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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000949
St000949: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> 2
[1,0,1,0]
=> 3
[1,1,0,0]
=> 5
[1,0,1,0,1,0]
=> 4
[1,0,1,1,0,0]
=> 7
[1,1,0,0,1,0]
=> 7
[1,1,0,1,0,0]
=> 9
[1,1,1,0,0,0]
=> 14
[1,0,1,0,1,0,1,0]
=> 5
[1,0,1,0,1,1,0,0]
=> 9
[1,0,1,1,0,0,1,0]
=> 10
[1,0,1,1,0,1,0,0]
=> 11
[1,0,1,1,1,0,0,0]
=> 19
[1,1,0,0,1,0,1,0]
=> 9
[1,1,0,0,1,1,0,0]
=> 16
[1,1,0,1,0,0,1,0]
=> 11
[1,1,0,1,0,1,0,0]
=> 15
[1,1,0,1,1,0,0,0]
=> 23
[1,1,1,0,0,0,1,0]
=> 19
[1,1,1,0,0,1,0,0]
=> 23
[1,1,1,0,1,0,0,0]
=> 28
[1,1,1,1,0,0,0,0]
=> 42
[1,0,1,0,1,0,1,0,1,0]
=> 6
[1,0,1,0,1,0,1,1,0,0]
=> 11
[1,0,1,0,1,1,0,0,1,0]
=> 13
[1,0,1,0,1,1,0,1,0,0]
=> 13
[1,0,1,0,1,1,1,0,0,0]
=> 24
[1,0,1,1,0,0,1,0,1,0]
=> 13
[1,0,1,1,0,0,1,1,0,0]
=> 23
[1,0,1,1,0,1,0,0,1,0]
=> 13
[1,0,1,1,0,1,0,1,0,0]
=> 18
[1,0,1,1,0,1,1,0,0,0]
=> 27
[1,0,1,1,1,0,0,0,1,0]
=> 26
[1,0,1,1,1,0,0,1,0,0]
=> 32
[1,0,1,1,1,0,1,0,0,0]
=> 33
[1,0,1,1,1,1,0,0,0,0]
=> 56
[1,1,0,0,1,0,1,0,1,0]
=> 11
[1,1,0,0,1,0,1,1,0,0]
=> 20
[1,1,0,0,1,1,0,0,1,0]
=> 23
[1,1,0,0,1,1,0,1,0,0]
=> 24
[1,1,0,0,1,1,1,0,0,0]
=> 43
[1,1,0,1,0,0,1,0,1,0]
=> 13
[1,1,0,1,0,0,1,1,0,0]
=> 24
[1,1,0,1,0,1,0,0,1,0]
=> 18
[1,1,0,1,0,1,0,1,0,0]
=> 22
[1,1,0,1,0,1,1,0,0,0]
=> 37
[1,1,0,1,1,0,0,0,1,0]
=> 32
[1,1,0,1,1,0,0,1,0,0]
=> 32
[1,1,0,1,1,0,1,0,0,0]
=> 43
[1,1,0,1,1,1,0,0,0,0]
=> 66
Description
Gives the number of generalised tilting modules of the corresponding LNakayama algebra.
