Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000770
Mapping
Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000770: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[1],[1],[1]]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1],[1],[1],[1],[1]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[2],[1],[1],[1]]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1,1],[1],[1],[1]]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1],[1],[1],[1],[1],[1]]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1
[[2],[1],[1],[1],[1]]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[2],[2],[1],[1]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[2],[2],[2]]
 => [2,2,2]
 => [2,2]
 => [2]
 => 2
[[1,1],[1],[1],[1],[1]]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,1],[1,1],[1],[1]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[1,1],[1,1],[1,1]]
 => [2,2,2]
 => [2,2]
 => [2]
 => 2
[[3],[1],[1],[1]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1],[1],[1],[1]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1,1,1],[1],[1],[1]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1],[1],[1],[1],[1],[1],[1]]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
[[2],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1
[[2],[2],[1],[1],[1]]
 => [2,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 1
[[2],[2],[2],[1]]
 => [2,2,2,1]
 => [2,2,1]
 => [2,1]
 => 4
[[1,1],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1
[[1,1],[1,1],[1],[1],[1]]
 => [2,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 1
[[1,1],[1,1],[1,1],[1]]
 => [2,2,2,1]
 => [2,2,1]
 => [2,1]
 => 4
[[3],[1],[1],[1],[1]]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[3],[2],[1],[1]]
 => [3,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[3],[2],[2]]
 => [3,2,2]
 => [2,2]
 => [2]
 => 2
[[2,1],[1],[1],[1],[1]]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[2,1],[2],[1],[1]]
 => [3,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[2,1],[2],[2]]
 => [3,2,2]
 => [2,2]
 => [2]
 => 2
[[2,1],[1,1],[1],[1]]
 => [3,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[2,1],[1,1],[1,1]]
 => [3,2,2]
 => [2,2]
 => [2]
 => 2
[[1,1,1],[1],[1],[1],[1]]
 => [3,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,1,1],[1,1],[1],[1]]
 => [3,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
[[1,1,1],[1,1],[1,1]]
 => [3,2,2]
 => [2,2]
 => [2]
 => 2
[[4],[1],[1],[1]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[3,1],[1],[1],[1]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[2,2],[1],[1],[1]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,1],[1],[1],[1]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1,1,1,1],[1],[1],[1]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
[[1],[1],[1],[1],[1],[1],[1],[1]]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 1
[[2],[1],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
[[2],[2],[1],[1],[1],[1]]
 => [2,2,1,1,1,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 1
[[2],[2],[2],[1],[1]]
 => [2,2,2,1,1]
 => [2,2,1,1]
 => [2,1,1]
 => 5
[[2],[2],[2],[2]]
 => [2,2,2,2]
 => [2,2,2]
 => [2,2]
 => 2
[[1,1],[1],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
[[1,1],[1,1],[1],[1],[1],[1]]
 => [2,2,1,1,1,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 1
[[1,1],[1,1],[1,1],[1],[1]]
 => [2,2,2,1,1]
 => [2,2,1,1]
 => [2,1,1]
 => 5
[[1,1],[1,1],[1,1],[1,1]]
 => [2,2,2,2]
 => [2,2,2]
 => [2,2]
 => 2
[[3],[1],[1],[1],[1],[1]]
 => [3,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1
[[3],[2],[1],[1],[1]]
 => [3,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 1
[[3],[2],[2],[1]]
 => [3,2,2,1]
 => [2,2,1]
 => [2,1]
 => 4
[[3],[3],[1],[1]]
 => [3,3,1,1]
 => [3,1,1]
 => [1,1]
 => 1
Description
The major index of an integer partition when read from bottom to top. This is the sum of the positions of the corners of the shape of an integer partition when reading from bottom to top. For example, the partition $\lambda = (8,6,6,4,3,3)$ has corners at positions 3,6,9, and 13, giving a major index of 31.
