Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000976
(load all 7 compositions to match this statistic)
Mapping
St000976: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => 0
[1,1,0,0]
 => 1
[1,0,1,0,1,0]
 => 0
[1,0,1,1,0,0]
 => 3
[1,1,0,0,1,0]
 => 1
[1,1,0,1,0,0]
 => 1
[1,1,1,0,0,0]
 => 3
[1,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,1,0,0]
 => 5
[1,0,1,1,0,0,1,0]
 => 3
[1,0,1,1,0,1,0,0]
 => 3
[1,0,1,1,1,0,0,0]
 => 7
[1,1,0,0,1,0,1,0]
 => 1
[1,1,0,0,1,1,0,0]
 => 6
[1,1,0,1,0,0,1,0]
 => 1
[1,1,0,1,0,1,0,0]
 => 1
[1,1,0,1,1,0,0,0]
 => 5
[1,1,1,0,0,0,1,0]
 => 3
[1,1,1,0,0,1,0,0]
 => 3
[1,1,1,0,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,0]
 => 6
[1,0,1,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,0,1,1,0,0]
 => 7
[1,0,1,0,1,1,0,0,1,0]
 => 5
[1,0,1,0,1,1,0,1,0,0]
 => 5
[1,0,1,0,1,1,1,0,0,0]
 => 11
[1,0,1,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,0,0,1,1,0,0]
 => 10
[1,0,1,1,0,1,0,0,1,0]
 => 3
[1,0,1,1,0,1,0,1,0,0]
 => 3
[1,0,1,1,0,1,1,0,0,0]
 => 9
[1,0,1,1,1,0,0,0,1,0]
 => 7
[1,0,1,1,1,0,0,1,0,0]
 => 7
[1,0,1,1,1,0,1,0,0,0]
 => 7
[1,0,1,1,1,1,0,0,0,0]
 => 12
[1,1,0,0,1,0,1,0,1,0]
 => 1
[1,1,0,0,1,0,1,1,0,0]
 => 8
[1,1,0,0,1,1,0,0,1,0]
 => 6
[1,1,0,0,1,1,0,1,0,0]
 => 6
[1,1,0,0,1,1,1,0,0,0]
 => 12
[1,1,0,1,0,0,1,0,1,0]
 => 1
[1,1,0,1,0,0,1,1,0,0]
 => 8
[1,1,0,1,0,1,0,0,1,0]
 => 1
[1,1,0,1,0,1,0,1,0,0]
 => 1
[1,1,0,1,0,1,1,0,0,0]
 => 7
[1,1,0,1,1,0,0,0,1,0]
 => 5
[1,1,0,1,1,0,0,1,0,0]
 => 5
[1,1,0,1,1,0,1,0,0,0]
 => 5
[1,1,0,1,1,1,0,0,0,0]
 => 10
[1,1,1,0,0,0,1,0,1,0]
 => 3
Description
The sum of the positions of double up-steps of a Dyck path. This is part of MacMahon's equal index of a word, see [1, p. 135].
Matching statistic: St000208
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000208: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 15%
Values
[1,0,1,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => []
 => ? ∊ {0,1}
[1,1,0,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => []
 => ? ∊ {0,1}
[1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => []
 => ? ∊ {0,1,1,3,3}
[1,0,1,1,0,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => []
 => ? ∊ {0,1,1,3,3}
[1,1,0,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => []
 => ? ∊ {0,1,1,3,3}
[1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => []
 => ? ∊ {0,1,1,3,3}
[1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => []
 => ? ∊ {0,1,1,3,3}
[1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => [2,2]
 => 3
[1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => 6
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => 6
[1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => 6
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => 3
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => 3
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => 3
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => 5
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,4]
 => 12
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,4]
 => 12
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,4]
 => 12
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [3,3]
 => 6
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,4]
 => 12
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,4]
 => 12
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,4]
 => 12
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [3,3]
 => 6
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,4]
 => 12
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,4]
 => 12
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [3,3]
 => 6
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [2,2,2]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [2,2,2]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [2,2,2]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [2,2]
 => 3
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,3,2]
 => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [4,4]
 => 12
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [4,4]
 => 12
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [4,4]
 => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => [3,3]
 => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [4,4]
 => 12
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [4,4]
 => 12
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [4,4]
 => 12
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => [3,3]
 => 6
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [4,4]
 => 12
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [4,4]
 => 12
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => [3,3]
 => 6
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [2,2,2,2]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [2,2,2,2]
 => 3
Description
Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. Given $\lambda$ count how many ''integer partitions'' $w$ (weight) there are, such that $P_{\lambda,w}$ is integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has only integer lattice points as vertices. See also [[St000205]], [[St000206]] and [[St000207]].
