Your data matches 36 different statistics following compositions of up to 3 maps.
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Matching statistic: St000074
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Mapping
St000074: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,0],[0]]
 => 0
[[1,0],[1]]
 => 0
[[2,0],[0]]
 => 0
[[2,0],[1]]
 => 1
[[2,0],[2]]
 => 0
[[1,1],[1]]
 => 0
[[1,0,0],[0,0],[0]]
 => 0
[[1,0,0],[1,0],[0]]
 => 0
[[1,0,0],[1,0],[1]]
 => 0
[[3,0],[0]]
 => 0
[[3,0],[1]]
 => 1
[[3,0],[2]]
 => 1
[[3,0],[3]]
 => 0
[[2,1],[1]]
 => 0
[[2,1],[2]]
 => 0
[[2,0,0],[0,0],[0]]
 => 0
[[2,0,0],[1,0],[0]]
 => 1
[[2,0,0],[1,0],[1]]
 => 1
[[2,0,0],[2,0],[0]]
 => 0
[[2,0,0],[2,0],[1]]
 => 1
[[2,0,0],[2,0],[2]]
 => 0
[[1,1,0],[1,0],[0]]
 => 0
[[1,1,0],[1,0],[1]]
 => 0
[[1,1,0],[1,1],[1]]
 => 0
[[1,0,0,0],[0,0,0],[0,0],[0]]
 => 0
[[1,0,0,0],[1,0,0],[0,0],[0]]
 => 0
[[1,0,0,0],[1,0,0],[1,0],[0]]
 => 0
[[1,0,0,0],[1,0,0],[1,0],[1]]
 => 0
[[4,0],[0]]
 => 0
[[4,0],[1]]
 => 1
[[4,0],[2]]
 => 1
[[4,0],[3]]
 => 1
[[4,0],[4]]
 => 0
[[3,1],[1]]
 => 0
[[3,1],[2]]
 => 1
[[3,1],[3]]
 => 0
[[2,2],[2]]
 => 0
[[3,0,0],[0,0],[0]]
 => 0
[[3,0,0],[1,0],[0]]
 => 1
[[3,0,0],[1,0],[1]]
 => 1
[[3,0,0],[2,0],[0]]
 => 1
[[3,0,0],[2,0],[1]]
 => 2
[[3,0,0],[2,0],[2]]
 => 1
[[3,0,0],[3,0],[0]]
 => 0
[[3,0,0],[3,0],[1]]
 => 1
[[3,0,0],[3,0],[2]]
 => 1
[[3,0,0],[3,0],[3]]
 => 0
[[2,1,0],[1,0],[0]]
 => 0
[[2,1,0],[1,0],[1]]
 => 0
[[2,1,0],[1,1],[1]]
 => 0
Description
The number of special entries. An entry $a_{i,j}$ of a Gelfand-Tsetlin pattern is special if $a_{i-1,j-i} > a_{i,j} > a_{i-1,j}$. That is, it is neither boxed nor circled.
Matching statistic: St001232
Mapping
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00077: Semistandard tableaux —shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 70% ●values known / values provided: 70%●distinct values known / distinct values provided: 100%
Values
[[1,0],[0]]
 => [[2]]
 => [1]
 => [1,0,1,0]
 => 1 = 0 + 1
[[1,0],[1]]
 => [[1]]
 => [1]
 => [1,0,1,0]
 => 1 = 0 + 1
[[2,0],[0]]
 => [[2,2]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0],[1]]
 => [[1,2]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0],[2]]
 => [[1,1]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[1,1],[1]]
 => [[1],[2]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 2 = 1 + 1
[[1,0,0],[0,0],[0]]
 => [[3]]
 => [1]
 => [1,0,1,0]
 => 1 = 0 + 1
[[1,0,0],[1,0],[0]]
 => [[2]]
 => [1]
 => [1,0,1,0]
 => 1 = 0 + 1
[[1,0,0],[1,0],[1]]
 => [[1]]
 => [1]
 => [1,0,1,0]
 => 1 = 0 + 1
[[3,0],[0]]
 => [[2,2,2]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0],[1]]
 => [[1,2,2]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0],[2]]
 => [[1,1,2]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0],[3]]
 => [[1,1,1]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[2,1],[1]]
 => [[1,2],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {1,1} + 1
[[2,1],[2]]
 => [[1,1],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {1,1} + 1
[[2,0,0],[0,0],[0]]
 => [[3,3]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0,0],[1,0],[0]]
 => [[2,3]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0,0],[1,0],[1]]
 => [[1,3]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0,0],[2,0],[0]]
 => [[2,2]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0,0],[2,0],[1]]
 => [[1,2]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0,0],[2,0],[2]]
 => [[1,1]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 2 = 1 + 1
[[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 2 = 1 + 1
[[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => [1,1]
 => [1,0,1,1,0,0]
 => 2 = 1 + 1
[[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => [1]
 => [1,0,1,0]
 => 1 = 0 + 1
[[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => [1]
 => [1,0,1,0]
 => 1 = 0 + 1
[[1,0,0,0],[1,0,0],[1,0],[0]]
 => [[2]]
 => [1]
 => [1,0,1,0]
 => 1 = 0 + 1
[[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => [1]
 => [1,0,1,0]
 => 1 = 0 + 1
[[4,0],[0]]
 => [[2,2,2,2]]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[[4,0],[1]]
 => [[1,2,2,2]]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[[4,0],[2]]
 => [[1,1,2,2]]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[[4,0],[3]]
 => [[1,1,1,2]]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[[4,0],[4]]
 => [[1,1,1,1]]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1 = 0 + 1
[[3,1],[1]]
 => [[1,2,2],[2]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {1,1,1} + 1
[[3,1],[2]]
 => [[1,1,2],[2]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {1,1,1} + 1
[[3,1],[3]]
 => [[1,1,1],[2]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {1,1,1} + 1
[[2,2],[2]]
 => [[1,1],[2,2]]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => 2 = 1 + 1
[[3,0,0],[0,0],[0]]
 => [[3,3,3]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0,0],[1,0],[0]]
 => [[2,3,3]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0,0],[1,0],[1]]
 => [[1,3,3]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0,0],[2,0],[0]]
 => [[2,2,3]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0,0],[2,0],[2]]
 => [[1,1,3]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0,0],[3,0],[0]]
 => [[2,2,2]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0,0],[3,0],[1]]
 => [[1,2,2]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0,0],[3,0],[2]]
 => [[1,1,2]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 1 = 0 + 1
[[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1} + 1
[[2,1,0],[1,0],[1]]
 => [[1,3],[3]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1} + 1
[[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1} + 1
[[2,1,0],[2,0],[0]]
 => [[2,2],[3]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1} + 1
[[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1} + 1
[[2,1,0],[2,0],[2]]
 => [[1,1],[3]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1} + 1
[[2,1,0],[2,1],[1]]
 => [[1,2],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1} + 1
[[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1} + 1
[[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 3 = 2 + 1
[[2,0,0,0],[0,0,0],[0,0],[0]]
 => [[4,4]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0,0,0],[1,0,0],[0,0],[0]]
 => [[3,4]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0,0,0],[1,0,0],[1,0],[0]]
 => [[2,4]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0,0,0],[1,0,0],[1,0],[1]]
 => [[1,4]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0,0,0],[2,0,0],[0,0],[0]]
 => [[3,3]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0,0,0],[2,0,0],[1,0],[0]]
 => [[2,3]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[2,0,0,0],[2,0,0],[1,0],[1]]
 => [[1,3]]
 => [2]
 => [1,1,0,0,1,0]
 => 1 = 0 + 1
[[4,1],[1]]
 => [[1,2,2,2],[2]]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? ∊ {1,1,1,1,1,1} + 1
[[4,1],[2]]
 => [[1,1,2,2],[2]]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? ∊ {1,1,1,1,1,1} + 1
[[4,1],[3]]
 => [[1,1,1,2],[2]]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? ∊ {1,1,1,1,1,1} + 1
[[4,1],[4]]
 => [[1,1,1,1],[2]]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? ∊ {1,1,1,1,1,1} + 1
[[3,2],[2]]
 => [[1,1,2],[2,2]]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => ? ∊ {1,1,1,1,1,1} + 1
[[3,2],[3]]
 => [[1,1,1],[2,2]]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => ? ∊ {1,1,1,1,1,1} + 1
[[3,1,0],[1,0],[0]]
 => [[2,3,3],[3]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[1,0],[1]]
 => [[1,3,3],[3]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[1,1],[1]]
 => [[1,3,3],[2]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[2,0],[0]]
 => [[2,2,3],[3]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[2,0],[1]]
 => [[1,2,3],[3]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[2,0],[2]]
 => [[1,1,3],[3]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[2,1],[1]]
 => [[1,2,3],[2]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[2,1],[2]]
 => [[1,1,3],[2]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[3,0],[0]]
 => [[2,2,2],[3]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[3,0],[1]]
 => [[1,2,2],[3]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[3,0],[2]]
 => [[1,1,2],[3]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[3,0],[3]]
 => [[1,1,1],[3]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[3,1],[1]]
 => [[1,2,2],[2]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[3,1],[2]]
 => [[1,1,2],[2]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[3,1,0],[3,1],[3]]
 => [[1,1,1],[2]]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[2,1,1],[1,1],[1]]
 => [[1,3],[2],[3]]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[2,1,1],[2,1],[1]]
 => [[1,2],[2],[3]]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[2,1,1],[2,1],[2]]
