 3
[2,1,4,3] => [1,4,2,3] => 001 => 3
[2,3,1,4] => [1,4,2,3] => 001 => 3
[2,3,4,1] => [1,2,3,4] => 000 => 0
[2,4,1,3] => [1,3,2,4] => 010 => 2
[2,4,3,1] => [1,2,4,3] => 001 => 3
[3,1,2,4] => [1,2,4,3] => 001 => 3
[3,1,4,2] => [1,4,2,3] => 001 => 3
[3,2,1,4] => [1,4,2,3] => 001 => 3
[3,2,4,1] => [1,2,4,3] => 001 => 3
[3,4,1,2] => [1,2,3,4] => 000 => 0
[3,4,2,1] => [1,2,3,4] => 000 => 0
[4,1,2,3] => [1,2,3,4] => 000 => 0
[4,1,3,2] => [1,3,2,4] => 010 => 2
[4,2,1,3] => [1,3,2,4] => 010 => 2
[4,2,3,1] => [1,2,3,4] => 000 => 0
[4,3,1,2] => [1,2,3,4] => 000 => 0
[4,3,2,1] => [1,2,3,4] => 000 => 0
[1,2,3,4,5] => [1,2,3,4,5] => 0000 => 0
[1,2,3,5,4] => [1,2,3,5,4] => 0001 => 4
[1,2,4,3,5] => [1,2,4,3,5] => 0010 => 3
[1,2,4,5,3] => [1,2,4,5,3] => 0001 => 4
[1,2,5,3,4] => [1,2,5,3,4] => 0001 => 4
[1,2,5,4,3] => [1,2,5,3,4] => 0001 => 4
[1,3,2,4,5] => [1,3,2,4,5] => 0100 => 2
[1,3,2,5,4] => [1,3,2,5,4] => 0101 => 6
[1,3,4,2,5] => [1,3,4,2,5] => 0010 => 3
[1,3,4,5,2] => [1,3,4,5,2] => 0001 => 4
[1,3,5,2,4] => [1,3,5,2,4] => 0001 => 4
[1,3,5,4,2] => [1,3,5,2,4] => 0001 => 4
[1,4,2,3,5] => [1,4,2,3,5] => 0010 => 3
[1,4,2,5,3] => [1,4,2,5,3] => 0011 => 7
[1,4,3,2,5] => [1,4,2,5,3] => 0011 => 7
[1,4,3,5,2] => [1,4,2,3,5] => 0010 => 3
[1,4,5,2,3] => [1,4,5,2,3] => 0001 => 4
[1,4,5,3,2] => [1,4,5,2,3] => 0001 => 4
Description
The sum of the positions of the ones in a binary word.
Matching statistic: St000008
Mapping
Mp00223: Permutations —runsort⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
St000008: Integer compositions ⟶ ℤResult quality: 86% ●values known / values provided: 99%●distinct values known / distinct values provided: 86%
Values
[1,2] => [1,2] => 0 => [2] => 0
[2,1] => [1,2] => 0 => [2] => 0
[1,2,3] => [1,2,3] => 00 => [3] => 0
[1,3,2] => [1,3,2] => 01 => [2,1] => 2
[2,1,3] => [1,3,2] => 01 => [2,1] => 2
[2,3,1] => [1,2,3] => 00 => [3] => 0
[3,1,2] => [1,2,3] => 00 => [3] => 0
[3,2,1] => [1,2,3] => 00 => [3] => 0
[1,2,3,4] => [1,2,3,4] => 000 => [4] => 0
[1,2,4,3] => [1,2,4,3] => 001 => [3,1] => 3
[1,3,2,4] => [1,3,2,4] => 010 => [2,2] => 2
[1,3,4,2] => [1,3,4,2] => 001 => [3,1] => 3
[1,4,2,3] => [1,4,2,3] => 001 => [3,1] => 3
[1,4,3,2] => [1,4,2,3] => 001 => [3,1] => 3
[2,1,3,4] => [1,3,4,2] => 001 => [3,1] => 3
[2,1,4,3] => [1,4,2,3] => 001 => [3,1] => 3
[2,3,1,4] => [1,4,2,3] => 001 => [3,1] => 3
[2,3,4,1] => [1,2,3,4] => 000 => [4] => 0
[2,4,1,3] => [1,3,2,4] => 010 => [2,2] => 2
[2,4,3,1] => [1,2,4,3] => 001 => [3,1] => 3
[3,1,2,4] => [1,2,4,3] => 001 => [3,1] => 3
[3,1,4,2] => [1,4,2,3] => 001 => [3,1] => 3
[3,2,1,4] => [1,4,2,3] => 001 => [3,1] => 3
[3,2,4,1] => [1,2,4,3] => 001 => [3,1] => 3
[3,4,1,2] => [1,2,3,4] => 000 => [4] => 0
[3,4,2,1] => [1,2,3,4] => 000 => [4] => 0
[4,1,2,3] => [1,2,3,4] => 000 => [4] => 0
[4,1,3,2] => [1,3,2,4] => 010 => [2,2] => 2
[4,2,1,3] => [1,3,2,4] => 010 => [2,2] => 2
[4,2,3,1] => [1,2,3,4] => 000 => [4] => 0
[4,3,1,2] => [1,2,3,4] => 000 => [4] => 0
[4,3,2,1] => [1,2,3,4] => 000 => [4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => 0000 => [5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => 0001 => [4,1] => 4
[1,2,4,3,5] => [1,2,4,3,5] => 0010 => [3,2] => 3
[1,2,4,5,3] => [1,2,4,5,3] => 0001 => [4,1] => 4
[1,2,5,3,4] => [1,2,5,3,4] => 0001 => [4,1] => 4
[1,2,5,4,3] => [1,2,5,3,4] => 0001 => [4,1] => 4
[1,3,2,4,5] => [1,3,2,4,5] => 0100 => [2,3] => 2
[1,3,2,5,4] => [1,3,2,5,4] => 0101 => [2,2,1] => 6
[1,3,4,2,5] => [1,3,4,2,5] => 0010 => [3,2] => 3
[1,3,4,5,2] => [1,3,4,5,2] => 0001 => [4,1] => 4
[1,3,5,2,4] => [1,3,5,2,4] => 0001 => [4,1] => 4
[1,3,5,4,2] => [1,3,5,2,4] => 0001 => [4,1] => 4
[1,4,2,3,5] => [1,4,2,3,5] => 0010 => [3,2] => 3
[1,4,2,5,3] => [1,4,2,5,3] => 0011 => [3,1,1] => 7