Matching statistic: St000104
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000104: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 18%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000104: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 18%
Values
[1,0]
=> [2,1] => [1,2] => ([(0,1)],2)
=> 3 = 2 + 1
[1,0,1,0]
=> [3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 6 = 5 + 1
[1,1,0,0]
=> [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 4 = 3 + 1
[1,0,1,0,1,0]
=> [4,1,2,3] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 10 = 9 + 1
[1,0,1,1,0,0]
=> [3,1,4,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? ∊ {7,7,14} + 1
[1,1,0,0,1,0]
=> [2,4,1,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? ∊ {7,7,14} + 1
[1,1,0,1,0,0]
=> [4,3,1,2] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? ∊ {7,7,14} + 1
[1,1,1,0,0,0]
=> [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 4 + 1
[1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => [3,4,5,1,2] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => [3,5,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => [4,1,5,3,2] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => [4,5,3,1,2] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => [5,1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => [1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => [4,5,2,1,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,0,1,1,0,0,0]
=> [4,3,1,5,2] => [5,2,1,4,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,1,0,0,1,0,0]
=> [2,5,4,1,3] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,1,0,1,0,0,0]
=> [5,3,4,1,2] => [5,2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 5 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [6,1,2,3,4,5] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,0,1,0,1,1,0,0]
=> [5,1,2,3,6,4] => [3,4,6,1,5,2] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,16),(1,18),(2,7),(2,17),(2,19),(3,11),(3,12),(3,16),(3,18),(4,10),(4,13),(4,18),(5,9),(5,10),(5,12),(5,18),(6,2),(6,9),(6,11),(6,13),(6,16),(7,20),(9,15),(9,17),(9,19),(9,22),(10,14),(10,19),(11,15),(11,17),(11,19),(11,22),(12,14),(12,15),(12,22),(13,7),(13,19),(13,22),(14,21),(15,20),(15,21),(16,17),(16,22),(17,20),(17,21),(18,14),(18,22),(19,20),(19,21),(20,8),(21,8),(22,20),(22,21)],23)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,0,1,1,0,0,1,0]
=> [4,1,2,6,3,5] => [3,5,1,6,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => [3,5,6,4,1,2] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,15),(2,6),(2,8),(2,18),(3,12),(3,13),(3,15),(4,10),(4,13),(4,15),(5,2),(5,10),(5,11),(5,12),(6,16),(6,17),(7,16),(7,17),(8,16),(10,14),(10,18),(11,8),(11,18),(12,6),(12,14),(12,18),(13,7),(13,14),(14,17),(15,7),(15,18),(16,9),(17,9),(18,16),(18,17)],19)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => [3,6,1,4,5,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,24),(1,25),(2,9),(2,11),(2,13),(2,15),(3,8),(3,10),(3,13),(3,14),(4,8),(4,11),(4,12),(4,16),(5,9),(5,10),(5,12),(5,17),(6,1),(6,14),(6,15),(6,16),(6,17),(8,20),(8,24),(9,20),(9,25),(10,20),(10,23),(10,25),(11,20),(11,23),(11,24),(12,19),(12,20),(13,18),(13,24),(13,25),(14,18),(14,23),(14,24),(15,18),(15,23),(15,25),(16,19),(16,23),(16,24),(16,25),(17,19),(17,23),(17,24),(17,25),(18,22),(19,21),(19,22),(20,21),(21,7),(22,7),(23,21),(23,22),(24,21),(24,22),(25,21),(25,22)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,0,0,1,0,1,0]
