Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000391
Mapping
Mp00064: Permutations —reverse⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
St000391: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [2,1] => 1 => 1
[2,1] => [1,2] => 0 => 0
[1,2,3] => [3,2,1] => 11 => 3
[1,3,2] => [2,3,1] => 10 => 1
[2,1,3] => [3,1,2] => 10 => 1
[2,3,1] => [1,3,2] => 01 => 2
[3,1,2] => [2,1,3] => 10 => 1
[3,2,1] => [1,2,3] => 00 => 0
[1,2,3,4] => [4,3,2,1] => 111 => 6
[1,2,4,3] => [3,4,2,1] => 110 => 3
[1,3,2,4] => [4,2,3,1] => 110 => 3
[1,3,4,2] => [2,4,3,1] => 101 => 4
[1,4,2,3] => [3,2,4,1] => 110 => 3
[1,4,3,2] => [2,3,4,1] => 100 => 1
[2,1,3,4] => [4,3,1,2] => 101 => 4
[2,1,4,3] => [3,4,1,2] => 100 => 1
[2,3,1,4] => [4,1,3,2] => 110 => 3
[2,3,4,1] => [1,4,3,2] => 011 => 5
[2,4,1,3] => [3,1,4,2] => 110 => 3
[2,4,3,1] => [1,3,4,2] => 010 => 2
[3,1,2,4] => [4,2,1,3] => 110 => 3
[3,1,4,2] => [2,4,1,3] => 100 => 1
[3,2,1,4] => [4,1,2,3] => 100 => 1
[3,2,4,1] => [1,4,2,3] => 010 => 2
[3,4,1,2] => [2,1,4,3] => 101 => 4
[3,4,2,1] => [1,2,4,3] => 001 => 3
[4,1,2,3] => [3,2,1,4] => 110 => 3
[4,1,3,2] => [2,3,1,4] => 100 => 1
[4,2,1,3] => [3,1,2,4] => 100 => 1
[4,2,3,1] => [1,3,2,4] => 010 => 2
[4,3,1,2] => [2,1,3,4] => 100 => 1
[4,3,2,1] => [1,2,3,4] => 000 => 0
[1,2,3,4,5] => [5,4,3,2,1] => 1111 => 10
[1,2,3,5,4] => [4,5,3,2,1] => 1110 => 6
[1,2,4,3,5] => [5,3,4,2,1] => 1110 => 6
[1,2,4,5,3] => [3,5,4,2,1] => 1101 => 7
[1,2,5,3,4] => [4,3,5,2,1] => 1110 => 6
[1,2,5,4,3] => [3,4,5,2,1] => 1100 => 3
[1,3,2,4,5] => [5,4,2,3,1] => 1101 => 7
[1,3,2,5,4] => [4,5,2,3,1] => 1100 => 3
[1,3,4,2,5] => [5,2,4,3,1] => 1110 => 6
[1,3,4,5,2] => [2,5,4,3,1] => 1011 => 8
[1,3,5,2,4] => [4,2,5,3,1] => 1110 => 6
[1,3,5,4,2] => [2,4,5,3,1] => 1010 => 4
[1,4,2,3,5] => [5,3,2,4,1] => 1110 => 6
[1,4,2,5,3] => [3,5,2,4,1] => 1100 => 3
[1,4,3,2,5] => [5,2,3,4,1] => 1100 => 3
[1,4,3,5,2] => [2,5,3,4,1] => 1010 => 4
[1,4,5,2,3] => [3,2,5,4,1] => 1101 => 7
[1,4,5,3,2] => [2,3,5,4,1] => 1001 => 5
Description
The sum of the positions of the ones in a binary word.