Matching statistic: St001583
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001583: Permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 12%
Values
[1,0,1,0]
 => [1]
 => [1,0]
 => [2,1] => 0
[1,1,0,0]
 => []
 => []
 => [1] => ? = 1
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 3
[1,0,1,1,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,3,1] => 1
[1,1,0,0,1,0]
 => [2]
 => [1,0,1,0]
 => [3,1,2] => 1
[1,1,0,1,0,0]
 => [1]
 => [1,0]
 => [2,1] => 0
[1,1,1,0,0,0]
 => []
 => []
 => [1] => ? = 3
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => ? ∊ {3,3,5,5,6,6,7}
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [2,5,4,1,3] => ? ∊ {3,3,5,5,6,6,7}
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [6,1,2,5,3,4] => ? ∊ {3,3,5,5,6,6,7}
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => ? ∊ {3,3,5,5,6,6,7}
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [4,3,1,2] => 1
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? ∊ {3,3,5,5,6,6,7}
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [2,3,4,1] => 3
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => ? ∊ {3,3,5,5,6,6,7}
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 3
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,3,1] => 1
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,0,1,0]
 => [3,1,2] => 1
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0]
 => [2,1] => 0
[1,1,1,1,0,0,0,0]
 => []
 => []
 => [1] => ? ∊ {3,3,5,5,6,6,7}
[1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [8,1,4,5,2,7,3,6] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [7,3,4,1,6,2,5] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [4,1,2,5,8,7,3,6] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [3,1,4,7,6,2,5] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [2,3,6,5,1,4] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
 => [7,1,4,8,2,3,5,6] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [6,3,7,1,2,4,5] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [4,1,2,8,7,3,5,6] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [3,1,7,6,2,4,5] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [2,6,5,1,3,4] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [8,1,2,3,7,4,5,6] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [7,1,2,6,3,4,5] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [5,4,1,2,3] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [6,1,4,5,2,7,3] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [5,3,4,1,6,2] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [4,1,2,5,6,7,3] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [7,1,4,6,2,3,5] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [6,3,5,1,2,4] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [4,1,2,7,6,3,5] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [2,5,4,1,3] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [7,1,2,3,6,4,5] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [6,1,2,5,3,4] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [4,3,1,2] => 1
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [5,3,4,1,2] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [4,1,2,5,6,3] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [2,3,4,1] => 3
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,3,1] => 1
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,0,1,0]
 => [3,1,2] => 1
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1,0]
 => [2,1] => 0
[1,1,1,1,1,0,0,0,0,0]
 => []
 => []
 => [1] => ? ∊ {1,3,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1]
 => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
 => [10,1,4,6,2,7,9,3,5,8] => ? ∊ {1,1,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,14,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,19}
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [4,4,3,2,1]
 => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
 => [9,3,5,1,6,8,2,4,7] => ? ∊ {1,1,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,14,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,19}
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [5,3,3,2,1]
 => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
 => [4,1,2,10,6,7,9,3,5,8] => ? ∊ {1,1,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,14,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,19}
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [4,3,3,2,1]
 => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
 => [3,1,9,5,6,8,2,4,7] => ? ∊ {1,1,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,14,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,19}
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [3,3,3,2,1]
 => [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
 => [2,8,4,5,7,1,3,6] => ? ∊ {1,1,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,14,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,19}
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,2,1]
 => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
 => [7,1,10,6,2,3,9,4,5,8] => ? ∊ {1,1,3,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,14,14,14,14,14,14,14,15,15,15,15,15,16,16,16,16,16,16,18,18,18,18,19}
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [4,3,1,2] => 1
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [2,3,4,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 3
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,3,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [3]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [2]
 => [1,0,1,0]
 => [3,1,2] => 1
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1]
 => [1,0]