[1,4,3,2,5] => [1,4,2,5,3] => 0011 => [3,1,1] => 7
[1,4,3,5,2] => [1,4,2,3,5] => 0010 => [3,2] => 3
[1,4,5,2,3] => [1,4,5,2,3] => 0001 => [4,1] => 4
[1,4,5,3,2] => [1,4,5,2,3] => 0001 => [4,1] => 4
[2,1,4,3,6,5,8,7,10,9] => [1,4,2,3,6,5,8,7,10,9] => 001010101 => [3,2,2,2,1] => ? = 24
[6,7,8,9,10,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => [10] => ? = 0
[9,7,5,10,3,8,2,6,1,4] => [1,4,2,6,3,8,5,10,7,9] => 001010101 => [3,2,2,2,1] => ? = 24
[10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => [10] => ? = 0
[9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[9,1,2,3,4,7,8,5,6] => [1,2,3,4,7,8,5,6,9] => 00000010 => [7,2] => ? = 7
[9,1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7,9] => 00000010 => [7,2] => ? = 7
[9,1,8,5,6,7,2,3,4] => [1,8,2,3,4,5,6,7,9] => 00000010 => [7,2] => ? = 7
[2,9,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,2,9] => 00000010 => [7,2] => ? = 7
[8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[9,7,8,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[2,3,4,5,6,7,9,1,8] => [1,8,2,3,4,5,6,7,9] => 00000010 => [7,2] => ? = 7
[2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[6,7,8,9,10,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => [10] => ? = 0
[2,3,4,5,6,8,9,1,7] => [1,7,2,3,4,5,6,8,9] => 00000100 => [6,3] => ? = 6
[2,3,5,6,7,8,9,1,4] => [1,4,2,3,5,6,7,8,9] => 00100000 => [3,6] => ? = 3
[2,4,5,6,7,8,9,1,3] => [1,3,2,4,5,6,7,8,9] => 01000000 => [2,7] => ? = 2
[3,4,5,6,7,8,9,1,2] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => [10] => ? = 0
[2,3,4,5,6,7,8,10,1,9] => [1,9,2,3,4,5,6,7,8,10] => 000000010 => [8,2] => ? = 8
[2,4,5,6,7,8,9,10,1,3] => [1,3,2,4,5,6,7,8,9,10] => 010000000 => [2,8] => ? = 2
[3,4,5,6,7,8,9,10,1,2] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => [10] => ? = 0
[10,8,9,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => [10] => ? = 0
[9,7,10,5,6,8,1,2,3,4] => [1,2,3,4,5,6,8,7,10,9] => 000000101 => [7,2,1] => ? = 16
[9,6,10,3,7,8,1,2,4,5] => [1,2,4,5,3,7,8,6,10,9] => 000100101 => [4,3,2,1] => ? = 20
[2,10,1,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,2,10] => 000000010 => [8,2] => ? = 8
[1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => [10] => ? = 0
[1,4,3,5,6,7,8,9,2] => [1,4,2,3,5,6,7,8,9] => 00100000 => [3,6] => ? = 3
[9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => [10] => ? = 0
[7,8,9,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => [10] => ? = 0
[10,9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => [10] => ? = 0
[11,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000 => [11] => ? = 0
[11,10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000 => [11] => ? = 0
[9,2,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,2,9] => 00000010 => [7,2] => ? = 7
[10,2,1,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,2,10] => 000000010 => [8,2] => ? = 8
[2,3,4,5,6,7,8,9,10,11,1] => [1,2,3,4,5,6,7,8,9,10,11] => 0000000000 => [11] => ? = 0
[4,5,8,9,10,1,2,3,6,7] => [1,2,3,6,7,4,5,8,9,10] => 000001000 => [6,4] => ? = 6
[10,1,4,5,6,7,8,9,2,3] => [1,4,5,6,7,8,9,2,3,10] => 000000010 => [8,2] => ? = 8
[1,2,3,6,4,7,8,9,5] => [1,2,3,6,4,7,8,9,5] => 00001001 => [5,3,1] => ? = 13
[1,2,5,3,6,7,8,9,4] => [1,2,5,3,6,7,8,9,4] => 00010001 => [4,4,1] => ? = 12
[1,4,2,5,6,7,8,9,3] => [1,4,2,5,6,7,8,9,3] => 00100001 => [3,5,1] => ? = 11
[9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[6,7,8,9,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
[9,6,7,8,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => 00000000 => [9] => ? = 0
Description
The major index of the composition. The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents. For details about the major index see [[Permutations/Descents-Major]].
