searching the database
Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000585
(load all 97 compositions to match this statistic)
(load all 97 compositions to match this statistic)
St000585: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> 0
{{1},{2}}
=> 0
{{1,2,3}}
=> 0
{{1,2},{3}}
=> 0
{{1,3},{2}}
=> 1
{{1},{2,3}}
=> 0
{{1},{2},{3}}
=> 0
{{1,2,3,4}}
=> 0
{{1,2,3},{4}}
=> 0
{{1,2,4},{3}}
=> 1
{{1,2},{3,4}}
=> 0
{{1,2},{3},{4}}
=> 0
{{1,3,4},{2}}
=> 1
{{1,3},{2,4}}
=> 1
{{1,3},{2},{4}}
=> 1
{{1,4},{2,3}}
=> 1
{{1},{2,3,4}}
=> 0
{{1},{2,3},{4}}
=> 0
{{1,4},{2},{3}}
=> 2
{{1},{2,4},{3}}
=> 1
{{1},{2},{3,4}}
=> 0
{{1},{2},{3},{4}}
=> 0
{{1,2,3,4,5}}
=> 0
{{1,2,3,4},{5}}
=> 0
{{1,2,3,5},{4}}
=> 1
{{1,2,3},{4,5}}
=> 0
{{1,2,3},{4},{5}}
=> 0
{{1,2,4,5},{3}}
=> 1
{{1,2,4},{3,5}}
=> 1
{{1,2,4},{3},{5}}
=> 1
{{1,2,5},{3,4}}
=> 1
{{1,2},{3,4,5}}
=> 0
{{1,2},{3,4},{5}}
=> 0
{{1,2,5},{3},{4}}
=> 2
{{1,2},{3,5},{4}}
=> 1
{{1,2},{3},{4,5}}
=> 0
{{1,2},{3},{4},{5}}
=> 0
{{1,3,4,5},{2}}
=> 1
{{1,3,4},{2,5}}
=> 1
{{1,3,4},{2},{5}}
=> 1
{{1,3,5},{2,4}}
=> 1
{{1,3},{2,4,5}}
=> 1
{{1,3},{2,4},{5}}
=> 1
{{1,3,5},{2},{4}}
=> 2
{{1,3},{2,5},{4}}
=> 2
{{1,3},{2},{4,5}}
=> 1
{{1,3},{2},{4},{5}}
=> 1
{{1,4,5},{2,3}}
=> 1
{{1,4},{2,3,5}}
=> 1
{{1,4},{2,3},{5}}
=> 1
Description
The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) are consecutive in a block.
Matching statistic: St001882
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001882: Signed permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 38%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001882: Signed permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 38%
Values
{{1,2}}
=> [2,1] => [2,1] => [2,1] => 0
{{1},{2}}
=> [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
=> [2,3,1] => [3,1,2] => [3,1,2] => 0
{{1,2},{3}}
=> [2,1,3] => [2,1,3] => [2,1,3] => 0
{{1,3},{2}}
=> [3,2,1] => [2,3,1] => [2,3,1] => 1
{{1},{2,3}}
=> [1,3,2] => [1,3,2] => [1,3,2] => 0
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
=> [2,3,4,1] => [4,1,2,3] => [4,1,2,3] => 0
{{1,2,3},{4}}
=> [2,3,1,4] => [3,1,2,4] => [3,1,2,4] => 0
{{1,2,4},{3}}
=> [2,4,3,1] => [3,4,1,2] => [3,4,1,2] => 1
{{1,2},{3,4}}
=> [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 0
{{1,3,4},{2}}
=> [3,2,4,1] => [2,4,1,3] => [2,4,1,3] => 1
{{1,3},{2,4}}
=> [3,4,1,2] => [3,1,4,2] => [3,1,4,2] => 1
{{1,3},{2},{4}}
=> [3,2,1,4] => [2,3,1,4] => [2,3,1,4] => 1
{{1,4},{2,3}}
=> [4,3,2,1] => [3,2,4,1] => [3,2,4,1] => 1
{{1},{2,3,4}}
=> [1,3,4,2] => [1,4,2,3] => [1,4,2,3] => 0
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [2,3,4,1] => [2,3,4,1] => 2
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,3,4,2] => [1,3,4,2] => 1
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 0
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [5,1,2,3,4] => [5,1,2,3,4] => ? = 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [4,1,2,3,5] => [4,1,2,3,5] => ? = 0
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [4,5,1,2,3] => [4,5,1,2,3] => ? = 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => ? = 0
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [3,1,2,4,5] => [3,1,2,4,5] => ? = 0
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [3,5,1,2,4] => [3,5,1,2,4] => ? = 1
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [4,1,2,5,3] => [4,1,2,5,3] => ? = 1
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [3,4,1,2,5] => [3,4,1,2,5] => ? = 1
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [4,3,5,1,2] => [4,3,5,1,2] => ? = 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [2,1,5,3,4] => [2,1,5,3,4] => ? = 0
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [3,4,5,1,2] => [3,4,5,1,2] => ? = 2
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [2,1,4,5,3] => [2,1,4,5,3] => ? = 1
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ? = 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [2,5,1,3,4] => [2,5,1,3,4] => ? = 1
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [4,1,3,5,2] => [4,1,3,5,2] => ? = 1
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [4,2,5,1,3] => [4,2,5,1,3] => ? = 1