Matching statistic: St000008
Mapping
Mp00064: Permutations —reverse⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
St000008: Integer compositions ⟶ ℤResult quality: 80% ●values known / values provided: 94%●distinct values known / distinct values provided: 80%
Values
[1,2] => [2,1] => 1 => [1,1] => 1
[2,1] => [1,2] => 0 => [2] => 0
[1,2,3] => [3,2,1] => 11 => [1,1,1] => 3
[1,3,2] => [2,3,1] => 10 => [1,2] => 1
[2,1,3] => [3,1,2] => 10 => [1,2] => 1
[2,3,1] => [1,3,2] => 01 => [2,1] => 2
[3,1,2] => [2,1,3] => 10 => [1,2] => 1
[3,2,1] => [1,2,3] => 00 => [3] => 0
[1,2,3,4] => [4,3,2,1] => 111 => [1,1,1,1] => 6
[1,2,4,3] => [3,4,2,1] => 110 => [1,1,2] => 3
[1,3,2,4] => [4,2,3,1] => 110 => [1,1,2] => 3
[1,3,4,2] => [2,4,3,1] => 101 => [1,2,1] => 4
[1,4,2,3] => [3,2,4,1] => 110 => [1,1,2] => 3
[1,4,3,2] => [2,3,4,1] => 100 => [1,3] => 1
[2,1,3,4] => [4,3,1,2] => 101 => [1,2,1] => 4
[2,1,4,3] => [3,4,1,2] => 100 => [1,3] => 1
[2,3,1,4] => [4,1,3,2] => 110 => [1,1,2] => 3
[2,3,4,1] => [1,4,3,2] => 011 => [2,1,1] => 5
[2,4,1,3] => [3,1,4,2] => 110 => [1,1,2] => 3
[2,4,3,1] => [1,3,4,2] => 010 => [2,2] => 2
[3,1,2,4] => [4,2,1,3] => 110 => [1,1,2] => 3
[3,1,4,2] => [2,4,1,3] => 100 => [1,3] => 1
[3,2,1,4] => [4,1,2,3] => 100 => [1,3] => 1
[3,2,4,1] => [1,4,2,3] => 010 => [2,2] => 2
[3,4,1,2] => [2,1,4,3] => 101 => [1,2,1] => 4
[3,4,2,1] => [1,2,4,3] => 001 => [3,1] => 3
[4,1,2,3] => [3,2,1,4] => 110 => [1,1,2] => 3
[4,1,3,2] => [2,3,1,4] => 100 => [1,3] => 1
[4,2,1,3] => [3,1,2,4] => 100 => [1,3] => 1
[4,2,3,1] => [1,3,2,4] => 010 => [2,2] => 2
[4,3,1,2] => [2,1,3,4] => 100 => [1,3] => 1
[4,3,2,1] => [1,2,3,4] => 000 => [4] => 0
[1,2,3,4,5] => [5,4,3,2,1] => 1111 => [1,1,1,1,1] => 10
[1,2,3,5,4] => [4,5,3,2,1] => 1110 => [1,1,1,2] => 6
[1,2,4,3,5] => [5,3,4,2,1] => 1110 => [1,1,1,2] => 6
[1,2,4,5,3] => [3,5,4,2,1] => 1101 => [1,1,2,1] => 7
[1,2,5,3,4] => [4,3,5,2,1] => 1110 => [1,1,1,2] => 6
[1,2,5,4,3] => [3,4,5,2,1] => 1100 => [1,1,3] => 3
[1,3,2,4,5] => [5,4,2,3,1] => 1101 => [1,1,2,1] => 7
[1,3,2,5,4] => [4,5,2,3,1] => 1100 => [1,1,3] => 3
[1,3,4,2,5] => [5,2,4,3,1] => 1110 => [1,1,1,2] => 6
[1,3,4,5,2] => [2,5,4,3,1] => 1011 => [1,2,1,1] => 8
[1,3,5,2,4] => [4,2,5,3,1] => 1110 => [1,1,1,2] => 6
[1,3,5,4,2] => [2,4,5,3,1] => 1010 => [1,2,2] => 4