=> [3,1,6,2,4,5] => [4,1,5,6,3,2] => ([(0,3),(0,4),(0,5),(0,6),(1,11),(1,16),(1,18),(2,12),(2,15),(3,9),(3,14),(4,8),(4,10),(4,14),(5,1),(5,8),(5,13),(5,14),(6,2),(6,9),(6,10),(6,13),(8,16),(8,18),(9,15),(9,17),(10,15),(10,17),(10,18),(11,19),(11,20),(12,19),(12,20),(13,11),(13,12),(13,17),(13,18),(14,16),(14,17),(15,19),(16,20),(17,19),(17,20),(18,19),(18,20),(19,7),(20,7)],21)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,0,0,1,1,0,0]
=> [3,1,5,2,6,4] => [4,1,6,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,19),(1,20),(2,15),(2,16),(2,19),(2,20),(3,9),(3,12),(3,13),(3,19),(4,8),(4,11),(4,13),(4,15),(4,20),(5,7),(5,11),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,16),(6,17),(7,21),(7,25),(7,26),(7,27),(8,21),(8,24),(8,26),(9,24),(9,25),(9,26),(11,18),(11,21),(11,25),(12,18),(12,25),(12,27),(13,18),(13,26),(13,27),(14,21),(14,27),(15,24),(15,25),(15,27),(16,24),(16,26),(17,24),(17,26),(17,27),(18,23),(19,24),(19,27),(20,21),(20,25),(20,26),(20,27),(21,22),(21,23),(22,10),(23,10),(24,22),(25,22),(25,23),(26,22),(26,23),(27,22),(27,23)],28)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,0,1,0,0,1,0]
=> [6,1,4,2,3,5] => [4,5,3,6,1,2] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,15),(2,6),(2,8),(2,18),(3,12),(3,13),(3,15),(4,10),(4,13),(4,15),(5,2),(5,10),(5,11),(5,12),(6,16),(6,17),(7,16),(7,17),(8,16),(10,14),(10,18),(11,8),(11,18),(12,6),(12,14),(12,18),(13,7),(13,14),(14,17),(15,7),(15,18),(16,9),(17,9),(18,16),(18,17)],19)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => [4,5,6,3,1,2] => ([(0,3),(0,4),(0,5),(1,14),(2,6),(2,7),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,13),(7,13),(7,14),(9,1),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(12,14),(13,8),(14,8)],15)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => [4,6,3,1,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,15),(1,16),(2,8),(2,11),(2,16),(2,18),(3,8),(3,10),(3,15),(3,17),(4,9),(4,13),(4,14),(4,17),(4,18),(5,10),(5,12),(5,13),(5,16),(5,18),(6,11),(6,12),(6,14),(6,15),(6,17),(8,21),(8,25),(9,23),(9,24),(10,21),(10,23),(10,25),(11,21),(11,24),(11,25),(12,23),(12,24),(12,25),(13,19),(13,23),(13,25),(14,19),(14,24),(14,25),(15,24),(15,25),(16,23),(16,25),(17,19),(17,21),(17,23),(17,24),(18,19),(18,21),(18,23),(18,24),(19,20),(19,22),(20,7),(21,20),(21,22),(22,7),(23,20),(23,22),(24,20),(24,22),(25,22)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5] => [5,1,3,6,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(1,12),(1,18),(1,20),(2,11),(2,13),(2,17),(2,18),(3,14),(3,15),(3,17),(3,18),(3,20),(4,9),(4,13),(4,15),(4,20),(5,7),(5,9),(5,12),(5,17),(6,7),(6,10),(6,11),(6,14),(6,20),(7,24),(7,25),(7,26),(9,19),(9,26),(10,24),(10,25),(11,21),(11,24),(11,25),(12,24),(12,26),(13,19),(13,21),(14,16),(14,24),(14,25),(15,16),(15,19),(15,21),(16,22),(16,23),(17,19),(17,25),(17,26),(18,21),(18,24),(18,26),(19,23),(20,16),(20,21),(20,25),(20,26),(21,22),(21,23),(22,8),(23,8),(24,22),(25,22),(25,23),(26,22),(26,23)],27)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => [5,1,