Matching statistic: St000726
Mapping
Mp00223: Permutations —runsort⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
St000726: Permutations ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 52%
Values
[1,2] => [1,2] => [2,1] => [1,2] => 0
[2,1] => [1,2] => [2,1] => [1,2] => 0
[1,2,3] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [3,2,1] => [2,1,3] => 2
[2,1,3] => [1,3,2] => [3,2,1] => [2,1,3] => 2
[2,3,1] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[3,2,1] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [2,4,3,1] => [1,3,2,4] => 3
[1,3,2,4] => [1,3,2,4] => [3,2,4,1] => [2,1,3,4] => 2
[1,3,4,2] => [1,3,4,2] => [4,2,3,1] => [2,3,1,4] => 3
[1,4,2,3] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[1,4,3,2] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[2,1,3,4] => [1,3,4,2] => [4,2,3,1] => [2,3,1,4] => 3
[2,1,4,3] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[2,3,1,4] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[2,3,4,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[2,4,1,3] => [1,3,2,4] => [3,2,4,1] => [2,1,3,4] => 2
[2,4,3,1] => [1,2,4,3] => [2,4,3,1] => [1,3,2,4] => 3
[3,1,2,4] => [1,2,4,3] => [2,4,3,1] => [1,3,2,4] => 3
[3,1,4,2] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[3,2,1,4] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[3,2,4,1] => [1,2,4,3] => [2,4,3,1] => [1,3,2,4] => 3
[3,4,1,2] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[3,4,2,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,1,2,3] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,1,3,2] => [1,3,2,4] => [3,2,4,1] => [2,1,3,4] => 2
[4,2,1,3] => [1,3,2,4] => [3,2,4,1] => [2,1,3,4] => 2
[4,2,3,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,3,1,2] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,5,4,1] => [1,2,4,3,5] => 4
[1,2,4,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => [1,3,2,4,5] => 3
[1,2,4,5,3] => [1,2,4,5,3] => [2,5,3,4,1] => [1,3,4,2,5] => 4
[1,2,5,3,4] => [1,2,5,3,4] => [2,4,5,3,1] => [1,4,2,3,5] => 4
[1,2,5,4,3] => [1,2,5,3,4] => [2,4,5,3,1] => [1,4,2,3,5] => 4
[1,3,2,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => [2,1,3,4,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => [3,2,5,4,1] => [2,1,4,3,5] => 6
[1,3,4,2,5] => [1,3,4,2,5] => [4,2,3,5,1] => [2,3,1,4,5] => 3
[1,3,4,5,2] => [1,3,4,5,2] => [5,2,3,4,1] => [2,3,4,1,5] => 4
[1,3,5,2,4] => [1,3,5,2,4] => [4,2,5,3,1] => [2,4,1,3,5] => 4
[1,3,5,4,2] => [1,3,5,2,4] => [4,2,5,3,1] => [2,4,1,3,5] => 4
[1,4,2,3,5] => [1,4,2,3,5] => [3,4,2,5,1] => [3,1,2,4,5] => 3
[1,4,2,5,3] => [1,4,2,5,3] => [3,5,2,4,1] => [3,1,4,2,5] => 7
[1,4,3,2,5] => [1,4,2,5,3] => [3,5,2,4,1] => [3,1,4,2,5] => 7
[1,4,3,5,2] => [1,4,2,3,5] => [3,4,2,5,1] => [3,1,2,4,5] => 3
[1,4,5,2,3] => [1,4,5,2,3] => [4,5,2,3,1] => [3,4,1,2,5] => 4
[1,4,5,3,2] => [1,4,5,2,3] => [4,5,2,3,1] => [3,4,1,2,5] => 4
[1,2,6,3,4,5,7] => [1,2,6,3,4,5,7] => [2,4,5,6,3,7,1] => [1,5,2,3,4,6,7] => ? = 5
[1,2,6,3,4,7,5] => [1,2,6,3,4,7,5] => [2,4,5,7,3,6,1] => [1,5,2,3,6,4,7] => ? = 11
[1,2,6,3,5,4,7] => [1,2,6,3,5,4,7] => [2,4,6,5,3,7,1] => [1,5,2,4,3,6,7] => ? = 9
[1,2,6,3,5,7,4] => [1,2,6,3,5,7,4] => [2,4,7,5,3,6,1] => [1,5,2,4,6,3,7] => ? = 11
[1,2,6,3,7,4,5] => [1,2,6,3,7,4,5] => [2,4,6,7,3,5,1] => [1,5,2,6,3,4,7] => ? = 11