[1,4,2,3,5] => [5,3,2,4,1] => 1110 => [1,1,1,2] => 6
[1,4,2,5,3] => [3,5,2,4,1] => 1100 => [1,1,3] => 3
[1,4,3,2,5] => [5,2,3,4,1] => 1100 => [1,1,3] => 3
[1,4,3,5,2] => [2,5,3,4,1] => 1010 => [1,2,2] => 4
[1,4,5,2,3] => [3,2,5,4,1] => 1101 => [1,1,2,1] => 7
[1,4,5,3,2] => [2,3,5,4,1] => 1001 => [1,3,1] => 5
[2,1,4,3,6,5,8,7,10,9] => [9,10,7,8,5,6,3,4,1,2] => 101010100 => [1,2,2,2,3] => ? = 16
[4,3,2,1,6,5,8,7,10,9] => [9,10,7,8,5,6,1,2,3,4] => 100010100 => [1,4,2,3] => ? = 13
[6,3,2,5,4,1,8,7,10,9] => [9,10,7,8,1,4,5,2,3,6] => 110000100 => [1,1,5,3] => ? = 10
[8,3,2,5,4,7,6,1,10,9] => [9,10,1,6,7,4,5,2,3,8] => 110100000 => [1,1,2,6] => ? = 7
[10,3,2,5,4,7,6,9,8,1] => [1,8,9,6,7,4,5,2,3,10] => 010101000 => [2,2,2,4] => ? = 12
[2,1,6,5,4,3,8,7,10,9] => [9,10,7,8,3,4,5,6,1,2] => 101000100 => [1,2,4,3] => ? = 11
[6,5,4,3,2,1,8,7,10,9] => [9,10,7,8,1,2,3,4,5,6] => 100000100 => [1,6,3] => ? = 8
[8,5,4,3,2,7,6,1,10,9] => [9,10,1,6,7,2,3,4,5,8] => 110000000 => [1,1,8] => ? = 3
[10,5,4,3,2,7,6,9,8,1] => [1,8,9,6,7,2,3,4,5,10] => 010001000 => [2,4,4] => ? = 8
[2,1,8,5,4,7,6,3,10,9] => [9,10,3,6,7,4,5,8,1,2] => 101100000 => [1,2,1,6] => ? = 8
[8,7,4,3,6,5,2,1,10,9] => [9,10,1,2,5,6,3,4,7,8] => 101000000 => [1,2,7] => ? = 4
[10,7,4,3,6,5,2,9,8,1] => [1,8,9,2,5,6,3,4,7,10] => 011000000 => [2,1,7] => ? = 5
[2,1,10,5,4,7,6,9,8,3] => [3,8,9,6,7,4,5,10,1,2] => 100101000 => [1,3,2,4] => ? = 11
[10,9,4,3,6,5,8,7,2,1] => [1,2,7,8,5,6,3,4,9,10] => 001010000 => [3,2,5] => ? = 8
[8,9,5,6,3,4,10,1,2,7] => [7,2,1,10,4,3,6,5,9,8] => 111110010 => [1,1,1,1,1,3,2] => ? = 23
[2,1,4,3,8,7,6,5,10,9] => [9,10,5,6,7,8,3,4,1,2] => 101010000 => [1,2,2,5] => ? = 9
[4,3,2,1,8,7,6,5,10,9] => [9,10,5,6,7,8,1,2,3,4] => 100010000 => [1,4,5] => ? = 6
[8,3,2,7,6,5,4,1,10,9] => [9,10,1,4,5,6,7,2,3,8] => 110000000 => [1,1,8] => ? = 3
[10,3,2,7,6,5,4,9,8,1] => [1,8,9,4,5,6,7,2,3,10] => 010100000 => [2,2,6] => ? = 6
[2,1,8,7,6,5,4,3,10,9] => [9,10,3,4,5,6,7,8,1,2] => 101000000 => [1,2,7] => ? = 4
[9,7,6,5,4,3,2,10,1,8] => [8,1,10,2,3,4,5,6,7,9] => 110000000 => [1,1,8] => ? = 3
[10,7,6,5,4,3,2,9,8,1] => [1,8,9,2,3,4,5,6,7,10] => 010000000 => [2,8] => ? = 2
[2,1,10,7,6,5,4,9,8,3] => [3,8,9,4,5,6,7,10,1,2] => 100100000 => [1,3,6] => ? = 5
[10,9,6,5,4,3,8,7,2,1] => [1,2,7,8,3,4,5,6,9,10] => 001000000 => [3,7] => ? = 3
