Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St000246
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St000246: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [1,2] => [1,2] => 1
{{1},{2}}
 => [1,2] => [2,1] => [2,1] => 0
{{1,2,3}}
 => [2,3,1] => [1,3,2] => [1,3,2] => 2
{{1,2},{3}}
 => [2,1,3] => [3,1,2] => [3,1,2] => 1
{{1,3},{2}}
 => [3,2,1] => [1,2,3] => [1,2,3] => 3
{{1},{2,3}}
 => [1,3,2] => [2,3,1] => [1,3,2] => 2
{{1},{2},{3}}
 => [1,2,3] => [3,2,1] => [3,2,1] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,4,3,2] => [1,4,3,2] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [4,1,3,2] => [4,1,3,2] => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [1,3,4,2] => [1,2,4,3] => 5
{{1,2},{3,4}}
 => [2,1,4,3] => [3,4,1,2] => [2,4,1,3] => 3
{{1,2},{3},{4}}
 => [2,1,3,4] => [4,3,1,2] => [4,3,1,2] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [1,4,2,3] => [1,4,2,3] => 4
{{1,3},{2,4}}
 => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 4
{{1,3},{2},{4}}
 => [3,2,1,4] => [4,1,2,3] => [4,1,2,3] => 3
{{1,4},{2,3}}
 => [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 6
{{1},{2,3,4}}
 => [1,3,4,2] => [2,4,3,1] => [1,4,3,2] => 3
{{1},{2,3},{4}}
 => [1,3,2,4] => [4,2,3,1] => [4,1,3,2] => 2
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 5
{{1},{2,4},{3}}
 => [1,4,3,2] => [2,3,4,1] => [1,2,4,3] => 5
{{1},{2},{3,4}}
 => [1,2,4,3] => [3,4,2,1] => [1,4,3,2] => 3
{{1},{2},{3},{4}}
 => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
Description
The number of non-inversions of a permutation. For a permutation of $\{1,\ldots,n\}$, this is given by $\operatorname{noninv}(\pi) = \binom{n}{2}-\operatorname{inv}(\pi)$.
Matching statistic: St001583
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St001583: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [1,2] => [1,2] => 1
{{1},{2}}
 => [1,2] => [2,1] => [2,1] => 0
{{1,2,3}}
 => [2,3,1] => [1,3,2] => [1,3,2] => 2
{{1,2},{3}}
 => [2,1,3] => [3,1,2] => [3,1,2] => 1
{{1,3},{2}}
 => [3,2,1] => [1,2,3] => [1,2,3] => 3
{{1},{2,3}}
 => [1,3,2] => [2,3,1] => [1,3,2] => 2
{{1},{2},{3}}
 => [1,2,3] => [3,2,1] => [3,2,1] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,4,3,2] => [1,4,3,2] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [4,1,3,2] => [4,1,3,2] => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [1,3,4,2] => [1,2,4,3] => 5
{{1,2},{3,4}}
 => [2,1,4,3] => [3,4,1,2] => [2,4,1,3] => 3
{{1,2},{3},{4}}
 => [2,1,3,4] => [4,3,1,2] => [4,3,1,2] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [1,4,2,3] => [1,4,2,3] => 4
{{1,3},{2,4}}
 => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 4
{{1,3},{2},{4}}
 => [3,2,1,4] => [4,1,2,3] => [4,1,2,3] => 3
{{1,4},{2,3}}
 => [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 6
{{1},{2,3,4}}
 => [1,3,4,2] => [2,4,3,1] => [1,4,3,2] => 3
{{1},{2,3},{4}}
 => [1,3,2,4] => [4,2,3,1] => [4,1,3,2] => 2
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 5
{{1},{2,4},{3}}
 => [1,4,3,2] => [2,3,4,1] => [1,2,4,3] => 5
{{1},{2},{3,4}}
 => [1,2,4,3] => [3,4,2,1] => [1,4,3,2] => 3
{{1},{2},{3},{4}}
 => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
Description
The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.