 => [2,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [4,3,1,2] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [2,3,4,1] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,3,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => [3]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [2]
 => [1,0,1,0]
 => [3,1,2] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1]
 => [1,0]
 => [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: St001232
(load all 2 compositions to match this statistic)
Mapping
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 15%
Values
[1,0,1,0]
 => [1,0,1,0]
 => [1,1,0,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[1,1,0,0]
 => [1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {0,1,3,3}
[1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? ∊ {0,1,3,3}
[1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? ∊ {0,1,3,3}
[1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? ∊ {0,1,3,3}
[1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,3,3,3,3,3,6,6,7}
[1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? ∊ {0,1,1,3,3,3,3,3,6,6,7}
[1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? ∊ {0,1,1,3,3,3,3,3,6,6,7}
[1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,3,3,3,3,3,6,6,7}
[1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? ∊ {0,1,1,3,3,3,3,3,6,6,7}
[1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,3,3,3,3,3,6,6,7}
[1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,3,3,3,3,3,6,6,7}
[1,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,3,3,3,3,3,6,6,7}
[1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,3,3,3,3,3,6,6,7}
[1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,3,3,3,3,3,6,6,7}
[1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,3,3,3,3,3,6,6,7}
[1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => 7
[1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => 5
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => 5
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => 7
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => 5
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => 7
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? ∊ {0,1,1,1,3,3,3,3,3,3,3,3,3,5,5,6,6,6,6,6,6,7,7,8,8,8,9,9,10,10,10,10,11,12,12}
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => 9
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0,1,0]
 => 7
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0,1,0]
 => 7
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0,1,0]
 => 7
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => 9
[1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0,1,0]
 => 5
[1,1,1,0,0,1,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0,1,0]
 => 5
[1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0,1,0]
 => 7
[1,1,1,0,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0,1,0]
 => 5
[1,1,1,0,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0,1,0]
 => 7
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => 9
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0,1,0]
 => 5
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0,1,0]
 => 7
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => 9
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001564
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001564: Integer partitions ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 8%
Values
[1,0,1,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => []
 => ? ∊ {0,1}
[1,1,0,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => []
 => ? ∊ {0,1}
[1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => []
 => ? ∊ {0,1,1,3,3}
[1,0,1,1,0,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => []
 => ? ∊ {0,1,1,3,3}
[1,1,0,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => []
 => ? ∊ {0,1,1,3,3}
[1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => []
 => ? ∊ {0,1,1,3,3}
[1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => []
 => ? ∊ {0,1,1,3,3}
[1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,3,3,3,3,5,5,6,6,7}
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => [2,2]
 => 3
[1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => 3
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => 3
[1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,1,0,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => []
 => ? ∊ {0,1,1,1,1,3,3,3,3,3,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,10,11,12,12}
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => 10
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => 10
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => 10
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [3,3]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [3,3]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [3,3]
 => 3
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [2,2,2]
 => 10
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [2,2,2]
 => 10
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [2,2,2]
 => 10
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [2,2]
 => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => [3,3]
 => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => [3,3]
 => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => [3,3]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [2,2,2]
 => 10
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [2,2,2]
 => 10
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [2,2,2]
 => 10
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => [2,2]
 => 3
Description
The value of the forgotten symmetric functions when all variables set to 1. Let $f_\lambda(x)$ denote the forgotten symmetric functions. Then the statistic associated with $\lambda$, where $\lambda$ has $\ell$ parts, is $f_\lambda(1,1,\dotsc,1)$ where there are $\ell$ variables substituted by $1$.