 => [[1,1],[2],[3]]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => ? ∊ {0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2} + 1
[[2,1,0,0],[1,0,0],[0,0],[0]]
 => [[3,4],[4]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[1,0,0],[1,0],[0]]
 => [[2,4],[4]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[1,0,0],[1,0],[1]]
 => [[1,4],[4]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[1,1,0],[1,0],[0]]
 => [[2,4],[3]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[1,1,0],[1,0],[1]]
 => [[1,4],[3]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[1,1,0],[1,1],[1]]
 => [[1,4],[2]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[2,0,0],[0,0],[0]]
 => [[3,3],[4]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[2,0,0],[1,0],[0]]
 => [[2,3],[4]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[2,0,0],[1,0],[1]]
 => [[1,3],[4]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[2,0,0],[2,0],[0]]
 => [[2,2],[4]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[2,0,0],[2,0],[1]]
 => [[1,2],[4]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[2,0,0],[2,0],[2]]
 => [[1,1],[4]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
[[2,1,0,0],[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => [2,1]
 => [1,0,1,0,1,0]
 => ? ∊ {0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1} + 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001767
Mapping
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00077: Semistandard tableaux —shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001767: Integer partitions ⟶ ℤResult quality: 45% ●values known / values provided: 45%●distinct values known / distinct values provided: 67%
Values
[[1,0],[0]]
 => [[2]]
 => [1]
 => []
 => ? ∊ {0,0}
[[1,0],[1]]
 => [[1]]
 => [1]
 => []
 => ? ∊ {0,0}
[[2,0],[0]]
 => [[2,2]]
 => [2]
 => []
 => ? ∊ {0,0,1}
[[2,0],[1]]
 => [[1,2]]
 => [2]
 => []
 => ? ∊ {0,0,1}
[[2,0],[2]]
 => [[1,1]]
 => [2]
 => []
 => ? ∊ {0,0,1}
[[1,1],[1]]
 => [[1],[2]]
 => [1,1]
 => [1]
 => 0
[[1,0,0],[0,0],[0]]
 => [[3]]
 => [1]
 => []
 => ? ∊ {0,0,0}
[[1,0,0],[1,0],[0]]
 => [[2]]
 => [1]
 => []
 => ? ∊ {0,0,0}
[[1,0,0],[1,0],[1]]
 => [[1]]
 => [1]
 => []
 => ? ∊ {0,0,0}
[[3,0],[0]]
 => [[2,2,2]]
 => [3]
 => []
 => ? ∊ {0,0,1,1}
[[3,0],[1]]
 => [[1,2,2]]
 => [3]
 => []
 => ? ∊ {0,0,1,1}
[[3,0],[2]]
 => [[1,1,2]]
 => [3]
 => []
 => ? ∊ {0,0,1,1}
[[3,0],[3]]
 => [[1,1,1]]
 => [3]
 => []
 => ? ∊ {0,0,1,1}
[[2,1],[1]]
 => [[1,2],[2]]
 => [2,1]
 => [1]
 => 0
[[2,1],[2]]
 => [[1,1],[2]]
 => [2,1]
 => [1]
 => 0
[[2,0,0],[0,0],[0]]
 => [[3,3]]
 => [2]
 => []
 => ? ∊ {0,0,0,1,1,1}
[[2,0,0],[1,0],[0]]
 => [[2,3]]
 => [2]
 => []
 => ? ∊ {0,0,0,1,1,1}
[[2,0,0],[1,0],[1]]
 => [[1,3]]
 => [2]
 => []
 => ? ∊ {0,0,0,1,1,1}
[[2,0,0],[2,0],[0]]
 => [[2,2]]
 => [2]
 => []
 => ? ∊ {0,0,0,1,1,1}
[[2,0,0],[2,0],[1]]
 => [[1,2]]
 => [2]
 => []
 => ? ∊ {0,0,0,1,1,1}
[[2,0,0],[2,0],[2]]
 => [[1,1]]
 => [2]
 => []
 => ? ∊ {0,0,0,1,1,1}
[[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => [1,1]
 => [1]
 => 0
[[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => [1,1]
 => [1]
 => 0
[[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => [1,1]
 => [1]
 => 0
[[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[0]]
 => [[2]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[4,0],[0]]
 => [[2,2,2,2]]
 => [4]
 => []
 => ? ∊ {0,0,1,1,1}
[[4,0],[1]]
 => [[1,2,2,2]]
 => [4]
 => []
 => ? ∊ {0,0,1,1,1}
[[4,0],[2]]
 => [[1,1,2,2]]
 => [4]
 => []
 => ? ∊ {0,0,1,1,1}
[[4,0],[3]]
 => [[1,1,1,2]]
 => [4]
 => []
 => ? ∊ {0,0,1,1,1}
[[4,0],[4]]
 => [[1,1,1,1]]
 => [4]
 => []
 => ? ∊ {0,0,1,1,1}
[[3,1],[1]]
 => [[1,2,2],[2]]
 => [3,1]
 => [1]
 => 0
[[3,1],[2]]
 => [[1,1,2],[2]]
 => [3,1]
 => [1]
 => 0
[[3,1],[3]]
 => [[1,1,1],[2]]
 => [3,1]
 => [1]
 => 0
[[2,2],[2]]
 => [[1,1],[2,2]]
 => [2,2]
 => [2]
 => 1
[[3,0,0],[0,0],[0]]
 => [[3,3,3]]
 => [3]
 => []
 => ? ∊ {0,0,0,1,1,1,1,1,1,2}
[[3,0,0],[1,0],[0]]
 => [[2,3,3]]
 => [3]
 => []
 => ? ∊ {0,0,0,1,1,1,1,1,1,2}
[[3,0,0],[1,0],[1]]
 => [[1,3,3]]
 => [3]
 => []
 => ? ∊ {0,0,0,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[0]]
 => [[2,2,3]]
 => [3]
 => []
 => ? ∊ {0,0,0,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => [3]
 => []
 => ? ∊ {0,0,0,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[2]]
 => [[1,1,3]]
 => [3]
 => []
 => ? ∊ {0,0,0,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[0]]
 => [[2,2,2]]
 => [3]
 => []
 => ? ∊ {0,0,0,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[1]]
 => [[1,2,2]]
 => [3]
 => []
 => ? ∊ {0,0,0,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[2]]
 => [[1,1,2]]
 => [3]
 => []
 => ? ∊ {0,0,0,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => [3]
 => []
 => ? ∊ {0,0,0,1,1,1,1,1,1,2}
[[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => [2,1]
 => [1]
 => 0
[[2,1,0],[1,0],[1]]
 => [[1,3],[3]]
 => [2,1]
 => [1]
 => 0
[[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => [2,1]
 => [1]
 => 0
[[2,1,0],[2,0],[0]]
 => [[2,2],[3]]
 => [2,1]
 => [1]
 => 0
[[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => [2,1]
 => [1]
 => 0
[[2,1,0],[2,0],[2]]
 => [[1,1],[3]]
 => [2,1]
 => [1]
 => 0
[[2,1,0],[2,1],[1]]
 => [[1,2],[2]]
 => [2,1]
 => [1]
 => 0
[[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => [2,1]
 => [1]
 => 0
[[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,0,0,0],[0,0,0],[0,0],[0]]
 => [[4,4]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[0,0],[0]]
 => [[3,4]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[0]]
 => [[2,4]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[1]]
 => [[1,4]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[0,0],[0]]
 => [[3,3]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[0]]
 => [[2,3]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[1]]
 => [[1,3]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[0]]
 => [[2,2]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[1]]
 => [[1,2]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[2]]
 => [[1,1]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,0,0],[0,0],[0]]
 => [[3],[4]]
 => [1,1]
 => [1]
 => 0
[[1,1,0,0],[1,0,0],[1,0],[0]]
 => [[2],[4]]
 => [1,1]
 => [1]
 => 0
[[1,1,0,0],[1,0,0],[1,0],[1]]
 => [[1],[4]]
 => [1,1]
 => [1]
 => 0
[[1,1,0,0],[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => [1,1]
 => [1]
 => 0
[[1,1,0,0],[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => [1,1]
 => [1]
 => 0
[[1,1,0,0],[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => [1,1]
 => [1]
 => 0
[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
 => [[5]]
 => [1]
 => []
 => ? ∊ {0,0,0,0,0}
[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => [1]
 => []
 => ? ∊ {0,0,0,0,0}
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => [1]
 => []
 => ? ∊ {0,0,0,0,0}
[[4,1],[1]]
 => [[1,2,2,2],[2]]
 => [4,1]
 => [1]
 => 0
[[4,1],[2]]
 => [[1,1,2,2],[2]]
 => [4,1]
 => [1]
 => 0
[[4,1],[3]]
 => [[1,1,1,2],[2]]
 => [4,1]
 => [1]
 => 0
[[4,1],[4]]
 => [[1,1,1,1],[2]]
 => [4,1]
 => [1]
 => 0
[[3,2],[2]]
 => [[1,1,2],[2,2]]
 => [3,2]
 => [2]
 => 1
[[3,2],[3]]
 => [[1,1,1],[2,2]]
 => [3,2]
 => [2]
 => 1
[[3,1,0],[1,0],[0]]
 => [[2,3,3],[3]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[1,0],[1]]
 => [[1,3,3],[3]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[1,1],[1]]
 => [[1,3,3],[2]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[2,0],[0]]
 => [[2,2,3],[3]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[2,0],[1]]
 => [[1,2,3],[3]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[2,0],[2]]
 => [[1,1,3],[3]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[2,1],[1]]
 => [[1,2,3],[2]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[2,1],[2]]
 => [[1,1,3],[2]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[3,0],[0]]
 => [[2,2,2],[3]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[3,0],[1]]
 => [[1,2,2],[3]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[3,0],[2]]
 => [[1,1,2],[3]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[3,0],[3]]
 => [[1,1,1],[3]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[3,1],[1]]
 => [[1,2,2],[2]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[3,1],[2]]
 => [[1,1,2],[2]]
 => [3,1]
 => [1]
 => 0
[[3,1,0],[3,1],[3]]
 => [[1,1,1],[2]]
 => [3,1]
 => [1]
 => 0
[[2,2,0],[2,0],[0]]
 => [[2,2],[3,3]]
 => [2,2]
 => [2]
 => 1
[[2,2,0],[2,0],[1]]
 => [[1,2],[3,3]]
 => [2,2]
 => [2]
 => 1
[[2,2,0],[2,0],[2]]
 => [[1,1],[3,3]]
 => [2,2]
 => [2]
 => 1
[[2,2,0],[2,1],[1]]
 => [[1,2],[2,3]]
 => [2,2]
 => [2]
 => 1
Description
The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. Assign to each cell of the Ferrers diagram an arrow pointing north, east, south or west. Then compute for each cell the number of arrows pointing towards it, and take the minimum of those. This statistic is the maximal minimum that can be obtained by assigning arrows in any way.
