Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001382
(load all 2 compositions to match this statistic)
Mapping
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001382: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,1]
 => [1]
 => 0
[1,2,3] => [1,1,1]
 => [1,1]
 => 1
[1,3,2] => [2,1]
 => [1]
 => 0
[2,1,3] => [2,1]
 => [1]
 => 0
[3,2,1] => [2,1]
 => [1]
 => 0
[1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 2
[1,2,4,3] => [2,1,1]
 => [1,1]
 => 1
[1,3,2,4] => [2,1,1]
 => [1,1]
 => 1
[1,3,4,2] => [3,1]
 => [1]
 => 0
[1,4,2,3] => [3,1]
 => [1]
 => 0
[1,4,3,2] => [2,1,1]
 => [1,1]
 => 1
[2,1,3,4] => [2,1,1]
 => [1,1]
 => 1
[2,1,4,3] => [2,2]
 => [2]
 => 1
[2,3,1,4] => [3,1]
 => [1]
 => 0
[2,4,3,1] => [3,1]
 => [1]
 => 0
[3,1,2,4] => [3,1]
 => [1]
 => 0
[3,2,1,4] => [2,1,1]
 => [1,1]
 => 1
[3,2,4,1] => [3,1]
 => [1]
 => 0
[3,4,1,2] => [2,2]
 => [2]
 => 1
[4,1,3,2] => [3,1]
 => [1]
 => 0
[4,2,1,3] => [3,1]
 => [1]
 => 0
[4,2,3,1] => [2,1,1]
 => [1,1]
 => 1
[4,3,2,1] => [2,2]
 => [2]
 => 1
[1,2,3,4,5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 3
[1,2,3,5,4] => [2,1,1,1]
 => [1,1,1]
 => 2
[1,2,4,3,5] => [2,1,1,1]
 => [1,1,1]
 => 2
[1,2,4,5,3] => [3,1,1]
 => [1,1]
 => 1
[1,2,5,3,4] => [3,1,1]
 => [1,1]
 => 1
[1,2,5,4,3] => [2,1,1,1]
 => [1,1,1]
 => 2
[1,3,2,4,5] => [2,1,1,1]
 => [1,1,1]
 => 2
[1,3,2,5,4] => [2,2,1]
 => [2,1]
 => 2
[1,3,4,2,5] => [3,1,1]
 => [1,1]
 => 1
[1,3,4,5,2] => [4,1]
 => [1]
 => 0
[1,3,5,2,4] => [4,1]
 => [1]
 => 0
[1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 1
[1,4,2,3,5] => [3,1,1]
 => [1,1]
 => 1
[1,4,2,5,3] => [4,1]
 => [1]
 => 0
[1,4,3,2,5] => [2,1,1,1]
 => [1,1,1]
 => 2
[1,4,3,5,2] => [3,1,1]
 => [1,1]
 => 1
[1,4,5,2,3] => [2,2,1]
 => [2,1]
 => 2
[1,4,5,3,2] => [4,1]
 => [1]
 => 0
[1,5,2,3,4] => [4,1]
 => [1]
 => 0
[1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 1
[1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 1
[1,5,3,4,2] => [2,1,1,1]
 => [1,1,1]
 => 2
[1,5,4,2,3] => [4,1]
 => [1]
 => 0
[1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 2
[2,1,3,4,5] => [2,1,1,1]
 => [1,1,1]
 => 2
[2,1,3,5,4] => [2,2,1]
 => [2,1]
 => 2
[2,1,4,3,5] => [2,2,1]
 => [2,1]
 => 2
Description
The number of boxes in the diagram of a partition that do not lie in its Durfee square.
Matching statistic: St000921
(load all 3 compositions to match this statistic)
Mapping
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000921: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,1]
 => [1]
 => 10 => 0
[1,2,3] => [1,1,1]
 => [1,1]
 => 110 => 1
[1,3,2] => [2,1]
 => [1]
 => 10 => 0
[2,1,3] => [2,1]
 => [1]
 => 10 => 0
[3,2,1] => [2,1]
 => [1]
 => 10 => 0
[1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1110 => 2
[1,2,4,3] => [2,1,1]
 => [1,1]
 => 110 => 1
[1,3,2,4] => [2,1,1]
 => [1,1]
 => 110 => 1
[1,3,4,2] => [3,1]
 => [1]
 => 10 => 0
[1,4,2,3] => [3,1]
 => [1]
 => 10 => 0
[1,4,3,2] => [2,1,1]
 => [1,1]
 => 110 => 1
[2,1,3,4] => [2,1,1]
 => [1,1]
 => 110 => 1
[2,1,4,3] => [2,2]
 => [2]
 => 100 => 1
[2,3,1,4] => [3,1]
 => [1]
 => 10 => 0
[2,4,3,1] => [3,1]
 => [1]
 => 10 => 0
[3,1,2,4] => [3,1]
 => [1]
 => 10 => 0
[3,2,1,4] => [2,1,1]
 => [1,1]
 => 110 => 1
[3,2,4,1] => [3,1]
 => [1]
 => 10 => 0
[3,4,1,2] => [2,2]
 => [2]
 => 100 => 1
[4,1,3,2] => [3,1]
 => [1]
 => 10 => 0
[4,2,1,3] => [3,1]
 => [1]
 => 10 => 0
[4,2,3,1] => [2,1,1]
 => [1,1]
 => 110 => 1
[4,3,2,1] => [2,2]
 => [2]
 => 100 => 1
[1,2,3,4,5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 11110 => 3
[1,2,3,5,4] => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
[1,2,4,3,5] => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
[1,2,4,5,3] => [3,1,1]
 => [1,1]
 => 110 => 1
[1,2,5,3,4] => [3,1,1]
 => [1,1]
 => 110 => 1
[1,2,5,4,3] => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
[1,3,2,4,5] => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
[1,3,2,5,4] => [2,2,1]
 => [2,1]
 => 1010 => 2
[1,3,4,2,5] => [3,1,1]
 => [1,1]
 => 110 => 1
[1,3,4,5,2] => [4,1]
 => [1]
 => 10 => 0
[1,3,5,2,4] => [4,1]
 => [1]
 => 10 => 0
[1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 110 => 1
[1,4,2,3,5] => [3,1,1]
 => [1,1]
 => 110 => 1
[1,4,2,5,3] => [4,1]
 => [1]
 => 10 => 0
[1,4,3,2,5] => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
[1,4,3,5,2] => [3,1,1]
 => [1,1]
 => 110 => 1
[1,4,5,2,3] => [2,2,1]
 => [2,1]
 => 1010 => 2
[1,4,5,3,2] => [4,1]
 => [1]
 => 10 => 0
[1,5,2,3,4] => [4,1]
 => [1]
 => 10 => 0
[1,5,2,4,3] => [3,1,1]
 => [1,1]
 => 110 => 1
[1,5,3,2,4] => [3,1,1]
 => [1,1]
 => 110 => 1
[1,5,3,4,2] => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
[1,5,4,2,3] => [4,1]
 => [1]
 => 10 => 0
[1,5,4,3,2] => [2,2,1]
 => [2,1]
 => 1010 => 2
[2,1,3,4,5] => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
[2,1,3,5,4] => [2,2,1]
 => [2,1]
 => 1010 => 2
[2,1,4,3,5] => [2,2,1]
 => [2,1]
 => 1010 => 2
Description
The number of internal inversions of a binary word. Let $\bar w$ be the non-decreasing rearrangement of $w$, that is, $\bar w$ is sorted. An internal inversion is a pair $i < j$ such that $w_i > w_j$ and $\bar w_i = \bar w_j$. For example, the word $110$ has two inversions, but only the second is internal.
Matching statistic: St001232
(load all 2 compositions to match this statistic)
Mapping
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 22% ●values known / values provided: 22%●distinct values known / distinct values provided: 60%
Values
[1,2] => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1 = 0 + 1
[1,2,3] => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ? = 1 + 1
[1,3,2] => [2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[2,1,3] => [2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[3,2,1] => [2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[1,2,3,4] => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2 + 1
[1,2,4,3] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 1 + 1
[1,3,2,4] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 1 + 1