[1,2,6,3,7,5,4] => [1,2,6,3,7,4,5] => [2,4,6,7,3,5,1] => [1,5,2,6,3,4,7] => ? = 11
[1,2,6,4,3,5,7] => [1,2,6,3,5,7,4] => [2,4,7,5,3,6,1] => [1,5,2,4,6,3,7] => ? = 11
[1,2,6,4,3,7,5] => [1,2,6,3,7,4,5] => [2,4,6,7,3,5,1] => [1,5,2,6,3,4,7] => ? = 11
[1,2,6,4,5,3,7] => [1,2,6,3,7,4,5] => [2,4,6,7,3,5,1] => [1,5,2,6,3,4,7] => ? = 11
[1,2,6,4,5,7,3] => [1,2,6,3,4,5,7] => [2,4,5,6,3,7,1] => [1,5,2,3,4,6,7] => ? = 5
[1,2,6,4,7,3,5] => [1,2,6,3,5,4,7] => [2,4,6,5,3,7,1] => [1,5,2,4,3,6,7] => ? = 9
[1,2,6,4,7,5,3] => [1,2,6,3,4,7,5] => [2,4,5,7,3,6,1] => [1,5,2,3,6,4,7] => ? = 11
[1,2,6,5,3,4,7] => [1,2,6,3,4,7,5] => [2,4,5,7,3,6,1] => [1,5,2,3,6,4,7] => ? = 11
[1,2,6,5,3,7,4] => [1,2,6,3,7,4,5] => [2,4,6,7,3,5,1] => [1,5,2,6,3,4,7] => ? = 11
[1,2,6,5,4,3,7] => [1,2,6,3,7,4,5] => [2,4,6,7,3,5,1] => [1,5,2,6,3,4,7] => ? = 11
[1,2,6,5,4,7,3] => [1,2,6,3,4,7,5] => [2,4,5,7,3,6,1] => [1,5,2,3,6,4,7] => ? = 11
[1,2,6,5,7,3,4] => [1,2,6,3,4,5,7] => [2,4,5,6,3,7,1] => [1,5,2,3,4,6,7] => ? = 5
[1,2,6,5,7,4,3] => [1,2,6,3,4,5,7] => [2,4,5,6,3,7,1] => [1,5,2,3,4,6,7] => ? = 5
[1,2,6,7,3,4,5] => [1,2,6,7,3,4,5] => [2,5,6,7,3,4,1] => [1,5,6,2,3,4,7] => ? = 6
[1,2,6,7,3,5,4] => [1,2,6,7,3,5,4] => [2,5,7,6,3,4,1] => [1,5,6,2,4,3,7] => ? = 10
[1,2,6,7,4,3,5] => [1,2,6,7,3,5,4] => [2,5,7,6,3,4,1] => [1,5,6,2,4,3,7] => ? = 10
[1,2,6,7,4,5,3] => [1,2,6,7,3,4,5] => [2,5,6,7,3,4,1] => [1,5,6,2,3,4,7] => ? = 6
[1,2,6,7,5,3,4] => [1,2,6,7,3,4,5] => [2,5,6,7,3,4,1] => [1,5,6,2,3,4,7] => ? = 6
[1,2,6,7,5,4,3] => [1,2,6,7,3,4,5] => [2,5,6,7,3,4,1] => [1,5,6,2,3,4,7] => ? = 6
[1,2,7,3,4,5,6] => [1,2,7,3,4,5,6] => [2,4,5,6,7,3,1] => [1,6,2,3,4,5,7] => ? = 6
[1,2,7,3,4,6,5] => [1,2,7,3,4,6,5] => [2,4,5,7,6,3,1] => [1,6,2,3,5,4,7] => ? = 11
[1,2,7,3,5,4,6] => [1,2,7,3,5,4,6] => [2,4,6,5,7,3,1] => [1,6,2,4,3,5,7] => ? = 10
[1,2,7,3,5,6,4] => [1,2,7,3,5,6,4] => [2,4,7,5,6,3,1] => [1,6,2,4,5,3,7] => ? = 11
[1,2,7,3,6,4,5] => [1,2,7,3,6,4,5] => [2,4,6,7,5,3,1] => [1,6,2,5,3,4,7] => ? = 11
[1,2,7,3,6,5,4] => [1,2,7,3,6,4,5] => [2,4,6,7,5,3,1] => [1,6,2,5,3,4,7] => ? = 11
[1,2,7,4,3,5,6] => [1,2,7,3,5,6,4] => [2,4,7,5,6,3,1] => [1,6,2,4,5,3,7] => ? = 11
[1,2,7,4,3,6,5] => [1,2,7,3,6,4,5] => [2,4,6,7,5,3,1] => [1,6,2,5,3,4,7] => ? = 11
[1,2,7,4,5,3,6] => [1,2,7,3,6,4,5] => [2,4,6,7,5,3,1] => [1,6,2,5,3,4,7] => ? = 11
[1,2,7,4,5,6,3] => [1,2,7,3,4,5,6] => [2,4,5,6,7,3,1] => [1,6,2,3,4,5,7] => ? = 6
[1,2,7,4,6,3,5] => [1,2,7,3,5,4,6] => [2,4,6,5,7,3,1] => [1,6,2,4,3,5,7] => ? = 10
[1,2,7,4,6,5,3] => [1,2,7,3,4,6,5] => [2,4,5,7,6,3,1] => [1,6,2,3,5,4,7] => ? = 11
[1,2,7,5,3,4,6] => [1,2,7,3,4,6,5] => [2,4,5,7,6,3,1] => [1,6,2,3,5,4,7] => ? = 11
[1,2,7,5,3,6,4] => [1,2,7,3,6,4,5] => [2,4,6,7,5,3,1] => [1,6,2,5,3,4,7] => ? = 11
[1,2,7,5,4,3,6] => [1,2,7,3,6,4,5] => [2,4,6,7,5,3,1] => [1,6,2,5,3,4,7] => ? = 11
[1,2,7,5,4,6,3] => [1,2,7,3,4,6,5] => [2,4,5,7,6,3,1] => [1,6,2,3,5,4,7] => ? = 11
[1,2,7,5,6,3,4] => [1,2,7,3,4,5,6] => [2,4,5,6,7,3,1] => [1,6,2,3,4,5,7] => ? = 6
[1,2,7,5,6,4,3] => [1,2,7,3,4,5,6] => [2,4,5,6,7,3,1] => [1,6,2,3,4,5,7] => ? = 6
[1,2,7,6,3,4,5] => [1,2,7,3,4,5,6] => [2,4,5,6,7,3,1] => [1,6,2,3,4,5,7] => ? = 6
[1,2,7,6,3,5,4] => [1,2,7,3,5,4,6] => [2,4,6,5,7,3,1] => [1,6,2,4,3,5,7] => ? = 10
[1,2,7,6,4,3,5] => [1,2,7,3,5,4,6] => [2,4,6,5,7,3,1] => [1,6,2,4,3,5,7] => ? = 10