Matching statistic: St000620
(load all 2 compositions to match this statistic)
Mapping
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000620: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 29%●distinct values known / distinct values provided: 67%
Values
[[1,0],[0]]
 => [[2]]
 => [1]
 => []
 => ? ∊ {0,0}
[[1,0],[1]]
 => [[1]]
 => [1]
 => []
 => ? ∊ {0,0}
[[2,0],[0]]
 => [[2,2]]
 => [2]
 => []
 => ? ∊ {0,0,0,1}
[[2,0],[1]]
 => [[1,2]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,1}
[[2,0],[2]]
 => [[1,1]]
 => [2]
 => []
 => ? ∊ {0,0,0,1}
[[1,1],[1]]
 => [[1],[2]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,1}
[[1,0,0],[0,0],[0]]
 => [[3]]
 => [1]
 => []
 => ? ∊ {0,0,0}
[[1,0,0],[1,0],[0]]
 => [[2]]
 => [1]
 => []
 => ? ∊ {0,0,0}
[[1,0,0],[1,0],[1]]
 => [[1]]
 => [1]
 => []
 => ? ∊ {0,0,0}
[[3,0],[0]]
 => [[2,2,2]]
 => [3]
 => []
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[1]]
 => [[1,2,2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[2]]
 => [[1,1,2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[3]]
 => [[1,1,1]]
 => [3]
 => []
 => ? ∊ {0,0,0,0,1,1}
[[2,1],[1]]
 => [[1,2],[2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,1,1}
[[2,1],[2]]
 => [[1,1],[2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,1,1}
[[2,0,0],[0,0],[0]]
 => [[3,3]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[2,0,0],[1,0],[0]]
 => [[2,3]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[2,0,0],[1,0],[1]]
 => [[1,3]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[2,0,0],[2,0],[0]]
 => [[2,2]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[2,0,0],[2,0],[1]]
 => [[1,2]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[2,0,0],[2,0],[2]]
 => [[1,1]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[0]]
 => [[2]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[4,0],[0]]
 => [[2,2,2,2]]
 => [4]
 => []
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[1]]
 => [[1,2,2,2]]
 => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[2]]
 => [[1,1,2,2]]
 => [2,2]
 => [2]
 => 0
[[4,0],[3]]
 => [[1,1,1,2]]
 => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[4]]
 => [[1,1,1,1]]
 => [4]
 => []
 => ? ∊ {0,0,1,1,1,1}
[[3,1],[1]]
 => [[1,2,2],[2]]
 => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[[3,1],[2]]
 => [[1,1,2],[2]]
 => [2,2]
 => [2]
 => 0
[[3,1],[3]]
 => [[1,1,1],[2]]
 => [3,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1}
[[2,2],[2]]
 => [[1,1],[2,2]]
 => [2,2]
 => [2]
 => 0
[[3,0,0],[0,0],[0]]
 => [[3,3,3]]
 => [3]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[3,0,0],[1,0],[0]]
 => [[2,3,3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[3,0,0],[1,0],[1]]
 => [[1,3,3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[3,0,0],[2,0],[0]]
 => [[2,2,3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => [1,1,1]
 => [1,1]
 => 1
[[3,0,0],[2,0],[2]]
 => [[1,1,3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[3,0,0],[3,0],[0]]
 => [[2,2,2]]
 => [3]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[3,0,0],[3,0],[1]]
 => [[1,2,2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[3,0,0],[3,0],[2]]
 => [[1,1,2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => [3]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[2,1,0],[1,0],[1]]
 => [[1,3],[3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,0],[2,0],[0]]
 => [[2,2],[3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,0],[2,0],[2]]
 => [[1,1],[3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[2,1,0],[2,1],[1]]
 => [[1,2],[2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,2}
[[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,0,0,0],[0,0,0],[0,0],[0]]
 => [[4,4]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[5,0],[2]]
 => [[1,1,2,2,2]]
 => [3,2]
 => [2]
 => 0
[[5,0],[3]]
 => [[1,1,1,2,2]]
 => [3,2]
 => [2]
 => 0
[[4,1],[2]]
 => [[1,1,2,2],[2]]
 => [3,2]
 => [2]
 => 0
[[4,1],[3]]
 => [[1,1,1,2],[2]]
 => [3,2]
 => [2]
 => 0
[[3,2],[2]]
 => [[1,1,2],[2,2]]
 => [3,2]
 => [2]
 => 0
[[3,2],[3]]
 => [[1,1,1],[2,2]]
 => [3,2]
 => [2]
 => 0
[[4,0,0],[2,0],[0]]
 => [[2,2,3,3]]
 => [2,2]
 => [2]
 => 0
[[4,0,0],[2,0],[1]]
 => [[1,2,3,3]]
 => [2,1,1]
 => [1,1]
 => 1
[[4,0,0],[2,0],[2]]
 => [[1,1,3,3]]
 => [2,2]
 => [2]
 => 0
[[4,0,0],[3,0],[1]]
 => [[1,2,2,3]]
 => [2,1,1]
 => [1,1]
 => 1
[[4,0,0],[3,0],[2]]
 => [[1,1,2,3]]
 => [2,1,1]
 => [1,1]
 => 1
[[4,0,0],[4,0],[2]]
 => [[1,1,2,2]]
 => [2,2]
 => [2]
 => 0
[[3,1,0],[1,1],[1]]
 => [[1,3,3],[2]]
 => [2,1,1]
 => [1,1]
 => 1
[[3,1,0],[2,0],[0]]
 => [[2,2,3],[3]]
 => [2,2]
 => [2]
 => 0
[[3,1,0],[2,0],[1]]
 => [[1,2,3],[3]]
 => [2,1,1]
 => [1,1]
 => 1
[[3,1,0],[2,0],[2]]
 => [[1,1,3],[3]]
 => [2,2]
 => [2]
 => 0
[[3,1,0],[2,1],[1]]
 => [[1,2,3],[2]]
 => [2,1,1]
 => [1,1]
 => 1
[[3,1,0],[2,1],[2]]
 => [[1,1,3],[2]]
 => [2,1,1]
 => [1,1]
 => 1
[[3,1,0],[3,0],[1]]
 => [[1,2,2],[3]]
 => [2,1,1]
 => [1,1]
 => 1
[[3,1,0],[3,0],[2]]
 => [[1,1,2],[3]]
 => [2,1,1]
 => [1,1]
 => 1
[[3,1,0],[3,1],[2]]
 => [[1,1,2],[2]]
 => [2,2]
 => [2]
 => 0
[[2,2,0],[2,0],[0]]
 => [[2,2],[3,3]]
 => [2,2]
 => [2]
 => 0
[[2,2,0],[2,0],[1]]
 => [[1,2],[3,3]]
 => [2,1,1]
 => [1,1]
 => 1
[[2,2,0],[2,0],[2]]
 => [[1,1],[3,3]]
 => [2,2]
 => [2]
 => 0
[[2,2,0],[2,1],[1]]
 => [[1,2],[2,3]]
 => [2,1,1]
 => [1,1]
 => 1
[[2,2,0],[2,1],[2]]
 => [[1,1],[2,3]]
 => [2,1,1]
 => [1,1]
 => 1
[[2,2,0],[2,2],[2]]
 => [[1,1],[2,2]]
 => [2,2]
 => [2]
 => 0
[[2,1,1],[1,1],[1]]
 => [[1,3],[2],[3]]
 => [2,1,1]
 => [1,1]
 => 1
[[2,1,1],[2,1],[1]]
 => [[1,2],[2],[3]]
 => [2,1,1]
 => [1,1]
 => 1
[[2,1,1],[2,1],[2]]
 => [[1,1],[2],[3]]
 => [2,1,1]
 => [1,1]
 => 1
[[3,0,0,0],[2,0,0],[1,0],[0]]
 => [[2,3,4]]
 => [1,1,1]
 => [1,1]
 => 1
[[3,0,0,0],[2,0,0],[1,0],[1]]
 => [[1,3,4]]
 => [1,1,1]
 => [1,1]
 => 1
[[3,0,0,0],[2,0,0],[2,0],[1]]
 => [[1,2,4]]
 => [1,1,1]
 => [1,1]
 => 1
[[3,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,0,0],[1,1,0],[1,0],[0]]
 => [[2,4],[3]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,0,0],[1,1,0],[1,0],[1]]
 => [[1,4],[3]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,0,0],[1,1,0],[1,1],[1]]
 => [[1,4],[2]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,0,0],[2,0,0],[1,0],[0]]
 => [[2,3],[4]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,0,0],[2,0,0],[1,0],[1]]
 => [[1,3],[4]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,0,0],[2,0,0],[2,0],[1]]
 => [[1,2],[4]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => [1,1,1]
 => [1,1]
 => 1
[[2,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => [1,1,1]
 => [1,1]
 => 1
[[1,1,1,0],[1,1,0],[1,0],[0]]
 => [[2],[3],[4]]
 => [1,1,1]
 => [1,1]
 => 1
Description
The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is odd. The case of an even minimum is [[St000621]].
Matching statistic: St000621
(load all 2 compositions to match this statistic)
Mapping
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000621: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 29%●distinct values known / distinct values provided: 67%
Values
[[1,0],[0]]
 => [[2]]
 => [1]
 => []
 => ? ∊ {0,0}
[[1,0],[1]]
 => [[1]]
 => [1]
 => []
 => ? ∊ {0,0}
[[2,0],[0]]
 => [[2,2]]
 => [2]
 => []
 => ? ∊ {0,0,0,1}
[[2,0],[1]]
 => [[1,2]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,1}
[[2,0],[2]]
 => [[1,1]]
 => [2]
 => []
 => ? ∊ {0,0,0,1}
[[1,1],[1]]
 => [[1],[2]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,1}
[[1,0,0],[0,0],[0]]
 => [[3]]
 => [1]
 => []
 => ? ∊ {0,0,0}
[[1,0,0],[1,0],[0]]
 => [[2]]
 => [1]
 => []
 => ? ∊ {0,0,0}
[[1,0,0],[1,0],[1]]
 => [[1]]
 => [1]
 => []
 => ? ∊ {0,0,0}
[[3,0],[0]]
 => [[2,2,2]]
 => [3]
 => []
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[1]]
 => [[1,2,2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[2]]
 => [[1,1,2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[3]]
 => [[1,1,1]]
 => [3]
 => []
 => ? ∊ {0,0,0,0,1,1}
[[2,1],[1]]
 => [[1,2],[2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,1,1}
[[2,1],[2]]