Matching statistic: St001232
Mapping
Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 29%
Values
[[1],[1],[1],[1]]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1],[1],[1],[1],[1]]
 => [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]
 => ? = 1 + 1
[[2],[1],[1],[1]]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1,1],[1],[1],[1]]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1],[1],[1],[1],[1],[1]]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2],[1],[1],[1],[1]]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2],[2],[1],[1]]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1 + 1
[[2],[2],[2]]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3 = 2 + 1
[[1,1],[1],[1],[1],[1]]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1,1],[1,1],[1],[1]]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1 + 1
[[1,1],[1,1],[1,1]]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3 = 2 + 1
[[3],[1],[1],[1]]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2,1],[1],[1],[1]]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1,1,1],[1],[1],[1]]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1],[1],[1],[1],[1],[1],[1]]
 => [1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2],[2],[1],[1],[1]]
 => [2,2,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2],[2],[2],[1]]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 4 + 1
[[1,1],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1,1],[1,1],[1],[1],[1]]
 => [2,2,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1,1],[1,1],[1,1],[1]]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 4 + 1
[[3],[1],[1],[1],[1]]
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[3],[2],[1],[1]]
 => [3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => ? = 1 + 1
[[3],[2],[2]]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3 = 2 + 1
[[2,1],[1],[1],[1],[1]]
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2,1],[2],[1],[1]]
 => [3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => ? = 1 + 1
[[2,1],[2],[2]]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3 = 2 + 1
[[2,1],[1,1],[1],[1]]
 => [3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => ? = 1 + 1
[[2,1],[1,1],[1,1]]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3 = 2 + 1
[[1,1,1],[1],[1],[1],[1]]
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1,1,1],[1,1],[1],[1]]
 => [3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => ? = 1 + 1
[[1,1,1],[1,1],[1,1]]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3 = 2 + 1
[[4],[1],[1],[1]]
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[3,1],[1],[1],[1]]
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2,2],[1],[1],[1]]
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2,1,1],[1],[1],[1]]
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1,1,1,1],[1],[1],[1]]
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1],[1],[1],[1],[1],[1],[1],[1]]
 => [1,1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2],[1],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2],[2],[1],[1],[1],[1]]
 => [2,2,1,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2],[2],[2],[1],[1]]
 => [2,2,2,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => ? = 5 + 1
[[2],[2],[2],[2]]
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 2 + 1
[[1,1],[1],[1],[1],[1],[1],[1]]
 => [2,1,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1,1],[1,1],[1],[1],[1],[1]]
 => [2,2,1,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[1,1],[1,1],[1,1],[1],[1]]
 => [2,2,2,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => ? = 5 + 1
[[1,1],[1,1],[1,1],[1,1]]
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 2 + 1
[[3],[1],[1],[1],[1],[1]]
 => [3,1,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[3],[2],[1],[1],[1]]
 => [3,2,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[3],[2],[2],[1]]
 => [3,2,2,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => ? = 4 + 1
[[3],[3],[1],[1]]
 => [3,3,1,1]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 1 + 1
[[3],[3],[2]]
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? = 2 + 1
[[2,1],[1],[1],[1],[1],[1]]
 => [3,1,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2,1],[2],[1],[1],[1]]
 => [3,2,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2,1],[2],[2],[1]]
 => [3,2,2,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => ? = 4 + 1
[[2,1],[1,1],[1],[1],[1]]
 => [3,2,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[[2,1],[1,1],[1,1],[1]]
 => [3,2,2,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => ? = 4 + 1
[[4],[2],[2]]
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[3,1],[2],[2]]
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[3,1],[1,1],[1,1]]
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[2,2],[2],[2]]
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[2,2],[1,1],[1,1]]
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[2,1,1],[2],[2]]
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[2,1,1],[1,1],[1,1]]
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[1,1,1,1],[1,1],[1,1]]
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[3],[3],[3]]
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[[2,1],[2,1],[2,1]]
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[[1,1,1],[1,1,1],[1,1,1]]
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[[5],[2],[2]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[4,1],[2],[2]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[4,1],[1,1],[1,1]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[3,2],[2],[2]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[3,2],[1,1],[1,1]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[3,1,1],[2],[2]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[3,1,1],[1,1],[1,1]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[2,2,1],[2],[2]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[2,2,1],[1,1],[1,1]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[2,1,1,1],[2],[2]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[2,1,1,1],[1,1],[1,1]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[1,1,1,1,1],[1,1],[1,1]]
 => [5,2,2]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3 = 2 + 1
[[4],[3],[3]]
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4 = 3 + 1
[[3,1],[3],[3]]
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4 = 3 + 1
[[3,1],[2,1],[2,1]]
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4 = 3 + 1
[[2,2],[2,1],[2,1]]
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4 = 3 + 1
[[2,1,1],[2,1],[2,1]]
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4 = 3 + 1
[[2,1,1],[1,1,1],[1,1,1]]
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4 = 3 + 1
[[1,1,1,1],[1,1,1],[1,1,1]]
 => [4,3,3]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4 = 3 + 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.