Matching statistic: St001759
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
St001759: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2,1] => [2,1] => 1
{{1},{2}}
 => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [2,3,1] => [3,1,2] => 2
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => [3,2,1] => 3
{{1},{2,3}}
 => [1,3,2] => [3,1,2] => [1,3,2] => 2
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [2,3,4,1] => [4,1,2,3] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [2,3,1,4] => [3,1,2,4] => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [4,2,3,1] => [4,1,3,2] => 5
{{1,2},{3,4}}
 => [2,1,4,3] => [2,4,1,3] => [1,3,4,2] => 3
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [3,2,4,1] => [4,2,1,3] => 4
{{1,3},{2,4}}
 => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => 4
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 3
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 6
{{1},{2,3,4}}
 => [1,3,4,2] => [3,4,1,2] => [1,4,2,3] => 3
{{1},{2,3},{4}}
 => [1,3,2,4] => [3,1,2,4] => [1,3,2,4] => 2
{{1,4},{2},{3}}
 => [4,2,3,1] => [2,4,3,1] => [4,2,3,1] => 5
{{1},{2,4},{3}}
 => [1,4,3,2] => [4,3,1,2] => [1,4,3,2] => 5
{{1},{2},{3,4}}
 => [1,2,4,3] => [4,1,2,3] => [1,2,4,3] => 3
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
Description
The Rajchgot index of a permutation. The '''Rajchgot index''' of a permutation $\sigma$ is the degree of the ''Grothendieck polynomial'' of $\sigma$. This statistic on permutations was defined by Pechenik, Speyer, and Weigandt [1]. It can be computed by taking the maximum major index [[St000004]] of the permutations smaller than or equal to $\sigma$ in the right ''weak Bruhat order''.
Matching statistic: St001645
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 43%
Values
{{1,2}}
 => [2,1] => [2,1] => ([(0,1)],2)
 => 2 = 1 + 1
{{1},{2}}
 => [1,2] => [1,2] => ([],2)
 => ? = 0 + 1
{{1,2,3}}
 => [2,3,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 1 + 1
{{1,3},{2}}
 => [3,2,1] => [2,3,1] => ([(0,2),(1,2)],3)
 => 4 = 3 + 1
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 2 + 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => ([],3)
 => ? = 0 + 1
{{1,2,3,4}}
 => [2,3,4,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
{{1,2,3},{4}}
 => [2,3,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2 + 1
{{1,2,4},{3}}
 => [2,4,3,1] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 5 + 1
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 3 + 1
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 1 + 1
{{1,3,4},{2}}
 => [3,2,4,1] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 4 + 1
{{1,3},{2,4}}
 => [3,4,1,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 4 + 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 3 + 1
{{1,4},{2,3}}
 => [4,3,2,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 6 + 1
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 3 + 1
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 2 + 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 5 + 1
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 5 + 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3 + 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 0 + 1
Description
The pebbling number of a connected graph.
Matching statistic: St001879
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 43%
Values
{{1,2}}
 => [2,1] => [1,2] => ([(0,1)],2)
 => ? = 1
{{1},{2}}
 => [1,2] => [2,1] => ([],2)
 => ? = 0
{{1,2,3}}
 => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
{{1,2},{3}}
 => [2,1,3] => [3,2,1] => ([],3)
 => ? = 1
{{1,3},{2}}
 => [3,2,1] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? = 3
{{1},{2,3}}
 => [1,3,2] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? = 2
{{1},{2},{3}}
 => [1,2,3] => [2,3,1] => ([(1,2)],3)
 => ? = 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [4,2,3,1] => ([(2,3)],4)
 => ? = 2
{{1,2,4},{3}}
 => [2,4,3,1] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
 => ? = 5
{{1,2},{3,4}}
 => [2,1,4,3] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => ? = 3
{{1,2},{3},{4}}
 => [2,1,3,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
 => ? = 1
{{1,3,4},{2}}
 => [3,2,4,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
{{1,3},{2,4}}
 => [3,4,1,2] => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? = 4
{{1,3},{2},{4}}
 => [3,2,1,4] => [4,3,2,1] => ([],4)
 => ? = 3
{{1,4},{2,3}}
 => [4,3,2,1] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
 => ? = 6
{{1},{2,3,4}}
 => [1,3,4,2] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? = 3
{{1},{2,3},{4}}
 => [1,3,2,4] => [2,4,3,1] => ([(1,2),(1,3)],4)
 => ? = 2
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
 => ? = 5
{{1},{2,4},{3}}
 => [1,4,3,2] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ? = 5
{{1},{2},{3,4}}
 => [1,2,4,3] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
{{1},{2},{3},{4}}
 => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? = 0
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.