 => [[1,1],[2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,1,1}
[[2,0,0],[0,0],[0]]
 => [[3,3]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[2,0,0],[1,0],[0]]
 => [[2,3]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[2,0,0],[1,0],[1]]
 => [[1,3]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[2,0,0],[2,0],[0]]
 => [[2,2]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[2,0,0],[2,0],[1]]
 => [[1,2]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[2,0,0],[2,0],[2]]
 => [[1,1]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,1,1,1}
[[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[0]]
 => [[2]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => [1]
 => []
 => ? ∊ {0,0,0,0}
[[4,0],[0]]
 => [[2,2,2,2]]
 => [4]
 => []
 => ? ∊ {0,0,0,0,0,1}
[[4,0],[1]]
 => [[1,2,2,2]]
 => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,1}
[[4,0],[2]]
 => [[1,1,2,2]]
 => [2,2]
 => [2]
 => 1
[[4,0],[3]]
 => [[1,1,1,2]]
 => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,1}
[[4,0],[4]]
 => [[1,1,1,1]]
 => [4]
 => []
 => ? ∊ {0,0,0,0,0,1}
[[3,1],[1]]
 => [[1,2,2],[2]]
 => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,1}
[[3,1],[2]]
 => [[1,1,2],[2]]
 => [2,2]
 => [2]
 => 1
[[3,1],[3]]
 => [[1,1,1],[2]]
 => [3,1]
 => [1]
 => ? ∊ {0,0,0,0,0,1}
[[2,2],[2]]
 => [[1,1],[2,2]]
 => [2,2]
 => [2]
 => 1
[[3,0,0],[0,0],[0]]
 => [[3,3,3]]
 => [3]
 => []
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[1,0],[0]]
 => [[2,3,3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[1,0],[1]]
 => [[1,3,3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[0]]
 => [[2,2,3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => [1,1,1]
 => [1,1]
 => 0
[[3,0,0],[2,0],[2]]
 => [[1,1,3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[0]]
 => [[2,2,2]]
 => [3]
 => []
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[1]]
 => [[1,2,2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[2]]
 => [[1,1,2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => [3]
 => []
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[1,0],[1]]
 => [[1,3],[3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => [1,1,1]
 => [1,1]
 => 0
[[2,1,0],[2,0],[0]]
 => [[2,2],[3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => [1,1,1]
 => [1,1]
 => 0
[[2,1,0],[2,0],[2]]
 => [[1,1],[3]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,1],[1]]
 => [[1,2],[2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => [2,1]
 => [1]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => [1,1,1]
 => [1,1]
 => 0
[[2,0,0,0],[0,0,0],[0,0],[0]]
 => [[4,4]]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[5,0],[2]]
 => [[1,1,2,2,2]]
 => [3,2]
 => [2]
 => 1
[[5,0],[3]]
 => [[1,1,1,2,2]]
 => [3,2]
 => [2]
 => 1
[[4,1],[2]]
 => [[1,1,2,2],[2]]
 => [3,2]
 => [2]
 => 1
[[4,1],[3]]
 => [[1,1,1,2],[2]]
 => [3,2]
 => [2]
 => 1
[[3,2],[2]]
 => [[1,1,2],[2,2]]
 => [3,2]
 => [2]
 => 1
[[3,2],[3]]
 => [[1,1,1],[2,2]]
 => [3,2]
 => [2]
 => 1
[[4,0,0],[2,0],[0]]
 => [[2,2,3,3]]
 => [2,2]
 => [2]
 => 1
[[4,0,0],[2,0],[1]]
 => [[1,2,3,3]]
 => [2,1,1]
 => [1,1]
 => 0
[[4,0,0],[2,0],[2]]
 => [[1,1,3,3]]
 => [2,2]
 => [2]
 => 1
[[4,0,0],[3,0],[1]]
 => [[1,2,2,3]]
 => [2,1,1]
 => [1,1]
 => 0
[[4,0,0],[3,0],[2]]
 => [[1,1,2,3]]
 => [2,1,1]
 => [1,1]
 => 0
[[4,0,0],[4,0],[2]]
 => [[1,1,2,2]]
 => [2,2]
 => [2]
 => 1
[[3,1,0],[1,1],[1]]
 => [[1,3,3],[2]]
 => [2,1,1]
 => [1,1]
 => 0
[[3,1,0],[2,0],[0]]
 => [[2,2,3],[3]]
 => [2,2]
 => [2]
 => 1
[[3,1,0],[2,0],[1]]
 => [[1,2,3],[3]]
 => [2,1,1]
 => [1,1]
 => 0
[[3,1,0],[2,0],[2]]
 => [[1,1,3],[3]]
 => [2,2]
 => [2]
 => 1
[[3,1,0],[2,1],[1]]
 => [[1,2,3],[2]]
 => [2,1,1]
 => [1,1]
 => 0
[[3,1,0],[2,1],[2]]
 => [[1,1,3],[2]]
 => [2,1,1]
 => [1,1]
 => 0
[[3,1,0],[3,0],[1]]
 => [[1,2,2],[3]]
 => [2,1,1]
 => [1,1]
 => 0
[[3,1,0],[3,0],[2]]
 => [[1,1,2],[3]]
 => [2,1,1]
 => [1,1]
 => 0
[[3,1,0],[3,1],[2]]
 => [[1,1,2],[2]]
 => [2,2]
 => [2]
 => 1
[[2,2,0],[2,0],[0]]
 => [[2,2],[3,3]]
 => [2,2]
 => [2]
 => 1
[[2,2,0],[2,0],[1]]
 => [[1,2],[3,3]]
 => [2,1,1]
 => [1,1]
 => 0
[[2,2,0],[2,0],[2]]
 => [[1,1],[3,3]]
 => [2,2]
 => [2]
 => 1
[[2,2,0],[2,1],[1]]
 => [[1,2],[2,3]]
 => [2,1,1]
 => [1,1]
 => 0
[[2,2,0],[2,1],[2]]
 => [[1,1],[2,3]]
 => [2,1,1]
 => [1,1]
 => 0
[[2,2,0],[2,2],[2]]
 => [[1,1],[2,2]]
 => [2,2]
 => [2]
 => 1
[[2,1,1],[1,1],[1]]
 => [[1,3],[2],[3]]
 => [2,1,1]
 => [1,1]
 => 0
[[2,1,1],[2,1],[1]]
 => [[1,2],[2],[3]]
 => [2,1,1]
 => [1,1]
 => 0
[[2,1,1],[2,1],[2]]
 => [[1,1],[2],[3]]
 => [2,1,1]
 => [1,1]
 => 0
[[3,0,0,0],[2,0,0],[1,0],[0]]
 => [[2,3,4]]
 => [1,1,1]
 => [1,1]
 => 0
[[3,0,0,0],[2,0,0],[1,0],[1]]
 => [[1,3,4]]
 => [1,1,1]
 => [1,1]
 => 0
[[3,0,0,0],[2,0,0],[2,0],[1]]
 => [[1,2,4]]
 => [1,1,1]
 => [1,1]
 => 0
[[3,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => [1,1,1]
 => [1,1]
 => 0
[[2,1,0,0],[1,1,0],[1,0],[0]]
 => [[2,4],[3]]
 => [1,1,1]
 => [1,1]
 => 0
[[2,1,0,0],[1,1,0],[1,0],[1]]
 => [[1,4],[3]]
 => [1,1,1]
 => [1,1]
 => 0
[[2,1,0,0],[1,1,0],[1,1],[1]]
 => [[1,4],[2]]
 => [1,1,1]
 => [1,1]
 => 0
[[2,1,0,0],[2,0,0],[1,0],[0]]
 => [[2,3],[4]]
 => [1,1,1]
 => [1,1]
 => 0
[[2,1,0,0],[2,0,0],[1,0],[1]]
 => [[1,3],[4]]
 => [1,1,1]
 => [1,1]
 => 0
[[2,1,0,0],[2,0,0],[2,0],[1]]
 => [[1,2],[4]]
 => [1,1,1]
 => [1,1]
 => 0
[[2,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => [1,1,1]
 => [1,1]
 => 0
[[2,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => [1,1,1]
 => [1,1]
 => 0
[[1,1,1,0],[1,1,0],[1,0],[0]]
 => [[2],[3],[4]]
 => [1,1,1]
 => [1,1]
 => 0
Description
The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is even. This notion was used in [1, Proposition 2.3], see also [2, Theorem 1.1]. The case of an odd minimum is [[St000620]].
Matching statistic: St000177
(load all 3 compositions to match this statistic)
Mapping
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00076: Semistandard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St000177: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 20% ●values known / values provided: 20%●distinct values known / distinct values provided: 67%
Values
[[1,0],[0]]
 => [[2]]
 => [[1,0],[0]]
 => ? = 0
[[1,0],[1]]
 => [[1]]
 => [[1]]
 => 0
[[2,0],[0]]
 => [[2,2]]
 => [[2,0],[0]]
 => 0
[[2,0],[1]]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[[2,0],[2]]
 => [[1,1]]
 => [[2]]
 => ? = 1
[[1,1],[1]]
 => [[1],[2]]
 => [[1,1],[1]]
 => 0
[[1,0,0],[0,0],[0]]
 => [[3]]
 => [[1,0,0],[0,0],[0]]
 => ? ∊ {0,0}
[[1,0,0],[1,0],[0]]
 => [[2]]
 => [[1,0],[0]]
 => ? ∊ {0,0}
[[1,0,0],[1,0],[1]]
 => [[1]]
 => [[1]]
 => 0
[[3,0],[0]]
 => [[2,2,2]]
 => [[3,0],[0]]
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[1]]
 => [[1,2,2]]
 => [[3,0],[1]]
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[2]]
 => [[1,1,2]]
 => [[3,0],[2]]
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[3]]
 => [[1,1,1]]
 => [[3]]
 => ? ∊ {0,0,0,0,1,1}
[[2,1],[1]]
 => [[1,2],[2]]
 => [[2,1],[1]]
 => ? ∊ {0,0,0,0,1,1}
[[2,1],[2]]
 => [[1,1],[2]]
 => [[2,1],[2]]
 => ? ∊ {0,0,0,0,1,1}
[[2,0,0],[0,0],[0]]
 => [[3,3]]
 => [[2,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,1,1,1}
[[2,0,0],[1,0],[0]]
 => [[2,3]]
 => [[2,0,0],[1,0],[0]]
 => ? ∊ {0,0,0,1,1,1}
[[2,0,0],[1,0],[1]]
 => [[1,3]]
 => [[2,0,0],[1,0],[1]]
 => ? ∊ {0,0,0,1,1,1}
[[2,0,0],[2,0],[0]]
 => [[2,2]]
 => [[2,0],[0]]
 => 0
[[2,0,0],[2,0],[1]]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[[2,0,0],[2,0],[2]]
 => [[1,1]]
 => [[2]]
 => ? ∊ {0,0,0,1,1,1}
[[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => [[1,1,0],[1,0],[0]]
 => ? ∊ {0,0,0,1,1,1}
[[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => [[1,1,0],[1,0],[1]]
 => ? ∊ {0,0,0,1,1,1}
[[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => [[1,1],[1]]
 => 0
[[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => [[1,0,0,0],[0,0,0],[0,0],[0]]
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => [[1,0,0],[0,0],[0]]
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[0]]
 => [[2]]
 => [[1,0],[0]]
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => [[1]]