[1,2,7,6,4,5,3] => [1,2,7,3,4,5,6] => [2,4,5,6,7,3,1] => [1,6,2,3,4,5,7] => ? = 6
[1,2,7,6,5,3,4] => [1,2,7,3,4,5,6] => [2,4,5,6,7,3,1] => [1,6,2,3,4,5,7] => ? = 6
[1,2,7,6,5,4,3] => [1,2,7,3,4,5,6] => [2,4,5,6,7,3,1] => [1,6,2,3,4,5,7] => ? = 6
[1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [3,2,4,5,6,7,1] => [2,1,3,4,5,6,7] => ? = 2
[1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [3,2,4,5,7,6,1] => [2,1,3,4,6,5,7] => ? = 8
Description
The normalized sum of the leaf labels of the increasing binary tree associated to a permutation. The sum of the leaf labels is at least the size of the permutation, equality is attained for the binary trees that have only one leaf. This statistic is the sum of the leaf labels minus the size of the permutation.
Matching statistic: St000111
Mapping
Mp00223: Permutations —runsort⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
St000111: Permutations ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 43%
Values
[1,2] => [1,2] => [2,1] => [1,2] => 0
[2,1] => [1,2] => [2,1] => [1,2] => 0
[1,2,3] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [3,2,1] => [2,1,3] => 2
[2,1,3] => [1,3,2] => [3,2,1] => [2,1,3] => 2
[2,3,1] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[3,2,1] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [2,4,3,1] => [1,3,2,4] => 3
[1,3,2,4] => [1,3,2,4] => [3,2,4,1] => [2,1,3,4] => 2
[1,3,4,2] => [1,3,4,2] => [4,2,3,1] => [2,3,1,4] => 3
[1,4,2,3] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[1,4,3,2] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[2,1,3,4] => [1,3,4,2] => [4,2,3,1] => [2,3,1,4] => 3
[2,1,4,3] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[2,3,1,4] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[2,3,4,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[2,4,1,3] => [1,3,2,4] => [3,2,4,1] => [2,1,3,4] => 2
[2,4,3,1] => [1,2,4,3] => [2,4,3,1] => [1,3,2,4] => 3
[3,1,2,4] => [1,2,4,3] => [2,4,3,1] => [1,3,2,4] => 3
[3,1,4,2] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[3,2,1,4] => [1,4,2,3] => [3,4,2,1] => [3,1,2,4] => 3
[3,2,4,1] => [1,2,4,3] => [2,4,3,1] => [1,3,2,4] => 3
[3,4,1,2] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[3,4,2,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,1,2,3] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,1,3,2] => [1,3,2,4] => [3,2,4,1] => [2,1,3,4] => 2
[4,2,1,3] => [1,3,2,4] => [3,2,4,1] => [2,1,3,4] => 2
[4,2,3,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,3,1,2] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,5,4,1] => [1,2,4,3,5] => 4
[1,2,4,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => [1,3,2,4,5] => 3
[1,2,4,5,3] => [1,2,4,5,3] => [2,5,3,4,1] => [1,3,4,2,5] => 4
[1,2,5,3,4] => [1,2,5,3,4] => [2,4,5,3,1] => [1,4,2,3,5] => 4
[1,2,5,4,3] => [1,2,5,3,4] => [2,4,5,3,1] => [1,4,2,3,5] => 4
[1,3,2,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => [2,1,3,4,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => [3,2,5,4,1] => [2,1,4,3,5] => 6
[1,3,4,2,5] => [1,3,4,2,5] => [4,2,3,5,1] => [2,3,1,4,5] => 3
[1,3,4,5,2] => [1,3,4,5,2] => [5,2,3,4,1] => [2,3,4,1,5] => 4
[1,3,5,2,4] => [1,3,5,2,4] => [4,2,5,3,1] => [2,4,1,3,5] => 4
[1,3,5,4,2] => [1,3,5,2,4] => [4,2,5,3,1] => [2,4,1,3,5] => 4
[1,4,2,3,5] => [1,4,2,3,5] => [3,4,2,5,1] => [3,1,2,4,5] => 3