[2,1,4,3,10,7,6,9,8,5] => [5,8,9,6,7,10,3,4,1,2] => 101001000 => [1,2,3,4] => ? = 10
[4,3,2,1,10,7,6,9,8,5] => [5,8,9,6,7,10,1,2,3,4] => 100001000 => [1,5,4] => ? = 7
[10,3,2,9,6,5,8,7,4,1] => [1,4,7,8,5,6,9,2,3,10] => 010010000 => [2,3,5] => ? = 7
[2,1,10,9,6,5,8,7,4,3] => [3,4,7,8,5,6,9,10,1,2] => 100010000 => [1,4,5] => ? = 6
[10,9,8,5,4,7,6,3,2,1] => [1,2,3,6,7,4,5,8,9,10] => 000100000 => [4,6] => ? = 4
[10,8,9,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,9,8,10] => 010101010 => [2,2,2,2,2] => ? = 20
[9,8,7,6,10,4,3,2,1,5] => [5,1,2,3,4,10,6,7,8,9] => 100001000 => [1,5,4] => ? = 7
[6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => 111101111 => [1,1,1,1,2,1,1,1,1] => ? = 40
[7,3,2,8,9,10,1,4,5,6] => [6,5,4,1,10,9,8,2,3,7] => 110110011 => [1,1,2,1,3,1,1] => ? = 29
[8,5,4,3,2,9,10,1,6,7] => [7,6,1,10,9,2,3,4,5,8] => 110001001 => [1,1,4,3,1] => ? = 18
[2,1,4,3,6,5,10,9,8,7] => [7,8,9,10,5,6,3,4,1,2] => 101010000 => [1,2,2,5] => ? = 9
[4,3,2,1,6,5,10,9,8,7] => [7,8,9,10,5,6,1,2,3,4] => 100010000 => [1,4,5] => ? = 6
[6,3,2,5,4,1,10,9,8,7] => [7,8,9,10,1,4,5,2,3,6] => 110000000 => [1,1,8] => ? = 3
[10,3,2,5,4,9,8,7,6,1] => [1,6,7,8,9,4,5,2,3,10] => 010100000 => [2,2,6] => ? = 6
[2,1,6,5,4,3,10,9,8,7] => [7,8,9,10,3,4,5,6,1,2] => 101000000 => [1,2,7] => ? = 4
[10,5,4,3,2,9,8,7,6,1] => [1,6,7,8,9,2,3,4,5,10] => 010000000 => [2,8] => ? = 2
[2,1,10,5,4,9,8,7,6,3] => [3,6,7,8,9,4,5,10,1,2] => 100100000 => [1,3,6] => ? = 5
[10,9,4,3,8,7,6,5,2,1] => [1,2,5,6,7,8,3,4,9,10] => 001000000 => [3,7] => ? = 3
[7,10,5,9,3,8,1,6,4,2] => [2,4,6,1,8,3,9,5,10,7] => 101010100 => [1,2,2,2,3] => ? = 16
[9,7,5,10,3,8,2,6,1,4] => [4,1,6,2,8,3,10,5,7,9] => 111010000 => [1,1,1,2,5] => ? = 11
[5,6,7,10,1,2,3,9,8,4] => [4,8,9,3,2,1,10,7,6,5] => 111011100 => [1,1,1,2,1,1,3] => ? = 24
[2,1,4,3,10,9,8,7,6,5] => [5,6,7,8,9,10,3,4,1,2] => 101000000 => [1,2,7] => ? = 4
[10,3,2,9,8,7,6,5,4,1] => [1,4,5,6,7,8,9,2,3,10] => 010000000 => [2,8] => ? = 2
[4,5,10,1,2,9,8,7,6,3] => [3,6,7,8,9,2,1,10,5,4] => 110110000 => [1,1,2,1,5] => ? = 12
[3,10,1,9,8,7,6,5,4,2] => [2,4,5,6,7,8,9,1,10,3] => 101000000 => [1,2,7] => ? = 4
[6,10,9,8,7,1,5,4,3,2] => [2,3,4,5,1,7,8,9,10,6] => 100001000 => [1,5,4] => ? = 7
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: St000472