[1,3,4,2] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[1,4,2,3] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[1,4,3,2] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 1 + 1
[2,1,3,4] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 1 + 1
[2,1,4,3] => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2 = 1 + 1
[2,3,1,4] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[2,4,3,1] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[3,1,2,4] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[3,2,1,4] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 1 + 1
[3,2,4,1] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[3,4,1,2] => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2 = 1 + 1
[4,1,3,2] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[4,2,1,3] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[4,2,3,1] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 1 + 1
[4,3,2,1] => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2 = 1 + 1
[1,2,3,4,5] => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 1
[1,2,3,5,4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
[1,2,4,3,5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
[1,2,4,5,3] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[1,2,5,3,4] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[1,2,5,4,3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
[1,3,2,4,5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
[1,3,2,5,4] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[1,3,4,2,5] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[1,3,4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[1,3,5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[1,3,5,4,2] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[1,4,2,3,5] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[1,4,2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[1,4,3,2,5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
[1,4,3,5,2] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[1,4,5,2,3] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[1,4,5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[1,5,2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[1,5,2,4,3] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[1,5,3,2,4] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[1,5,3,4,2] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
[1,5,4,2,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[1,5,4,3,2] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[2,1,3,4,5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
[2,1,3,5,4] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[2,1,4,3,5] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[2,1,4,5,3] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[2,1,5,3,4] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[2,1,5,4,3] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[2,3,1,4,5] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[2,3,1,5,4] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[2,3,4,1,5] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[2,3,5,4,1] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[2,4,1,3,5] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[2,4,3,1,5] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[2,4,3,5,1] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[2,4,5,1,3] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[2,5,1,4,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[2,5,3,1,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[2,5,3,4,1] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[2,5,4,3,1] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[3,1,2,4,5] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[3,1,2,5,4] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[3,1,4,2,5] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[3,1,5,4,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[3,2,1,4,5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
[3,2,1,5,4] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[3,2,4,1,5] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[3,2,4,5,1] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[3,2,5,1,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[3,2,5,4,1] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[3,4,1,2,5] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[3,4,1,5,2] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[3,4,2,1,5] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[3,4,5,2,1] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[3,5,1,2,4] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[3,5,1,4,2] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[3,5,2,4,1] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[3,5,4,1,2] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[4,1,2,3,5] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[4,1,3,2,5] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[4,1,3,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[4,1,5,2,3] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[4,2,1,3,5] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[4,2,1,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[4,2,3,1,5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
[4,2,3,5,1] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[4,2,5,1,3] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[4,2,5,3,1] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[4,3,1,2,5] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[4,3,2,1,5] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[4,3,2,5,1] => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2 = 1 + 1
[4,5,3,1,2] => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2 + 1
[5,1,3,4,2] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[5,2,1,4,3] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
[5,2,3,1,4] => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1 + 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.