[1,4,2,5,3] => [1,4,2,5,3] => [3,5,2,4,1] => [3,1,4,2,5] => 7
[1,4,3,2,5] => [1,4,2,5,3] => [3,5,2,4,1] => [3,1,4,2,5] => 7
[1,4,3,5,2] => [1,4,2,3,5] => [3,4,2,5,1] => [3,1,2,4,5] => 3
[1,4,5,2,3] => [1,4,5,2,3] => [4,5,2,3,1] => [3,4,1,2,5] => 4
[1,4,5,3,2] => [1,4,5,2,3] => [4,5,2,3,1] => [3,4,1,2,5] => 4
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => ? = 0
[1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [2,3,4,5,7,6,1] => [1,2,3,4,6,5,7] => ? = 6
[1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [2,3,4,6,5,7,1] => [1,2,3,5,4,6,7] => ? = 5
[1,2,3,4,6,7,5] => [1,2,3,4,6,7,5] => [2,3,4,7,5,6,1] => [1,2,3,5,6,4,7] => ? = 6
[1,2,3,4,7,5,6] => [1,2,3,4,7,5,6] => [2,3,4,6,7,5,1] => [1,2,3,6,4,5,7] => ? = 6
[1,2,3,4,7,6,5] => [1,2,3,4,7,5,6] => [2,3,4,6,7,5,1] => [1,2,3,6,4,5,7] => ? = 6
[1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [2,3,5,4,6,7,1] => [1,2,4,3,5,6,7] => ? = 4
[1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [2,3,5,4,7,6,1] => [1,2,4,3,6,5,7] => ? = 10
[1,2,3,5,6,4,7] => [1,2,3,5,6,4,7] => [2,3,6,4,5,7,1] => [1,2,4,5,3,6,7] => ? = 5
[1,2,3,5,6,7,4] => [1,2,3,5,6,7,4] => [2,3,7,4,5,6,1] => [1,2,4,5,6,3,7] => ? = 6
[1,2,3,5,7,4,6] => [1,2,3,5,7,4,6] => [2,3,6,4,7,5,1] => [1,2,4,6,3,5,7] => ? = 6
[1,2,3,5,7,6,4] => [1,2,3,5,7,4,6] => [2,3,6,4,7,5,1] => [1,2,4,6,3,5,7] => ? = 6
[1,2,3,6,4,5,7] => [1,2,3,6,4,5,7] => [2,3,5,6,4,7,1] => [1,2,5,3,4,6,7] => ? = 5
[1,2,3,6,4,7,5] => [1,2,3,6,4,7,5] => [2,3,5,7,4,6,1] => [1,2,5,3,6,4,7] => ? = 11
[1,2,3,6,5,4,7] => [1,2,3,6,4,7,5] => [2,3,5,7,4,6,1] => [1,2,5,3,6,4,7] => ? = 11
[1,2,3,6,5,7,4] => [1,2,3,6,4,5,7] => [2,3,5,6,4,7,1] => [1,2,5,3,4,6,7] => ? = 5
[1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => [2,3,6,7,4,5,1] => [1,2,5,6,3,4,7] => ? = 6
[1,2,3,6,7,5,4] => [1,2,3,6,7,4,5] => [2,3,6,7,4,5,1] => [1,2,5,6,3,4,7] => ? = 6
[1,2,3,7,4,5,6] => [1,2,3,7,4,5,6] => [2,3,5,6,7,4,1] => [1,2,6,3,4,5,7] => ? = 6
[1,2,3,7,4,6,5] => [1,2,3,7,4,6,5] => [2,3,5,7,6,4,1] => [1,2,6,3,5,4,7] => ? = 11
[1,2,3,7,5,4,6] => [1,2,3,7,4,6,5] => [2,3,5,7,6,4,1] => [1,2,6,3,5,4,7] => ? = 11
[1,2,3,7,5,6,4] => [1,2,3,7,4,5,6] => [2,3,5,6,7,4,1] => [1,2,6,3,4,5,7] => ? = 6
[1,2,3,7,6,4,5] => [1,2,3,7,4,5,6] => [2,3,5,6,7,4,1] => [1,2,6,3,4,5,7] => ? = 6
[1,2,3,7,6,5,4] => [1,2,3,7,4,5,6] => [2,3,5,6,7,4,1] => [1,2,6,3,4,5,7] => ? = 6
[1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [2,4,3,5,6,7,1] => [1,3,2,4,5,6,7] => ? = 3
[1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [2,4,3,5,7,6,1] => [1,3,2,4,6,5,7] => ? = 9
[1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [2,4,3,6,5,7,1] => [1,3,2,5,4,6,7] => ? = 8
[1,2,4,3,6,7,5] => [1,2,4,3,6,7,5] => [2,4,3,7,5,6,1] => [1,3,2,5,6,4,7] => ? = 9
[1,2,4,3,7,5,6] => [1,2,4,3,7,5,6] => [2,4,3,6,7,5,1] => [1,3,2,6,4,5,7] => ? = 9
[1,2,4,3,7,6,5] => [1,2,4,3,7,5,6] => [2,4,3,6,7,5,1] => [1,3,2,6,4,5,7] => ? = 9
[1,2,4,5,3,6,7] => [1,2,4,5,3,6,7] => [2,5,3,4,6,7,1] => [1,3,4,2,5,6,7] => ? = 4
[1,2,4,5,3,7,6] => [1,2,4,5,3,7,6] => [2,5,3,4,7,6,1] => [1,3,4,2,6,5,7] => ? = 10
[1,2,4,5,6,3,7] => [1,2,4,5,6,3,7] => [2,6,3,4,5,7,1] => [1,3,4,5,2,6,7] => ? = 5
[1,2,4,5,6,7,3] => [1,2,4,5,6,7,3] => [2,7,3,4,5,6,1] => [1,3,4,5,6,2,7] => ? = 6
[1,2,4,5,7,3,6] => [1,2,4,5,7,3,6] => [2,6,3,4,7,5,1] => [1,3,4,6,2,5,7] => ? = 6