(load all 4 compositions to match this statistic)
Mapping
St000472: Permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 46%
Values
[1,2] => 1
[2,1] => 0
[1,2,3] => 3
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 1
[3,2,1] => 0
[1,2,3,4] => 6
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 4
[1,4,2,3] => 3
[1,4,3,2] => 1
[2,1,3,4] => 4
[2,1,4,3] => 1
[2,3,1,4] => 3
[2,3,4,1] => 5
[2,4,1,3] => 3
[2,4,3,1] => 2
[3,1,2,4] => 3
[3,1,4,2] => 1
[3,2,1,4] => 1
[3,2,4,1] => 2
[3,4,1,2] => 4
[3,4,2,1] => 3
[4,1,2,3] => 3
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => 2
[4,3,1,2] => 1
[4,3,2,1] => 0
[1,2,3,4,5] => 10
[1,2,3,5,4] => 6
[1,2,4,3,5] => 6
[1,2,4,5,3] => 7
[1,2,5,3,4] => 6
[1,2,5,4,3] => 3
[1,3,2,4,5] => 7
[1,3,2,5,4] => 3
[1,3,4,2,5] => 6
[1,3,4,5,2] => 8
[1,3,5,2,4] => 6
[1,3,5,4,2] => 4
[1,4,2,3,5] => 6
[1,4,2,5,3] => 3
[1,4,3,2,5] => 3
[1,4,3,5,2] => 4
[1,4,5,2,3] => 7
[1,4,5,3,2] => 5
[1,4,6,5,7,2,3] => ? = 12
[1,4,6,5,7,3,2] => ? = 10
[1,4,6,7,2,3,5] => ? = 16
[1,4,6,7,2,5,3] => ? = 13
[1,4,6,7,3,2,5] => ? = 13
[1,4,6,7,3,5,2] => ? = 14
[1,4,6,7,5,2,3] => ? = 13
[1,4,6,7,5,3,2] => ? = 11
[1,4,7,2,3,5,6] => ? = 15
[1,4,7,2,3,6,5] => ? = 10
[1,4,7,2,5,3,6] => ? = 10
[1,4,7,2,5,6,3] => ? = 12
[1,4,7,2,6,3,5] => ? = 10
[1,4,7,2,6,5,3] => ? = 7
[1,4,7,3,2,5,6] => ? = 12
[1,4,7,3,2,6,5] => ? = 7
[1,4,7,3,5,2,6] => ? = 10
[1,4,7,3,5,6,2] => ? = 13
[1,4,7,3,6,2,5] => ? = 10
[1,4,7,3,6,5,2] => ? = 8
[1,4,7,5,2,3,6] => ? = 10
[1,4,7,5,2,6,3] => ? = 7
[1,4,7,5,3,2,6] => ? = 7
[1,4,7,5,3,6,2] => ? = 8
[1,4,7,5,6,2,3] => ? = 12
[1,4,7,5,6,3,2] => ? = 10
[1,4,7,6,2,3,5] => ? = 10
[1,4,7,6,2,5,3] => ? = 7
[1,4,7,6,3,2,5] => ? = 7
[1,4,7,6,3,5,2] => ? = 8
[1,4,7,6,5,2,3] => ? = 7
[1,4,7,6,5,3,2] => ? = 5
[1,5,2,3,4,6,7] => ? = 16
[1,5,2,3,4,7,6] => ? = 10
[1,5,2,3,6,4,7] => ? = 10
[1,5,2,3,6,7,4] => ? = 12
[1,5,2,3,7,4,6] => ? = 10
[1,5,2,3,7,6,4] => ? = 6
[1,5,2,4,3,6,7] => ? = 12
[1,5,2,4,3,7,6] => ? = 6
[1,5,2,4,6,3,7] => ? = 10
[1,5,2,4,6,7,3] => ? = 13
[1,5,2,4,7,3,6] => ? = 10
[1,5,2,4,7,6,3] => ? = 7
[1,5,2,6,3,4,7] => ? = 10
[1,5,2,6,3,7,4] => ? = 6
[1,5,2,6,4,3,7] => ? = 6
[1,5,2,6,4,7,3] => ? = 7
[1,5,2,6,7,3,4] => ? = 12
[1,5,2,6,7,4,3] => ? = 9
Description
The sum of the ascent bottoms of a permutation.