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [3,1,5,2,4] => [3,1,5,2,4] => ? = 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [3,1,4,2,5] => [3,1,4,2,5] => ? = 1
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [2,4,5,1,3] => [2,4,5,1,3] => ? = 2
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [3,1,4,5,2] => [3,1,4,5,2] => ? = 2
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [2,3,1,5,4] => [2,3,1,5,4] => ? = 1
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ? = 1
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [3,2,5,1,4] => [3,2,5,1,4] => ? = 1
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [4,1,5,2,3] => [4,1,5,2,3] => ? = 1
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [3,2,4,1,5] => [3,2,4,1,5] => ? = 1
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => [4,2,3,5,1] => [4,2,3,5,1] => ? = 1
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,5,2,3,4] => [1,5,2,3,4] => 0
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,4,2,3,5] => [1,4,2,3,5] => 0
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [3,2,4,5,1] => [3,2,4,5,1] => ? = 2
{{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [1,4,5,2,3] => [1,4,5,2,3] => 1
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
{{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 0
{{1,4,5},{2},{3}}
=> [4,2,3,5,1] => [2,3,5,1,4] => [2,3,5,1,4] => ? = 2
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => [3,4,1,5,2] => [3,4,1,5,2] => ? = 3
{{1,4},{2},{3,5}}
=> [4,2,5,1,3] => [2,4,1,5,3] => [2,4,1,5,3] => ? = 2
{{1,4},{2},{3},{5}}
=> [4,2,3,1,5] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 2
{{1,5},{2,4},{3}}
=> [5,4,3,2,1] => [3,4,2,5,1] => [3,4,2,5,1] => ? = 3
{{1},{2,4,5},{3}}
=> [1,4,3,5,2] => [1,3,5,2,4] => [1,3,5,2,4] => 1
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [1,4,2,5,3] => [1,4,2,5,3] => 1
{{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => [1,3,4,2,5] => [1,3,4,2,5] => 1
{{1,5},{2},{3,4}}
=> [5,2,4,3,1] => [2,4,3,5,1] => [2,4,3,5,1] => ? = 2
{{1},{2,5},{3,4}}
=> [1,5,4,3,2] => [1,4,3,5,2] => [1,4,3,5,2] => 1
{{1},{2},{3,4,5}}
=> [1,2,4,5,3] => [1,2,5,3,4] => [1,2,5,3,4] => 0
{{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 0
{{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => [2,3,4,5,1] => [2,3,4,5,1] => ? = 3
{{1},{2,5},{3},{4}}
=> [1,5,3,4,2] => [1,3,4,5,2] => [1,3,4,5,2] => 2
{{1},{2},{3,5},{4}}
=> [1,2,5,4,3] => [1,2,4,5,3] => [1,2,4,5,3] => 1
{{1},{2},{3},{4,5}}
=> [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 0
{{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => ? = 0
{{1,2,3,4,5},{6}}
=> [2,3,4,5,1,6] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => ? = 0
{{1,2,3,4,6},{5}}
=> [2,3,4,6,5,1] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 1
{{1,2,3,4},{5,6}}
=> [2,3,4,1,6,5] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => ? = 0
{{1,2,3,4},{5},{6}}
=> [2,3,4,1,5,6] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => ? = 0
{{1,2,3,5,6},{4}}
=> [2,3,5,4,6,1] => [4,6,1,2,3,5] => [4,6,1,2,3,5] => ? = 1
{{1,2,3,5},{4,6}}
=> [2,3,5,6,1,4] => [5,1,2,3,6,4] => [5,1,2,3,6,4] => ? = 1
{{1,2,3,5},{4},{6}}
=> [2,3,5,4,1,6] => [4,5,1,2,3,6] => [4,5,1,2,3,6] => ? = 1
{{1,2,3,6},{4,5}}
=> [2,3,6,5,4,1] => [5,4,6,1,2,3] => [5,4,6,1,2,3] => ? = 1
{{1,2,3},{4,5,6}}
=> [2,3,1,5,6,4] => [3,1,2,6,4,5] => [3,1,2,6,4,5] => ? = 0
{{1,2,3},{4,5},{6}}
=> [2,3,1,5,4,6] => [3,1,2,5,4,6] => [3,1,2,5,4,6] => ? = 0
{{1,2,3,6},{4},{5}}
=> [2,3,6,4,5,1] => [4,5,6,1,2,3] => [4,5,6,1,2,3] => ? = 2
{{1,2,3},{4,6},{5}}
=> [2,3,1,6,5,4] => [3,1,2,5,6,4] => [3,1,2,5,6,4] => ? = 1
Description
The number of occurrences of a type-B 231 pattern in a signed permutation.
For a signed permutation $\pi\in\mathfrak H_n$, a triple $-n \leq i < j < k\leq n$ is an occurrence of the type-B $231$ pattern, if $1 \leq j < k$, $\pi(i) < \pi(j)$ and $\pi(i)$ is one larger than $\pi(k)$, i.e., $\pi(i) = \pi(k) + 1$ if $\pi(k) \neq -1$ and $\pi(i) = 1$ otherwise.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!