[1,2,4,5,7,6,3] => [1,2,4,5,7,3,6] => [2,6,3,4,7,5,1] => [1,3,4,6,2,5,7] => ? = 6
[1,2,4,6,3,5,7] => [1,2,4,6,3,5,7] => [2,5,3,6,4,7,1] => [1,3,5,2,4,6,7] => ? = 5
[1,2,4,6,3,7,5] => [1,2,4,6,3,7,5] => [2,5,3,7,4,6,1] => [1,3,5,2,6,4,7] => ? = 11
[1,2,4,6,5,3,7] => [1,2,4,6,3,7,5] => [2,5,3,7,4,6,1] => [1,3,5,2,6,4,7] => ? = 11
[1,2,4,6,5,7,3] => [1,2,4,6,3,5,7] => [2,5,3,6,4,7,1] => [1,3,5,2,4,6,7] => ? = 5
[1,2,4,6,7,3,5] => [1,2,4,6,7,3,5] => [2,6,3,7,4,5,1] => [1,3,5,6,2,4,7] => ? = 6
[1,2,4,6,7,5,3] => [1,2,4,6,7,3,5] => [2,6,3,7,4,5,1] => [1,3,5,6,2,4,7] => ? = 6
[1,2,4,7,3,5,6] => [1,2,4,7,3,5,6] => [2,5,3,6,7,4,1] => [1,3,6,2,4,5,7] => ? = 6
[1,2,4,7,3,6,5] => [1,2,4,7,3,6,5] => [2,5,3,7,6,4,1] => [1,3,6,2,5,4,7] => ? = 11
[1,2,4,7,5,3,6] => [1,2,4,7,3,6,5] => [2,5,3,7,6,4,1] => [1,3,6,2,5,4,7] => ? = 11
[1,2,4,7,5,6,3] => [1,2,4,7,3,5,6] => [2,5,3,6,7,4,1] => [1,3,6,2,4,5,7] => ? = 6
[1,2,4,7,6,3,5] => [1,2,4,7,3,5,6] => [2,5,3,6,7,4,1] => [1,3,6,2,4,5,7] => ? = 6
[1,2,4,7,6,5,3] => [1,2,4,7,3,5,6] => [2,5,3,6,7,4,1] => [1,3,6,2,4,5,7] => ? = 6
[1,2,5,3,4,6,7] => [1,2,5,3,4,6,7] => [2,4,5,3,6,7,1] => [1,4,2,3,5,6,7] => ? = 4
[1,2,5,3,4,7,6] => [1,2,5,3,4,7,6] => [2,4,5,3,7,6,1] => [1,4,2,3,6,5,7] => ? = 10
Description
The sum of the descent tops (or Genocchi descents) of a permutation. This statistic is given by $$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} \pi_i.$$
Matching statistic: St001207
(load all 19 compositions to match this statistic)
Mapping
Mp00223: Permutations —runsort⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 14%
Values
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [1,2] => [1,2] => [1,2] => 0
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => [2,3,1] => 2
[2,1,3] => [1,3,2] => [1,3,2] => [2,3,1] => 2
[2,3,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[3,2,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => [2,3,4,1] => 3
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => [2,3,1,4] => 2
[1,3,4,2] => [1,3,4,2] => [1,4,3,2] => [3,4,2,1] => 3
[1,4,2,3] => [1,4,2,3] => [1,4,3,2] => [3,4,2,1] => 3
[1,4,3,2] => [1,4,2,3] => [1,4,3,2] => [3,4,2,1] => 3
[2,1,3,4] => [1,3,4,2] => [1,4,3,2] => [3,4,2,1] => 3
[2,1,4,3] => [1,4,2,3] => [1,4,3,2] => [3,4,2,1] => 3
[2,3,1,4] => [1,4,2,3] => [1,4,3,2] => [3,4,2,1] => 3
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[2,4,1,3] => [1,3,2,4] => [1,3,2,4] => [2,3,1,4] => 2
[2,4,3,1] => [1,2,4,3] => [1,2,4,3] => [2,3,4,1] => 3
[3,1,2,4] => [1,2,4,3] => [1,2,4,3] => [2,3,4,1] => 3
[3,1,4,2] => [1,4,2,3] => [1,4,3,2] => [3,4,2,1] => 3
[3,2,1,4] => [1,4,2,3] => [1,4,3,2] => [3,4,2,1] => 3
[3,2,4,1] => [1,2,4,3] => [1,2,4,3] => [2,3,4,1] => 3
[3,4,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[3,4,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,2,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,3,2] => [1,3,2,4] => [1,3,2,4] => [2,3,1,4] => 2
[4,2,1,3] => [1,3,2,4] => [1,3,2,4] => [2,3,1,4] => 2
[4,2,3,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => ? = 4
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [2,3,4,1,5] => ? = 3
[1,2,4,5,3] => [1,2,4,5,3] => [1,2,5,4,3] => [3,4,5,2,1] => ? = 4
[1,2,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => [3,4,5,2,1] => ? = 4