6,4,3,2] => ([(0,2),(0,3),(0,4),(0,6),(1,15),(1,17),(2,12),(2,13),(3,7),(3,12),(4,8),(4,12),(4,13),(5,1),(5,10),(5,11),(5,14),(6,5),(6,7),(6,8),(6,13),(7,10),(7,16),(8,11),(8,14),(8,16),(10,15),(10,17),(11,15),(11,17),(12,16),(13,14),(13,16),(14,15),(14,17),(15,9),(16,17),(17,9)],18)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => [5,6,3,4,1,2] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(1,12),(2,6),(2,7),(2,12),(3,5),(3,7),(3,12),(5,9),(5,10),(6,9),(6,11),(7,9),(7,10),(7,11),(8,4),(9,13),(10,8),(10,13),(11,8),(11,13),(12,10),(12,11),(13,4)],14)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => [6,1,3,4,5,2] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,0,1,0,1,0,1,0]
=> [2,6,1,3,4,5] => [1,4,5,6,2,3] => ([(0,3),(0,4),(0,5),(1,14),(2,6),(2,8),(2,14),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,13),(6,15),(8,13),(8,15),(9,12),(9,14),(10,8),(10,12),(11,6),(11,12),(11,14),(12,13),(12,15),(13,7),(14,15),(15,7)],16)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => [1,4,6,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,19),(2,10),(2,13),(2,19),(2,20),(3,9),(3,13),(3,18),(3,20),(4,12),(4,14),(4,18),(4,19),(4,20),(5,11),(5,14),(5,18),(5,19),(5,20),(6,8),(6,9),(6,10),(6,11),(6,12),(8,21),(8,22),(9,15),(9,21),(9,25),(10,15),(10,22),(10,25),(11,16),(11,21),(11,22),(11,25),(12,16),(12,21),(12,22),(12,25),(13,15),(13,25),(14,16),(14,17),(14,25),(15,24),(16,23),(16,24),(17,23),(18,17),(18,21),(18,25),(19,17),(19,22),(19,25),(20,17),(20,25),(21,23),(21,24),(22,23),(22,24),(23,7),(24,7),(25,23),(25,24)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => [1,5,2,6,4,3] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,17),(1,19),(2,7),(2,18),(2,22),(3,9),(3,11),(3,19),(4,10),(4,12),(4,17),(4,19),(5,11),(5,12),(5,13),(5,19),(6,2),(6,9),(6,10),(6,13),(6,17),(7,20),(7,21),(9,16),(9,18),(9,22),(10,15),(10,18),(10,22),(11,14),(11,16),(12,14),(12,15),(12,22),(13,7),(13,15),(13,16),(13,22),(14,21),(15,20),(15,21),(16,20),(16,21),(17,18),(17,22),(18,20),(19,14),(19,22),(20,8),(21,8),(22,20),(22,21)],23)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,6,1,5,3,4] => [1,5,6,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(1,9),(2,9),(2,10),(2,12),(3,8),(3,10),(3,11),(4,7),(4,11),(4,12),(5,17),(7,14),(7,15),(8,13),(8,14),(9,13),(9,15),(10,13),(10,16),(11,5),(11,14),(11,16),(12,5),(12,15),(12,16),(13,18),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,6),(18,6)],19)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => [1,6,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,0,0,1,0,1,0]
=> [6,3,1,2,4,5] => [4,2,5,6,1,3] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,16),(1,18),(2,7),(2,17),(2,19),(3,11),(3,12),(3,16),(3,18),(4,10),(4,13),(4,18),(5,9),(5,10),(5,12),(5,18),(6,2),(6,9),(6,11),(6,13),(6,16),(7,20),(9,15),(9,17),(9,19),(9,22),(10,14),(10,19),(11,15),(11,17),(11,19),(11,22),(12,14),(12,15),(12,22),(13,7),(13,19),(13,22),(14,21),(15,20),(15,21),(16,17),(16,22),(17,20),(17,21),(18,14),(18,22),(19,20),(19,21),(20,8),(21,8),(22,20),(22,21)],23)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,0,0,1,1,0,0]