Matching statistic: St000154
(load all 5 compositions to match this statistic)
Mapping
Mp00064: Permutations —reverse⟶ Permutations
St000154: Permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 35%
Values
[1,2] => [2,1] => 1
[2,1] => [1,2] => 0
[1,2,3] => [3,2,1] => 3
[1,3,2] => [2,3,1] => 1
[2,1,3] => [3,1,2] => 1
[2,3,1] => [1,3,2] => 2
[3,1,2] => [2,1,3] => 1
[3,2,1] => [1,2,3] => 0
[1,2,3,4] => [4,3,2,1] => 6
[1,2,4,3] => [3,4,2,1] => 3
[1,3,2,4] => [4,2,3,1] => 3
[1,3,4,2] => [2,4,3,1] => 4
[1,4,2,3] => [3,2,4,1] => 3
[1,4,3,2] => [2,3,4,1] => 1
[2,1,3,4] => [4,3,1,2] => 4
[2,1,4,3] => [3,4,1,2] => 1
[2,3,1,4] => [4,1,3,2] => 3
[2,3,4,1] => [1,4,3,2] => 5
[2,4,1,3] => [3,1,4,2] => 3
[2,4,3,1] => [1,3,4,2] => 2
[3,1,2,4] => [4,2,1,3] => 3
[3,1,4,2] => [2,4,1,3] => 1
[3,2,1,4] => [4,1,2,3] => 1
[3,2,4,1] => [1,4,2,3] => 2
[3,4,1,2] => [2,1,4,3] => 4
[3,4,2,1] => [1,2,4,3] => 3
[4,1,2,3] => [3,2,1,4] => 3
[4,1,3,2] => [2,3,1,4] => 1
[4,2,1,3] => [3,1,2,4] => 1
[4,2,3,1] => [1,3,2,4] => 2
[4,3,1,2] => [2,1,3,4] => 1
[4,3,2,1] => [1,2,3,4] => 0
[1,2,3,4,5] => [5,4,3,2,1] => 10
[1,2,3,5,4] => [4,5,3,2,1] => 6
[1,2,4,3,5] => [5,3,4,2,1] => 6
[1,2,4,5,3] => [3,5,4,2,1] => 7
[1,2,5,3,4] => [4,3,5,2,1] => 6
[1,2,5,4,3] => [3,4,5,2,1] => 3
[1,3,2,4,5] => [5,4,2,3,1] => 7
[1,3,2,5,4] => [4,5,2,3,1] => 3
[1,3,4,2,5] => [5,2,4,3,1] => 6
[1,3,4,5,2] => [2,5,4,3,1] => 8
[1,3,5,2,4] => [4,2,5,3,1] => 6
[1,3,5,4,2] => [2,4,5,3,1] => 4
[1,4,2,3,5] => [5,3,2,4,1] => 6
[1,4,2,5,3] => [3,5,2,4,1] => 3
[1,4,3,2,5] => [5,2,3,4,1] => 3
[1,4,3,5,2] => [2,5,3,4,1] => 4
[1,4,5,2,3] => [3,2,5,4,1] => 7
[1,4,5,3,2] => [2,3,5,4,1] => 5
[1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => ? = 21
[1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => ? = 15
[1,2,3,4,6,5,7] => [7,5,6,4,3,2,1] => ? = 15
[1,2,3,4,6,7,5] => [5,7,6,4,3,2,1] => ? = 16
[1,2,3,4,7,5,6] => [6,5,7,4,3,2,1] => ? = 15
[1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => ? = 10
[1,2,3,5,4,6,7] => [7,6,4,5,3,2,1] => ? = 16
[1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => ? = 10