 => 0
[[4,0],[0]]
 => [[2,2,2,2]]
 => [[4,0],[0]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[4,0],[1]]
 => [[1,2,2,2]]
 => [[4,0],[1]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[4,0],[2]]
 => [[1,1,2,2]]
 => [[4,0],[2]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[4,0],[3]]
 => [[1,1,1,2]]
 => [[4,0],[3]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[4,0],[4]]
 => [[1,1,1,1]]
 => [[4]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[3,1],[1]]
 => [[1,2,2],[2]]
 => [[3,1],[1]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[3,1],[2]]
 => [[1,1,2],[2]]
 => [[3,1],[2]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[3,1],[3]]
 => [[1,1,1],[2]]
 => [[3,1],[3]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[2,2],[2]]
 => [[1,1],[2,2]]
 => [[2,2],[2]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[3,0,0],[0,0],[0]]
 => [[3,3,3]]
 => [[3,0,0],[0,0],[0]]
 => 0
[[3,0,0],[1,0],[0]]
 => [[2,3,3]]
 => [[3,0,0],[1,0],[0]]
 => 1
[[3,0,0],[1,0],[1]]
 => [[1,3,3]]
 => [[3,0,0],[1,0],[1]]
 => 0
[[3,0,0],[2,0],[0]]
 => [[2,2,3]]
 => [[3,0,0],[2,0],[0]]
 => 1
[[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[[3,0,0],[2,0],[2]]
 => [[1,1,3]]
 => [[3,0,0],[2,0],[2]]
 => 0
[[3,0,0],[3,0],[0]]
 => [[2,2,2]]
 => [[3,0],[0]]
 => ? ∊ {0,1,1,1,1,2}
[[3,0,0],[3,0],[1]]
 => [[1,2,2]]
 => [[3,0],[1]]
 => ? ∊ {0,1,1,1,1,2}
[[3,0,0],[3,0],[2]]
 => [[1,1,2]]
 => [[3,0],[2]]
 => ? ∊ {0,1,1,1,1,2}
[[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => [[3]]
 => ? ∊ {0,1,1,1,1,2}
[[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => [[2,1,0],[1,0],[0]]
 => 0
[[2,1,0],[1,0],[1]]
 => [[1,3],[3]]
 => [[2,1,0],[1,0],[1]]
 => 0
[[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 0
[[2,1,0],[2,0],[0]]
 => [[2,2],[3]]
 => [[2,1,0],[2,0],[0]]
 => 0
[[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => 0
[[2,1,0],[2,0],[2]]
 => [[1,1],[3]]
 => [[2,1,0],[2,0],[2]]
 => 0
[[2,1,0],[2,1],[1]]
 => [[1,2],[2]]
 => [[2,1],[1]]
 => ? ∊ {0,1,1,1,1,2}
[[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => [[2,1],[2]]
 => ? ∊ {0,1,1,1,1,2}
[[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => 0
[[2,0,0,0],[0,0,0],[0,0],[0]]
 => [[4,4]]
 => [[2,0,0,0],[0,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[0,0],[0]]
 => [[3,4]]
 => [[2,0,0,0],[1,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[0]]
 => [[2,4]]
 => [[2,0,0,0],[1,0,0],[1,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[1]]
 => [[1,4]]
 => [[2,0,0,0],[1,0,0],[1,0],[1]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[0,0],[0]]
 => [[3,3]]
 => [[2,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[0]]
 => [[2,3]]
 => [[2,0,0],[1,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[1]]
 => [[1,3]]
 => [[2,0,0],[1,0],[1]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[0]]
 => [[2,2]]
 => [[2,0],[0]]
 => 0
[[2,0,0,0],[2,0,0],[2,0],[1]]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[[2,0,0,0],[2,0,0],[2,0],[2]]
 => [[1,1]]
 => [[2]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,0,0],[0,0],[0]]
 => [[3],[4]]
 => [[1,1,0,0],[1,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,0,0],[1,0],[0]]
 => [[2],[4]]
 => [[1,1,0,0],[1,0,0],[1,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,0,0],[1,0],[1]]
 => [[1],[4]]
 => [[1,1,0,0],[1,0,0],[1,0],[1]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => [[1,1,0],[1,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => [[1,1,0],[1,0],[1]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => [[1,1],[1]]
 => 0
[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
 => [[5]]
 => [[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0}
[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => [[1,0,0,0],[0,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0}
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => [[1,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0}
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => [[1]]
 => 0
[[3,0,0,0],[3,0,0],[0,0],[0]]
 => [[3,3,3]]
 => [[3,0,0],[0,0],[0]]
 => 0
[[3,0,0,0],[3,0,0],[1,0],[0]]
 => [[2,3,3]]
 => [[3,0,0],[1,0],[0]]
 => 1
[[3,0,0,0],[3,0,0],[1,0],[1]]
 => [[1,3,3]]
 => [[3,0,0],[1,0],[1]]
 => 0
[[3,0,0,0],[3,0,0],[2,0],[0]]
 => [[2,2,3]]
 => [[3,0,0],[2,0],[0]]
 => 1
[[3,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[[3,0,0,0],[3,0,0],[2,0],[2]]
 => [[1,1,3]]
 => [[3,0,0],[2,0],[2]]
 => 0
[[2,1,0,0],[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => [[2,1,0],[1,0],[0]]
 => 0
[[2,1,0,0],[2,1,0],[1,0],[1]]
 => [[1,3],[3]]
 => [[2,1,0],[1,0],[1]]
 => 0
[[2,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 0
[[2,1,0,0],[2,1,0],[2,0],[0]]
 => [[2,2],[3]]
 => [[2,1,0],[2,0],[0]]
 => 0
[[2,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => 0
[[2,1,0,0],[2,1,0],[2,0],[2]]
 => [[1,1],[3]]
 => [[2,1,0],[2,0],[2]]
 => 0
[[1,1,1,0],[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => 0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]
 => [[2,2]]
 => [[2,0],[0]]
 => 0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => [[1,1],[1]]
 => 0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => [[1]]
 => 0
Description
The number of free tiles in the pattern. The ''tiling'' of a pattern is the finest partition of the entries in the pattern, such that adjacent (NW,NE,SW,SE) entries that are equal belong to the same part. These parts are called ''tiles'', and each entry in a pattern belong to exactly one tile. A tile is ''free'' if it does not intersect any of the first and the last row.
Matching statistic: St000178
(load all 3 compositions to match this statistic)
Mapping
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00076: Semistandard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St000178: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 20% ●values known / values provided: 20%●distinct values known / distinct values provided: 67%
Values
[[1,0],[0]]
 => [[2]]
 => [[1,0],[0]]
 => ? = 0
[[1,0],[1]]
 => [[1]]
 => [[1]]
 => 0
[[2,0],[0]]
 => [[2,2]]
 => [[2,0],[0]]
 => 0
[[2,0],[1]]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[[2,0],[2]]
 => [[1,1]]
 => [[2]]
 => ? = 1
[[1,1],[1]]
 => [[1],[2]]
 => [[1,1],[1]]
 => 0
[[1,0,0],[0,0],[0]]
 => [[3]]
 => [[1,0,0],[0,0],[0]]
 => ? ∊ {0,0}
[[1,0,0],[1,0],[0]]
 => [[2]]
 => [[1,0],[0]]
 => ? ∊ {0,0}
[[1,0,0],[1,0],[1]]
 => [[1]]
 => [[1]]
 => 0
[[3,0],[0]]
 => [[2,2,2]]
 => [[3,0],[0]]
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[1]]
 => [[1,2,2]]
 => [[3,0],[1]]
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[2]]
 => [[1,1,2]]
 => [[3,0],[2]]
 => ? ∊ {0,0,0,0,1,1}
[[3,0],[3]]
 => [[1,1,1]]
 => [[3]]
 => ? ∊ {0,0,0,0,1,1}
[[2,1],[1]]
 => [[1,2],[2]]
 => [[2,1],[1]]
 => ? ∊ {0,0,0,0,1,1}
[[2,1],[2]]
 => [[1,1],[2]]
 => [[2,1],[2]]
 => ? ∊ {0,0,0,0,1,1}
[[2,0,0],[0,0],[0]]
 => [[3,3]]
 => [[2,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,1,1,1}
[[2,0,0],[1,0],[0]]
 => [[2,3]]
 => [[2,0,0],[1,0],[0]]
 => ? ∊ {0,0,0,1,1,1}
[[2,0,0],[1,0],[1]]
 => [[1,3]]
 => [[2,0,0],[1,0],[1]]
 => ? ∊ {0,0,0,1,1,1}
[[2,0,0],[2,0],[0]]
 => [[2,2]]
 => [[2,0],[0]]
 => 0
[[2,0,0],[2,0],[1]]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[[2,0,0],[2,0],[2]]
 => [[1,1]]
 => [[2]]
 => ? ∊ {0,0,0,1,1,1}
[[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => [[1,1,0],[1,0],[0]]
 => ? ∊ {0,0,0,1,1,1}
[[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => [[1,1,0],[1,0],[1]]
 => ? ∊ {0,0,0,1,1,1}
[[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => [[1,1],[1]]
 => 0
[[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => [[1,0,0,0],[0,0,0],[0,0],[0]]
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => [[1,0,0],[0,0],[0]]
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[0]]
 => [[2]]
 => [[1,0],[0]]
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => [[1]]
 => 0
[[4,0],[0]]
 => [[2,2,2,2]]
 => [[4,0],[0]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[4,0],[1]]
 => [[1,2,2,2]]