=> [5,3,1,2,6,4] => [4,2,6,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(1,13),(1,16),(1,17),(2,9),(2,13),(2,15),(2,17),(3,12),(3,14),(3,15),(3,17),(4,11),(4,14),(4,16),(4,17),(5,8),(5,11),(5,12),(5,15),(5,16),(6,8),(6,9),(6,10),(6,15),(6,16),(8,19),(8,20),(9,19),(9,22),(9,23),(10,20),(10,22),(10,23),(11,19),(11,22),(11,24),(12,20),(12,22),(12,24),(13,22),(13,23),(14,22),(14,24),(15,19),(15,20),(15,23),(15,24),(16,19),(16,20),(16,23),(16,24),(17,23),(17,24),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,21),(23,18),(23,21),(24,18),(24,21)],25)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => [4,5,2,6,1,3] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,16),(1,18),(2,8),(2,17),(2,19),(2,22),(3,11),(3,12),(3,18),(4,13),(4,14),(4,16),(4,18),(5,10),(5,11),(5,13),(5,16),(6,2),(6,10),(6,12),(6,14),(6,18),(7,20),(8,20),(8,21),(10,15),(10,19),(10,22),(11,15),(11,22),(12,15),(12,17),(12,19),(13,7),(13,19),(13,22),(14,8),(14,17),(14,19),(14,22),(15,21),(16,7),(16,22),(17,20),(17,21),(18,17),(18,22),(19,20),(19,21),(20,9),(21,9),(22,20),(22,21)],23)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,0,1,1,0,0,0]
=> [5,4,1,2,6,3] => [4,6,2,1,5,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,21),(2,11),(2,13),(2,15),(3,12),(3,14),(3,15),(4,8),(4,10),(4,12),(4,15),(5,9),(5,10),(5,13),(5,15),(6,1),(6,8),(6,9),(6,11),(6,14),(8,17),(8,18),(8,19),(8,20),(9,17),(9,18),(9,19),(9,20),(10,20),(10,21),(11,17),(11,19),(12,18),(12,20),(13,17),(13,21),(14,18),(14,19),(14,21),(15,19),(15,20),(15,21),(16,7),(17,16),(17,22),(18,16),(18,22),(19,16),(19,22),(20,16),(20,22),(21,22),(22,7)],23)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,1,0,0,0,1,0]
=> [4,3,1,6,2,5] => [5,2,1,6,4,3] => ([(0,3),(0,4),(0,5),(0,6),(1,12),(1,19),(2,16),(2,19),(3,8),(3,13),(4,7),(4,9),(4,13),(5,2),(5,9),(5,10),(5,13),(6,1),(6,7),(6,8),(6,10),(7,14),(7,17),(7,19),(8,17),(8,19),(9,14),(9,16),(9,19),(10,12),(10,14),(10,16),(10,17),(12,15),(12,18),(13,16),(13,17),(14,15),(14,18),(15,11),(16,15),(16,18),(17,15),(17,18),(18,11),(19,18)],20)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,1,0,0,1,0,0]
=> [6,3,1,5,2,4] => [5,2,6,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,15),(1,16),(2,8),(2,11),(2,16),(2,18),(3,8),(3,10),(3,15),(3,17),(4,9),(4,13),(4,14),(4,17),(4,18),(5,10),(5,12),(5,13),(5,16),(5,18),(6,11),(6,12),(6,14),(6,15),(6,17),(8,21),(8,25),(9,23),(9,24),(10,21),(10,23),(10,25),(11,21),(11,24),(11,25),(12,23),(12,24),(12,25),(13,19),(13,23),(13,25),(14,19),(14,24),(14,25),(15,24),(15,25),(16,23),(16,25),(17,19),(17,21),(17,23),(17,24),(18,19),(18,21),(18,23),(18,24),(19,20),(19,22),(20,7),(21,20),(21,22),(22,7),(23,20),(23,22),(24,20),(24,22),(25,22)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,1,0,1,0,0,0]
=> [6,4,1,5,2,3] => [5,6,2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,10),(1,15),(1,16),(2,11),(2,15),(2,16),(3,13),(3,15),(3,16),(4,12),(4,15),(4,16),(5,8),(5,9),(5,14),(5,20),(6,5),(6,10),(6,11),(6,12),(6,13),(8,17),(8,19),(9,17),(9,19),(10,18),(10,20),(11,14),(11,18),(11,20),(12,8),(12,18),(12,20),(13,9),(13,18),(13,20),(14,17),(14,19),(15,14),(15,20),(16,14),(16,18),(17,7),(18,19),(19,7),(20,17),(20,19)],21)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,1,1,0,0,0,0]