[1,2,5,4,3] => [1,2,5,3,4] => [1,2,5,4,3] => [3,4,5,2,1] => ? = 4
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [2,3,1,4,5] => ? = 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [3,4,2,5,1] => ? = 6
[1,3,4,2,5] => [1,3,4,2,5] => [1,4,3,2,5] => [3,4,2,1,5] => ? = 3
[1,3,4,5,2] => [1,3,4,5,2] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 4
[1,3,5,2,4] => [1,3,5,2,4] => [1,4,5,2,3] => [2,1,5,3,4] => ? = 4
[1,3,5,4,2] => [1,3,5,2,4] => [1,4,5,2,3] => [2,1,5,3,4] => ? = 4
[1,4,2,3,5] => [1,4,2,3,5] => [1,4,3,2,5] => [3,4,2,1,5] => ? = 3
[1,4,2,5,3] => [1,4,2,5,3] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 7
[1,4,3,2,5] => [1,4,2,5,3] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 7
[1,4,3,5,2] => [1,4,2,3,5] => [1,4,3,2,5] => [3,4,2,1,5] => ? = 3
[1,4,5,2,3] => [1,4,5,2,3] => [1,5,4,3,2] => [4,5,3,2,1] => ? = 4
[1,4,5,3,2] => [1,4,5,2,3] => [1,5,4,3,2] => [4,5,3,2,1] => ? = 4
[1,5,2,3,4] => [1,5,2,3,4] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 4
[1,5,2,4,3] => [1,5,2,4,3] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 7
[1,5,3,2,4] => [1,5,2,4,3] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 7
[1,5,3,4,2] => [1,5,2,3,4] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 4
[1,5,4,2,3] => [1,5,2,3,4] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 4
[1,5,4,3,2] => [1,5,2,3,4] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 4
[2,1,3,4,5] => [1,3,4,5,2] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 4
[2,1,3,5,4] => [1,3,5,2,4] => [1,4,5,2,3] => [2,1,5,3,4] => ? = 4
[2,1,4,3,5] => [1,4,2,3,5] => [1,4,3,2,5] => [3,4,2,1,5] => ? = 3
[2,1,4,5,3] => [1,4,5,2,3] => [1,5,4,3,2] => [4,5,3,2,1] => ? = 4
[2,1,5,3,4] => [1,5,2,3,4] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 4
[2,1,5,4,3] => [1,5,2,3,4] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 4
[2,3,1,4,5] => [1,4,5,2,3] => [1,5,4,3,2] => [4,5,3,2,1] => ? = 4
[2,3,1,5,4] => [1,5,2,3,4] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 4
[2,3,4,1,5] => [1,5,2,3,4] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 4
[2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
[2,3,5,1,4] => [1,4,2,3,5] => [1,4,3,2,5] => [3,4,2,1,5] => ? = 3
[2,3,5,4,1] => [1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => ? = 4
[2,4,1,3,5] => [1,3,5,2,4] => [1,4,5,2,3] => [2,1,5,3,4] => ? = 4
[2,4,1,5,3] => [1,5,2,4,3] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 7
[2,4,3,1,5] => [1,5,2,4,3] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 7
[2,4,3,5,1] => [1,2,4,3,5] => [1,2,4,3,5] => [2,3,4,1,5] => ? = 3
[2,4,5,1,3] => [1,3,2,4,5] => [1,3,2,4,5] => [2,3,1,4,5] => ? = 2
[2,4,5,3,1] => [1,2,4,5,3] => [1,2,5,4,3] => [3,4,5,2,1] => ? = 4
[2,5,1,3,4] => [1,3,4,2,5] => [1,4,3,2,5] => [3,4,2,1,5] => ? = 3
[2,5,1,4,3] => [1,4,2,5,3] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 7
[2,5,3,1,4] => [1,4,2,5,3] => [1,5,3,4,2] => [3,5,1,4,2] => ? = 7
[2,5,3,4,1] => [1,2,5,3,4] => [1,2,5,4,3] => [3,4,5,2,1] => ? = 4
[2,5,4,1,3] => [1,3,2,5,4] => [1,3,2,5,4] => [3,4,2,5,1] => ? = 6
[2,5,4,3,1] => [1,2,5,3,4] => [1,2,5,4,3] => [3,4,5,2,1] => ? = 4
[3,1,2,4,5] => [1,2,4,5,3] => [1,2,5,4,3] => [3,4,5,2,1] => ? = 4
[3,1,2,5,4] => [1,2,5,3,4] => [1,2,5,4,3] => [3,4,5,2,1] => ? = 4
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.