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: St000249
(load all 25 compositions to match this statistic)
(load all 25 compositions to match this statistic)
St000249: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> 2
{{1},{2}}
=> 2
{{1,2,3}}
=> 3
{{1,2},{3}}
=> 2
{{1,3},{2}}
=> 2
{{1},{2,3}}
=> 2
{{1},{2},{3}}
=> 3
{{1,2,3,4}}
=> 4
{{1,2,3},{4}}
=> 3
{{1,2,4},{3}}
=> 3
{{1,2},{3,4}}
=> 2
{{1,2},{3},{4}}
=> 3
{{1,3,4},{2}}
=> 3
{{1,3},{2,4}}
=> 0
{{1,3},{2},{4}}
=> 2
{{1,4},{2,3}}
=> 2
{{1},{2,3,4}}
=> 3
{{1},{2,3},{4}}
=> 3
{{1,4},{2},{3}}
=> 3
{{1},{2,4},{3}}
=> 2
{{1},{2},{3,4}}
=> 3
{{1},{2},{3},{4}}
=> 4
{{1,2,3,4,5}}
=> 5
{{1,2,3,4},{5}}
=> 4
{{1,2,3,5},{4}}
=> 4
{{1,2,3},{4,5}}
=> 3
{{1,2,3},{4},{5}}
=> 4
{{1,2,4,5},{3}}
=> 4
{{1,2,4},{3,5}}
=> 1
{{1,2,4},{3},{5}}
=> 3
{{1,2,5},{3,4}}
=> 3
{{1,2},{3,4,5}}
=> 3
{{1,2},{3,4},{5}}
=> 3
{{1,2,5},{3},{4}}
=> 4
{{1,2},{3,5},{4}}
=> 2
{{1,2},{3},{4,5}}
=> 3
{{1,2},{3},{4},{5}}
=> 4
{{1,3,4,5},{2}}
=> 4
{{1,3,4},{2,5}}
=> 1
{{1,3,4},{2},{5}}
=> 3
{{1,3,5},{2,4}}
=> 1
{{1,3},{2,4,5}}
=> 1
{{1,3},{2,4},{5}}
=> 1
{{1,3,5},{2},{4}}
=> 3
{{1,3},{2,5},{4}}
=> 1
{{1,3},{2},{4,5}}
=> 2
{{1,3},{2},{4},{5}}
=> 3
{{1,4,5},{2,3}}
=> 3
{{1,4},{2,3,5}}
=> 1
{{1,4},{2,3},{5}}
=> 2
Description
The number of singletons ([[St000247]]) plus the number of antisingletons ([[St000248]]) of a set partition.
Matching statistic: St000236
(load all 21 compositions to match this statistic)
(load all 21 compositions to match this statistic)
Mp00080: Set partitions —to permutation⟶ Permutations
St000236: Permutations ⟶ ℤResult quality: 23% ●values known / values provided: 23%●distinct values known / distinct values provided: 78%
St000236: Permutations ⟶ ℤResult quality: 23% ●values known / values provided: 23%●distinct values known / distinct values provided: 78%
Values
{{1,2}}
=> [2,1] => 2
{{1},{2}}
=> [1,2] => 2
{{1,2,3}}
=> [2,3,1] => 3
{{1,2},{3}}
=> [2,1,3] => 2
{{1,3},{2}}
=> [3,2,1] => 2
{{1},{2,3}}
=> [1,3,2] => 2
{{1},{2},{3}}
=> [1,2,3] => 3
{{1,2,3,4}}
=> [2,3,4,1] => 4
{{1,2,3},{4}}
=> [2,3,1,4] => 3
{{1,2,4},{3}}
=> [2,4,3,1] => 3
{{1,2},{3,4}}
=> [2,1,4,3] => 2
{{1,2},{3},{4}}
=> [2,1,3,4] => 3
{{1,3,4},{2}}
=> [3,2,4,1] => 3
{{1,3},{2,4}}
=> [3,4,1,2] => 0
{{1,3},{2},{4}}
=> [3,2,1,4] => 2
{{1,4},{2,3}}
=> [4,3,2,1] => 2
{{1},{2,3,4}}
=> [1,3,4,2] => 3
{{1},{2,3},{4}}
=> [1,3,2,4] => 3
{{1,4},{2},{3}}
=> [4,2,3,1] => 3
{{1},{2,4},{3}}
=> [1,4,3,2] => 2
{{1},{2},{3,4}}
=> [1,2,4,3] => 3
{{1},{2},{3},{4}}
=> [1,2,3,4] => 4
{{1,2,3,4,5}}
=> [2,3,4,5,1] => 5
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => 4
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => 4
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => 3
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => 4
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => 4
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => 1
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => 3
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => 3
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => 3
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => 3
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => 4
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => 2
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => 3
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => 4
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => 4