 => [[4,0],[1]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[4,0],[2]]
 => [[1,1,2,2]]
 => [[4,0],[2]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[4,0],[3]]
 => [[1,1,1,2]]
 => [[4,0],[3]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[4,0],[4]]
 => [[1,1,1,1]]
 => [[4]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[3,1],[1]]
 => [[1,2,2],[2]]
 => [[3,1],[1]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[3,1],[2]]
 => [[1,1,2],[2]]
 => [[3,1],[2]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[3,1],[3]]
 => [[1,1,1],[2]]
 => [[3,1],[3]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[2,2],[2]]
 => [[1,1],[2,2]]
 => [[2,2],[2]]
 => ? ∊ {0,0,0,0,0,1,1,1,1}
[[3,0,0],[0,0],[0]]
 => [[3,3,3]]
 => [[3,0,0],[0,0],[0]]
 => 0
[[3,0,0],[1,0],[0]]
 => [[2,3,3]]
 => [[3,0,0],[1,0],[0]]
 => 1
[[3,0,0],[1,0],[1]]
 => [[1,3,3]]
 => [[3,0,0],[1,0],[1]]
 => 0
[[3,0,0],[2,0],[0]]
 => [[2,2,3]]
 => [[3,0,0],[2,0],[0]]
 => 1
[[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[[3,0,0],[2,0],[2]]
 => [[1,1,3]]
 => [[3,0,0],[2,0],[2]]
 => 0
[[3,0,0],[3,0],[0]]
 => [[2,2,2]]
 => [[3,0],[0]]
 => ? ∊ {0,1,1,1,1,2}
[[3,0,0],[3,0],[1]]
 => [[1,2,2]]
 => [[3,0],[1]]
 => ? ∊ {0,1,1,1,1,2}
[[3,0,0],[3,0],[2]]
 => [[1,1,2]]
 => [[3,0],[2]]
 => ? ∊ {0,1,1,1,1,2}
[[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => [[3]]
 => ? ∊ {0,1,1,1,1,2}
[[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => [[2,1,0],[1,0],[0]]
 => 0
[[2,1,0],[1,0],[1]]
 => [[1,3],[3]]
 => [[2,1,0],[1,0],[1]]
 => 0
[[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 0
[[2,1,0],[2,0],[0]]
 => [[2,2],[3]]
 => [[2,1,0],[2,0],[0]]
 => 0
[[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => 0
[[2,1,0],[2,0],[2]]
 => [[1,1],[3]]
 => [[2,1,0],[2,0],[2]]
 => 0
[[2,1,0],[2,1],[1]]
 => [[1,2],[2]]
 => [[2,1],[1]]
 => ? ∊ {0,1,1,1,1,2}
[[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => [[2,1],[2]]
 => ? ∊ {0,1,1,1,1,2}
[[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => 0
[[2,0,0,0],[0,0,0],[0,0],[0]]
 => [[4,4]]
 => [[2,0,0,0],[0,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[0,0],[0]]
 => [[3,4]]
 => [[2,0,0,0],[1,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[0]]
 => [[2,4]]
 => [[2,0,0,0],[1,0,0],[1,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[1]]
 => [[1,4]]
 => [[2,0,0,0],[1,0,0],[1,0],[1]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[0,0],[0]]
 => [[3,3]]
 => [[2,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[0]]
 => [[2,3]]
 => [[2,0,0],[1,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[1]]
 => [[1,3]]
 => [[2,0,0],[1,0],[1]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[0]]
 => [[2,2]]
 => [[2,0],[0]]
 => 0
[[2,0,0,0],[2,0,0],[2,0],[1]]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[[2,0,0,0],[2,0,0],[2,0],[2]]
 => [[1,1]]
 => [[2]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,0,0],[0,0],[0]]
 => [[3],[4]]
 => [[1,1,0,0],[1,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,0,0],[1,0],[0]]
 => [[2],[4]]
 => [[1,1,0,0],[1,0,0],[1,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,0,0],[1,0],[1]]
 => [[1],[4]]
 => [[1,1,0,0],[1,0,0],[1,0],[1]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => [[1,1,0],[1,0],[0]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => [[1,1,0],[1,0],[1]]
 => ? ∊ {0,0,0,0,0,0,0,1,1,1,1,1,1}
[[1,1,0,0],[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => [[1,1],[1]]
 => 0
[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
 => [[5]]
 => [[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0}
[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => [[1,0,0,0],[0,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0}
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => [[1,0,0],[0,0],[0]]
 => ? ∊ {0,0,0,0}
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => [[1]]
 => 0
[[3,0,0,0],[3,0,0],[0,0],[0]]
 => [[3,3,3]]
 => [[3,0,0],[0,0],[0]]
 => 0
[[3,0,0,0],[3,0,0],[1,0],[0]]
 => [[2,3,3]]
 => [[3,0,0],[1,0],[0]]
 => 1
[[3,0,0,0],[3,0,0],[1,0],[1]]
 => [[1,3,3]]
 => [[3,0,0],[1,0],[1]]
 => 0
[[3,0,0,0],[3,0,0],[2,0],[0]]
 => [[2,2,3]]
 => [[3,0,0],[2,0],[0]]
 => 1
[[3,0,0,0],[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[[3,0,0,0],[3,0,0],[2,0],[2]]
 => [[1,1,3]]
 => [[3,0,0],[2,0],[2]]
 => 0
[[2,1,0,0],[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => [[2,1,0],[1,0],[0]]
 => 0
[[2,1,0,0],[2,1,0],[1,0],[1]]
 => [[1,3],[3]]
 => [[2,1,0],[1,0],[1]]
 => 0
[[2,1,0,0],[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 0
[[2,1,0,0],[2,1,0],[2,0],[0]]
 => [[2,2],[3]]
 => [[2,1,0],[2,0],[0]]
 => 0
[[2,1,0,0],[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => 0
[[2,1,0,0],[2,1,0],[2,0],[2]]
 => [[1,1],[3]]
 => [[2,1,0],[2,0],[2]]
 => 0
[[1,1,1,0],[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => 0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]]
 => [[2,2]]
 => [[2,0],[0]]
 => 0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]]
 => [[1,2]]
 => [[2,0],[1]]
 => 0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => [[1,1],[1]]
 => 0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => [[1]]
 => 0
Description
Number of free entries. The ''tiling'' of a pattern is the finest partition of the entries in the pattern, such that adjacent (NW,NE,SW,SE) entries that are equal belong to the same part. These parts are called ''tiles'', and each entry in a pattern belong to exactly one tile. A tile is ''free'' if it do not intersect any of the first and the last row. This statistic is the total number of entries that belong to a free tile.
Matching statistic: St000259
Mapping
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 33%
Values
[[1,0],[0]]
 => [[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
[[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[2,0],[0]]
 => [[2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,1}
[[2,0],[1]]
 => [[1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,1}
[[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0],[0,0],[0]]
 => [[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0}
[[1,0,0],[1,0],[0]]
 => [[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0}
[[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[3,0],[0]]
 => [[2,2,2]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,1,1}
[[3,0],[1]]
 => [[1,2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,1,1}
[[3,0],[2]]
 => [[1,1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1}
[[3,0],[3]]
 => [[1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[2,1],[1]]
 => [[1,2],[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1}
[[2,1],[2]]
 => [[1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[2,0,0],[0,0],[0]]
 => [[3,3]]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[1,0],[0]]
 => [[2,3]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[1,0],[1]]
 => [[1,3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[2,0],[0]]
 => [[2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[2,0],[1]]
 => [[1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,1,1,1}
[[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,1,1,1}
[[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[0]]
 => [[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[4,0],[0]]
 => [[2,2,2,2]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[1]]
 => [[1,2,2,2]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[2]]
 => [[1,1,2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[3]]
 => [[1,1,1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[4]]
 => [[1,1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[3,1],[1]]
 => [[1,2,2],[2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,1,1,1,1}
[[3,1],[2]]
 => [[1,1,2],[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1,1,1}
[[3,1],[3]]
 => [[1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[2,2],[2]]
 => [[1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[3,0,0],[0,0],[0]]
 => [[3,3,3]]
 => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