[1,2,3,5,6,4,7] => [7,4,6,5,3,2,1] => ? = 15
[1,2,3,5,6,7,4] => [4,7,6,5,3,2,1] => ? = 17
[1,2,3,5,7,4,6] => [6,4,7,5,3,2,1] => ? = 15
[1,2,3,5,7,6,4] => [4,6,7,5,3,2,1] => ? = 11
[1,2,3,6,4,5,7] => [7,5,4,6,3,2,1] => ? = 15
[1,2,3,6,4,7,5] => [5,7,4,6,3,2,1] => ? = 10
[1,2,3,6,5,4,7] => [7,4,5,6,3,2,1] => ? = 10
[1,2,3,6,5,7,4] => [4,7,5,6,3,2,1] => ? = 11
[1,2,3,6,7,4,5] => [5,4,7,6,3,2,1] => ? = 16
[1,2,3,6,7,5,4] => [4,5,7,6,3,2,1] => ? = 12
[1,2,3,7,4,5,6] => [6,5,4,7,3,2,1] => ? = 15
[1,2,3,7,4,6,5] => [5,6,4,7,3,2,1] => ? = 10
[1,2,3,7,5,4,6] => [6,4,5,7,3,2,1] => ? = 10
[1,2,3,7,5,6,4] => [4,6,5,7,3,2,1] => ? = 11
[1,2,3,7,6,4,5] => [5,4,6,7,3,2,1] => ? = 10
[1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => ? = 6
[1,2,4,3,5,6,7] => [7,6,5,3,4,2,1] => ? = 17
[1,2,4,3,5,7,6] => [6,7,5,3,4,2,1] => ? = 11
[1,2,4,3,6,5,7] => [7,5,6,3,4,2,1] => ? = 11
[1,2,4,3,6,7,5] => [5,7,6,3,4,2,1] => ? = 12
[1,2,4,3,7,5,6] => [6,5,7,3,4,2,1] => ? = 11
[1,2,4,3,7,6,5] => [5,6,7,3,4,2,1] => ? = 6
[1,2,4,5,3,6,7] => [7,6,3,5,4,2,1] => ? = 16
[1,2,4,5,3,7,6] => [6,7,3,5,4,2,1] => ? = 10
[1,2,4,5,6,3,7] => [7,3,6,5,4,2,1] => ? = 15
[1,2,4,5,6,7,3] => [3,7,6,5,4,2,1] => ? = 18
[1,2,4,5,7,3,6] => [6,3,7,5,4,2,1] => ? = 15
[1,2,4,5,7,6,3] => [3,6,7,5,4,2,1] => ? = 12
[1,2,4,6,3,5,7] => [7,5,3,6,4,2,1] => ? = 15
[1,2,4,6,3,7,5] => [5,7,3,6,4,2,1] => ? = 10
[1,2,4,6,5,3,7] => [7,3,5,6,4,2,1] => ? = 10
[1,2,4,6,5,7,3] => [3,7,5,6,4,2,1] => ? = 12
[1,2,4,6,7,3,5] => [5,3,7,6,4,2,1] => ? = 16
[1,2,4,6,7,5,3] => [3,5,7,6,4,2,1] => ? = 13
[1,2,4,7,3,5,6] => [6,5,3,7,4,2,1] => ? = 15
[1,2,4,7,3,6,5] => [5,6,3,7,4,2,1] => ? = 10
[1,2,4,7,5,3,6] => [6,3,5,7,4,2,1] => ? = 10
[1,2,4,7,5,6,3] => [3,6,5,7,4,2,1] => ? = 12
[1,2,4,7,6,3,5] => [5,3,6,7,4,2,1] => ? = 10
[1,2,4,7,6,5,3] => [3,5,6,7,4,2,1] => ? = 7
[1,2,5,3,4,6,7] => [7,6,4,3,5,2,1] => ? = 16
[1,2,5,3,4,7,6] => [6,7,4,3,5,2,1] => ? = 10
Description
The sum of the descent bottoms of a permutation. This statistic is given by $$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} \pi_{i+1}.$$ For the descent tops, see [[St000111]].