=> [4,3,1,5,6,2] => [6,2,1,4,5,3] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,15),(1,18),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,9),(4,10),(4,13),(5,1),(5,8),(5,11),(5,13),(6,19),(6,20),(8,14),(8,18),(9,14),(9,16),(10,16),(10,17),(11,15),(11,17),(11,18),(12,15),(12,16),(12,18),(13,6),(13,14),(13,17),(14,19),(15,20),(16,19),(16,20),(17,19),(17,20),(18,19),(18,20),(19,7),(20,7)],21)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,0,0,1,0,1,0]
=> [2,3,6,1,4,5] => [1,2,5,6,3,4] => ([(0,2),(0,3),(0,4),(1,8),(1,9),(2,1),(2,10),(2,11),(3,6),(3,7),(3,11),(4,6),(4,7),(4,10),(6,14),(7,12),(7,14),(8,13),(8,15),(9,13),(9,15),(10,8),(10,12),(10,14),(11,9),(11,12),(11,14),(12,13),(12,15),(13,5),(14,15),(15,5)],16)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => [1,2,6,3,5,4] => ([(0,1),(0,2),(0,4),(0,5),(1,9),(1,16),(2,10),(2,16),(3,6),(3,7),(3,15),(4,9),(4,11),(4,16),(5,3),(5,10),(5,11),(5,16),(6,13),(7,13),(7,14),(9,12),(10,6),(10,15),(11,7),(11,12),(11,15),(12,14),(13,8),(14,8),(15,13),(15,14),(16,12),(16,15)],17)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,0,1,0,0,1,0]
=> [2,6,4,1,3,5] => [1,5,3,6,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,17),(1,18),(2,12),(2,14),(2,18),(2,19),(3,11),(3,14),(3,17),(3,19),(4,10),(4,13),(4,17),(4,18),(4,19),(5,9),(5,13),(5,17),(5,18),(5,19),(6,8),(6,9),(6,10),(6,11),(6,12),(8,21),(8,22),(9,20),(9,21),(9,22),(9,25),(10,20),(10,21),(10,22),(10,25),(11,15),(11,20),(11,21),(12,15),(12,20),(12,22),(13,16),(13,25),(14,15),(14,25),(15,24),(16,23),(17,16),(17,21),(17,25),(18,16),(18,22),(18,25),(19,16),(19,20),(19,25),(20,23),(20,24),(21,23),(21,24),(22,23),(22,24),(23,7),(24,7),(25,23),(25,24)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,0,1,0,1,0,0]
=> [2,6,5,1,3,4] => [1,5,6,3,2,4] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,15),(1,18),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,9),(4,10),(4,13),(5,1),(5,8),(5,11),(5,13),(6,19),(6,20),(8,14),(8,18),(9,14),(9,16),(10,16),(10,17),(11,15),(11,17),(11,18),(12,15),(12,16),(12,18),(13,6),(13,14),(13,17),(14,19),(15,20),(16,19),(16,20),(17,19),(17,20),(18,19),(18,20),(19,7),(20,7)],21)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,0,1,1,0,0,0]
=> [2,5,4,1,6,3] => [1,6,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(1,11),(1,12),(2,8),(2,9),(2,12),(3,6),(3,7),(3,9),(3,11),(4,6),(4,7),(4,8),(4,10),(6,14),(6,19),(7,13),(7,15),(7,19),(8,13),(8,19),(9,13),(9,16),(9,19),(10,14),(10,15),(10,19),(11,14),(11,15),(11,16),(12,16),(12,19),(13,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,5),(18,5),(19,17),(19,18)],20)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,1,0,0,0,1,0]
=> [6,3,4,1,2,5] => [5,2,3,6,1,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,24),(1,25),(2,9),(2,11),(2,13),(2,15),(3,8),(3,10),(3,13),(3,14),(4,8),(4,11),(4,12),(4,16),(5,9),(5,10),(5,12),(5,17),(6,1),(6,14),(6,15),(6,16),(6,17),(8,20),(8,24),(9,20),(9,25),(10,20),(10,23),(10,25),(11,20),(11,23),(11,24),(12,19),(12,20),(13,18),(13,24),(13,25),(14,18),(14,23),(14,24),(15,18),(15,23),(15,25),(16,19),(16,23),(16,24),(16,25),(17,19),(17,23),(17,24),(17,25),(18,22),(19,21),(19,22),(20,21),(21,7),(22,7),(23,21),(23,22),(24,21),(24,22),(25,21),(25,22)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 7 = 6 + 1
Description
The number of facets in the order polytope of this poset.