 => ([(4,9),(5,8),(6,7),(7,9),(8,9)],10)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[1,0],[0]]
 => [[2,3,3]]
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[1,0],[1]]
 => [[1,3,3]]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[0]]
 => [[2,2,3]]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[2]]
 => [[1,1,3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[0]]
 => [[2,2,2]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[1]]
 => [[1,2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[2]]
 => [[1,1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
 => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[1,0],[1]]
 => [[1,3],[3]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,0],[0]]
 => [[2,2],[3]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,0],[2]]
 => [[1,1],[3]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,1],[1]]
 => [[1,2],[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => ([],1)
 => ([],1)
 => 0
[[2,0,0,0],[0,0,0],[0,0],[0]]
 => [[4,4]]
 => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
 => ([(4,9),(5,8),(6,7),(7,9),(8,9)],10)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[0,0],[0]]
 => [[3,4]]
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[0]]
 => [[2,4]]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[1]]
 => [[1,4]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[0,0],[0]]
 => [[3,3]]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[0]]
 => [[2,3]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[1]]
 => [[1,3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[0]]
 => [[2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[1]]
 => [[1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,0,0],[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[5,0],[5]]
 => [[1,1,1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[4,1],[4]]
 => [[1,1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[3,2],[3]]
 => [[1,1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[4,0,0],[4,0],[4]]
 => [[1,1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[3,1,0],[3,1],[3]]
 => [[1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[2,2,0],[2,2],[2]]
 => [[1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[2,1,1],[2,1],[2]]
 => [[1,1],[2],[3]]
 => ([],1)
 => ([],1)
 => 0
[[3,0,0,0],[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[2,1,0,0],[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,1,0],[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => ([],1)
 => ([],1)
 => 0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[5,1],[5]]
 => [[1,1,1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[4,2],[4]]
 => [[1,1,1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[3,3],[3]]
 => [[1,1,1],[2,2,2]]
 => ([],1)
 => ([],1)
 => 0
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St000260
Mapping
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 33%
Values
[[1,0],[0]]
 => [[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
[[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[2,0],[0]]
 => [[2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,1}
[[2,0],[1]]
 => [[1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,1}
[[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0],[0,0],[0]]
 => [[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0}
[[1,0,0],[1,0],[0]]
 => [[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0}
[[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[3,0],[0]]
 => [[2,2,2]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,1,1}
[[3,0],[1]]
 => [[1,2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,1,1}
[[3,0],[2]]
 => [[1,1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1}
[[3,0],[3]]
 => [[1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[2,1],[1]]
 => [[1,2],[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1}
[[2,1],[2]]
 => [[1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[2,0,0],[0,0],[0]]
 => [[3,3]]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[1,0],[0]]
 => [[2,3]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[1,0],[1]]
 => [[1,3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[2,0],[0]]
 => [[2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[2,0],[1]]
 => [[1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,1,1,1}
[[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,1,1,1}
[[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[0]]
 => [[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[4,0],[0]]
 => [[2,2,2,2]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[1]]
 => [[1,2,2,2]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[2]]
 => [[1,1,2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[3]]
 => [[1,1,1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[4]]
 => [[1,1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[3,1],[1]]
 => [[1,2,2],[2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,1,1,1,1}
[[3,1],[2]]
 => [[1,1,2],[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1,1,1}
[[3,1],[3]]
 => [[1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[2,2],[2]]
 => [[1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[3,0,0],[0,0],[0]]
 => [[3,3,3]]
 => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
 => ([(4,9),(5,8),(6,7),(7,9),(8,9)],10)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[1,0],[0]]
 => [[2,3,3]]
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[1,0],[1]]
 => [[1,3,3]]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[0]]
 => [[2,2,3]]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[2]]
 => [[1,1,3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[0]]
 => [[2,2,2]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[1]]
 => [[1,2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[2]]
 => [[1,1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
 => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[1,0],[1]]
 => [[1,3],[3]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,0],[0]]
 => [[2,2],[3]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,0],[2]]
 => [[1,1],[3]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,1],[1]]
 => [[1,2],[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => ([],1)
 => ([],1)
 => 0
[[2,0,0,0],[0,0,0],[0,0],[0]]
 => [[4,4]]
 => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
 => ([(4,9),(5,8),(6,7),(7,9),(8,9)],10)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[0,0],[0]]
 => [[3,4]]
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[0]]
 => [[2,4]]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[1]]
 => [[1,4]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[0,0],[0]]
 => [[3,3]]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[0]]
 => [[2,3]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[1]]
 => [[1,3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[0]]
 => [[2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[1]]
 => [[1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,0,0],[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[5,0],[5]]
 => [[1,1,1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[4,1],[4]]
 => [[1,1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[3,2],[3]]
 => [[1,1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[4,0,0],[4,0],[4]]
 => [[1,1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[3,1,0],[3,1],[3]]
 => [[1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[2,2,0],[2,2],[2]]
 => [[1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[2,1,1],[2,1],[2]]
 => [[1,1],[2],[3]]
 => ([],1)
 => ([],1)
 => 0
[[3,0,0,0],[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[2,1,0,0],[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,1,0],[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => ([],1)
 => ([],1)
 => 0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[5,1],[5]]
 => [[1,1,1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[4,2],[4]]