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => 1
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => 3
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => 1
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => 1
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => 1
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => 3
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => 1
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => 2
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => 3
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => 3
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => 1
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => 2
{{1,2,3,4,5,6,7}}
=> [2,3,4,5,6,7,1] => ? = 7
{{1,2,3,4,5,6},{7}}
=> [2,3,4,5,6,1,7] => ? = 6
{{1,2,3,4,5,7},{6}}
=> [2,3,4,5,7,6,1] => ? = 6
{{1,2,3,4,5},{6,7}}
=> [2,3,4,5,1,7,6] => ? = 5
{{1,2,3,4,5},{6},{7}}
=> [2,3,4,5,1,6,7] => ? = 6
{{1,2,3,4,6,7},{5}}
=> [2,3,4,6,5,7,1] => ? = 6
{{1,2,3,4,6},{5,7}}
=> [2,3,4,6,7,1,5] => ? = 3
{{1,2,3,4,6},{5},{7}}
=> [2,3,4,6,5,1,7] => ? = 5
{{1,2,3,4,7},{5,6}}
=> [2,3,4,7,6,5,1] => ? = 5
{{1,2,3,4},{5,6,7}}
=> [2,3,4,1,6,7,5] => ? = 5
{{1,2,3,4},{5,6},{7}}
=> [2,3,4,1,6,5,7] => ? = 5
{{1,2,3,4,7},{5},{6}}
=> [2,3,4,7,5,6,1] => ? = 6
{{1,2,3,4},{5,7},{6}}
=> [2,3,4,1,7,6,5] => ? = 4
{{1,2,3,4},{5},{6,7}}
=> [2,3,4,1,5,7,6] => ? = 5
{{1,2,3,4},{5},{6},{7}}
=> [2,3,4,1,5,6,7] => ? = 6
{{1,2,3,5,6,7},{4}}
=> [2,3,5,4,6,7,1] => ? = 6
{{1,2,3,5,6},{4,7}}
=> [2,3,5,7,6,1,4] => ? = 3
{{1,2,3,5,6},{4},{7}}
=> [2,3,5,4,6,1,7] => ? = 5
{{1,2,3,5,7},{4,6}}
=> [2,3,5,6,7,4,1] => ? = 3
{{1,2,3,5},{4,6,7}}
=> [2,3,5,6,1,7,4] => ? = 3
{{1,2,3,5},{4,6},{7}}
=> [2,3,5,6,1,4,7] => ? = 3
{{1,2,3,5,7},{4},{6}}
=> [2,3,5,4,7,6,1] => ? = 5
{{1,2,3,5},{4,7},{6}}
=> [2,3,5,7,1,6,4] => ? = 3
{{1,2,3,5},{4},{6,7}}
=> [2,3,5,4,1,7,6] => ? = 4
{{1,2,3,5},{4},{6},{7}}
=> [2,3,5,4,1,6,7] => ? = 5
{{1,2,3,6,7},{4,5}}
=> [2,3,6,5,4,7,1] => ? = 5
{{1,2,3,6},{4,5,7}}
=> [2,3,6,5,7,1,4] => ? = 3
{{1,2,3,6},{4,5},{7}}
=> [2,3,6,5,4,1,7] => ? = 4
{{1,2,3,7},{4,5,6}}
=> [2,3,7,5,6,4,1] => ? = 5
{{1,2,3},{4,5,6,7}}
=> [2,3,1,5,6,7,4] => ? = 5
{{1,2,3},{4,5,6},{7}}
=> [2,3,1,5,6,4,7] => ? = 5
{{1,2,3,7},{4,5},{6}}
=> [2,3,7,5,4,6,1] => ? = 5
{{1,2,3},{4,5,7},{6}}
=> [2,3,1,5,7,6,4] => ? = 4
{{1,2,3},{4,5},{6,7}}
=> [2,3,1,5,4,7,6] => ? = 4
{{1,2,3},{4,5},{6},{7}}
=> [2,3,1,5,4,6,7] => ? = 5
{{1,2,3,6,7},{4},{5}}
=> [2,3,6,4,5,7,1] => ? = 6
{{1,2,3,6},{4,7},{5}}
=> [2,3,6,7,5,1,4] => ? = 3
{{1,2,3,6},{4},{5,7}}
=> [2,3,6,4,7,1,5] => ? = 3
{{1,2,3,6},{4},{5},{7}}
=> [2,3,6,4,5,1,7] => ? = 5
{{1,2,3,7},{4,6},{5}}
=> [2,3,7,6,5,4,1] => ? = 4
{{1,2,3},{4,6,7},{5}}
=> [2,3,1,6,5,7,4] => ? = 4
{{1,2,3},{4,6},{5,7}}
=> [2,3,1,6,7,4,5] => ? = 2
{{1,2,3},{4,6},{5},{7}}
=> [2,3,1,6,5,4,7] => ? = 4
{{1,2,3,7},{4},{5,6}}
=> [2,3,7,4,6,5,1] => ? = 5
{{1,2,3},{4,7},{5,6}}
=> [2,3,1,7,6,5,4] => ? = 3
{{1,2,3},{4},{5,6,7}}
=> [2,3,1,4,6,7,5] => ? = 5
{{1,2,3},{4},{5,6},{7}}
=> [2,3,1,4,6,5,7] => ? = 5
{{1,2,3,7},{4},{5},{6}}
=> [2,3,7,4,5,6,1] => ? = 6
{{1,2,3},{4,7},{5},{6}}
=> [2,3,1,7,5,6,4] => ? = 4
{{1,2,3},{4},{5,7},{6}}
=> [2,3,1,4,7,6,5] => ? = 4
Description
The number of cyclical small weak excedances.
A cyclical small weak excedance is an index $i$ such that $\pi_i \in \{ i,i+1 \}$ considered cyclically.
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!