Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001024
Mapping
Mp00182: Skew partitions —outer shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00142: Dyck paths —promotion⟶ Dyck paths
St001024: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 1
[[2],[]]
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,1,0,0,0]
 => 1
[[1,1],[]]
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[[2,1],[1]]
 => [2,1]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => 2
[[3],[]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 1
[[2,1],[]]
 => [2,1]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => 2
[[3,1],[1]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 2
[[2,2],[1]]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[[3,2],[2]]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => 1
[[1,1,1],[]]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,0,0]
 => 1
[[2,2,1],[1,1]]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 3
[[2,1,1],[1]]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
[[3,2,1],[2,1]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 2
[[4],[]]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 1
[[3,1],[]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 2
[[4,1],[1]]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 2
[[2,2],[]]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[[3,2],[1]]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => 1
[[4,2],[2]]
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 1
[[2,1,1],[]]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
[[3,2,1],[1,1]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 2
[[3,1,1],[1]]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => 2
[[4,2,1],[2,1]]
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 2
[[3,3],[2]]
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[[4,3],[3]]
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 1
[[2,2,1],[1]]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 3
[[3,3,1],[2,1]]
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 3
[[3,2,1],[2]]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 2
[[4,3,1],[3,1]]
 => [4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => 2
[[2,2,2],[1,1]]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1
[[3,3,2],[2,2]]
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => 1
[[3,2,2],[2,1]]
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => 2
[[4,3,2],[3,2]]
 => [4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
[[1,1,1,1],[]]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 1
[[2,2,2,1],[1,1,1]]
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => 3
[[2,2,1,1],[1,1]]
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => 2
[[3,3,2,1],[2,2,1]]
 => [3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 3
[[2,1,1,1],[1]]
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => 2
[[3,2,2,1],[2,1,1]]
 => [3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 4
[[3,2,1,1],[2,1]]
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 3
[[4,3,2,1],[3,2,1]]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3
[[5],[]]
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 1
[[4,1],[]]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 2
[[5,1],[1]]
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 2
[[3,2],[]]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => 1
[[4,2],[1]]
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 1
[[5,2],[2]]
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 1
[[3,1,1],[]]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => 2
[[4,2,1],[1,1]]
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 2
[[4,1,1],[1]]
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 2
Description
Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path.