 => [[1,1,1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[3,3],[3]]
 => [[1,1,1],[2,2,2]]
 => ([],1)
 => ([],1)
 => 0
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000302
Mapping
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00214: Semistandard tableaux —subcrystal⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000302: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 33%
Values
[[1,0],[0]]
 => [[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
[[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[2,0],[0]]
 => [[2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,1}
[[2,0],[1]]
 => [[1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,1}
[[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0],[0,0],[0]]
 => [[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0}
[[1,0,0],[1,0],[0]]
 => [[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0}
[[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[3,0],[0]]
 => [[2,2,2]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,1,1}
[[3,0],[1]]
 => [[1,2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,1,1}
[[3,0],[2]]
 => [[1,1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1}
[[3,0],[3]]
 => [[1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[2,1],[1]]
 => [[1,2],[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1}
[[2,1],[2]]
 => [[1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[2,0,0],[0,0],[0]]
 => [[3,3]]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[1,0],[0]]
 => [[2,3]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[1,0],[1]]
 => [[1,3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[2,0],[0]]
 => [[2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[2,0],[1]]
 => [[1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,1,1,1}
[[2,0,0],[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,0],[1,0],[0]]
 => [[2],[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,1,1,1}
[[1,1,0],[1,0],[1]]
 => [[1],[3]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,1,1,1}
[[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0,0],[0,0,0],[0,0],[0]]
 => [[4]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[0,0],[0]]
 => [[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[0]]
 => [[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0}
[[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[4,0],[0]]
 => [[2,2,2,2]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[1]]
 => [[1,2,2,2]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[2]]
 => [[1,1,2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[3]]
 => [[1,1,1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1,1,1}
[[4,0],[4]]
 => [[1,1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[3,1],[1]]
 => [[1,2,2],[2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,1,1,1,1}
[[3,1],[2]]
 => [[1,1,2],[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,1,1,1,1}
[[3,1],[3]]
 => [[1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[2,2],[2]]
 => [[1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[3,0,0],[0,0],[0]]
 => [[3,3,3]]
 => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
 => ([(4,9),(5,8),(6,7),(7,9),(8,9)],10)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[1,0],[0]]
 => [[2,3,3]]
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[1,0],[1]]
 => [[1,3,3]]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[0]]
 => [[2,2,3]]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[1]]
 => [[1,2,3]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[2,0],[2]]
 => [[1,1,3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[0]]
 => [[2,2,2]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[1]]
 => [[1,2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[2]]
 => [[1,1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[2,1,0],[1,0],[0]]
 => [[2,3],[3]]
 => ([(0,5),(0,6),(1,7),(2,7),(3,2),(4,1),(5,3),(6,4)],8)
 => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[1,0],[1]]
 => [[1,3],[3]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[1,1],[1]]
 => [[1,3],[2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,0],[0]]
 => [[2,2],[3]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,0],[1]]
 => [[1,2],[3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,0],[2]]
 => [[1,1],[3]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,1],[1]]
 => [[1,2],[2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2}
[[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => ([],1)
 => ([],1)
 => 0
[[2,0,0,0],[0,0,0],[0,0],[0]]
 => [[4,4]]
 => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
 => ([(4,9),(5,8),(6,7),(7,9),(8,9)],10)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[0,0],[0]]
 => [[3,4]]
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[0]]
 => [[2,4]]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[1,0,0],[1,0],[1]]
 => [[1,4]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[0,0],[0]]
 => [[3,3]]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[0]]
 => [[2,3]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[1,0],[1]]
 => [[1,3]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[0]]
 => [[2,2]]
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[1]]
 => [[1,2]]
 => ([(0,1)],2)
 => ([],2)
 => ? ∊ {0,0,0,0,0,0,0,0,1,1,1,1,1,1}
[[2,0,0,0],[2,0,0],[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,0,0],[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[5,0],[5]]
 => [[1,1,1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[4,1],[4]]
 => [[1,1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[3,2],[3]]
 => [[1,1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[4,0,0],[4,0],[4]]
 => [[1,1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[3,1,0],[3,1],[3]]
 => [[1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[2,2,0],[2,2],[2]]
 => [[1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[2,1,1],[2,1],[2]]
 => [[1,1],[2],[3]]
 => ([],1)
 => ([],1)
 => 0
[[3,0,0,0],[3,0,0],[3,0],[3]]
 => [[1,1,1]]
 => ([],1)
 => ([],1)
 => 0
[[2,1,0,0],[2,1,0],[2,1],[2]]
 => [[1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,1,0],[1,1,1],[1,1],[1]]
 => [[1],[2],[3]]
 => ([],1)
 => ([],1)
 => 0
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]]
 => [[1,1]]
 => ([],1)
 => ([],1)
 => 0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]]
 => [[1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]]
 => [[1]]
 => ([],1)
 => ([],1)
 => 0
[[5,1],[5]]
 => [[1,1,1,1,1],[2]]
 => ([],1)
 => ([],1)
 => 0
[[4,2],[4]]
 => [[1,1,1,1],[2,2]]
 => ([],1)
 => ([],1)
 => 0
[[3,3],[3]]
 => [[1,1,1],[2,2,2]]
 => ([],1)
 => ([],1)
 => 0
Description
The determinant of the distance matrix of a connected graph.
The following 26 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph. St000455The second largest eigenvalue of a graph if it is integral. St000284The Plancherel distribution on integer partitions. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000567The sum of the products of all pairs of parts. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000706The product of the factorials of the multiplicities of an integer partition. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000929The constant term of the character polynomial of an integer partition. St000934The 2-degree of an integer partition. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St000941The number of characters of the symmetric group whose value on the partition is even. St000993The multiplicity of the largest part of an integer partition. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001098The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for vertex labelled trees. St001099The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled binary trees. St001100The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled trees. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001128The exponens consonantiae of a partition. St001568The smallest positive integer that does not appear twice in the partition.