Matching statistic: St000151
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000151: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 18%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000151: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 18%
Values
[1,0]
=> [2,1] => [1,2] => ([(0,1)],2)
=> 3 = 2 + 1
[1,0,1,0]
=> [3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 6 = 5 + 1
[1,1,0,0]
=> [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 4 = 3 + 1
[1,0,1,0,1,0]
=> [4,1,2,3] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 10 = 9 + 1
[1,0,1,1,0,0]
=> [3,1,4,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? ∊ {7,7,14} + 1
[1,1,0,0,1,0]
=> [2,4,1,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? ∊ {7,7,14} + 1
[1,1,0,1,0,0]
=> [4,3,1,2] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? ∊ {7,7,14} + 1
[1,1,1,0,0,0]
=> [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 4 + 1
[1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => [3,4,5,1,2] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => [3,5,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => [4,1,5,3,2] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => [4,5,3,1,2] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => [5,1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => [1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => [4,5,2,1,3] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,0,1,1,0,0,0]
=> [4,3,1,5,2] => [5,2,1,4,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,1,0,0,1,0,0]
=> [2,5,4,1,3] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,1,0,1,0,0,0]
=> [5,3,4,1,2] => [5,2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? ∊ {9,9,10,11,11,15,16,19,19,23,23,28,42} + 1
[1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 5 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [6,1,2,3,4,5] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,0,1,0,1,1,0,0]
=> [5,1,2,3,6,4] => [3,4,6,1,5,2] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,16),(1,18),(2,7),(2,17),(2,19),(3,11),(3,12),(3,16),(3,18),(4,10),(4,13),(4,18),(5,9),(5,10),(5,12),(5,18),(6,2),(6,9),(6,11),(6,13),(6,16),(7,20),(9,15),(9,17),(9,19),(9,22),(10,14),(10,19),(11,15),(11,17),(11,19),(11,22),(12,14),(12,15),(12,22),(13,7),(13,19),(13,22),(14,21),(15,20),(15,21),(16,17),(16,22),(17,20),(17,21),(18,14),(18,22),(19,20),(19,21),(20,8),(21,8),(22,20),(22,21)],23)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,0,1,1,0,0,1,0]
=> [4,1,2,6,3,5] => [3,5,1,6,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => [3,5,6,4,1,2] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,15),(2,6),(2,8),(2,18),(3,12),(3,13),(3,15),(4,10),(4,13),(4,15),(5,2),(5,10),(5,11),(5,12),(6,16),(6,17),(7,16),(7,17),(8,16),(10,14),(10,18),(11,8),(11,18),(12,6),(12,14),(12,18),(13,7),(13,14),(14,17),(15,7),(15,18),(16,9),(17,9),(18,16),(18,17)],19)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => [3,6,1,4,5,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,24),(1,25),(2,9),(2,11),(2,13),(2,15),(3,8),(3,10),(3,13),(3,14),(4,8),(4,11),(4,12),(4,16),(5,9),(5,10),(5,12),(5,17),(6,1),(6,14),(6,15),(6,16),(6,17),(8,20),(8,24),(9,20),(9,25),(10,20),(10,23),(10,25),(11,20),(11,23),(11,24),(12,19),(12,20),(13,18),(13,24),(13,25),(14,18),(14,23),(14,24),(15,18),(15,23),(15,25),(16,19),(16,23),(16,24),(16,25),(17,19),(17,23),(17,24),(17,25),(18,22),(19,21),(19,22),(20,21),(21,7),(22,7),(23,21),(23,22),(24,21),(24,22),(25,21),(25,22)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,0,0,1,0,1,0]
=> [3,1,6,2,4,5] => [4,1,5,6,3,2] => ([(0,3),(0,4),(0,5),(0,6),(1,11),(1,16),(1,18),(2,12),(2,15),(3,9),(3,14),(4,8),(4,10),(4,14),(5,1),(5,8),(5,13),(5,14),(6,2),(6,9),(6,10),(6,13),(8,16),(8,18),(9,15),(9,17),(10,15),(10,17),(10,18),(11,19),(11,20),(12,19),(12,20),(13,11),(13,12),(13,17),(13,18),(14,16),(14,17),(15,19),(16,20),(17,19),(17,20),(18,19),(18,20),(19,7),(20,7)],21)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,0,0,1,1,0,0]
=> [3,1,5,2,6,4] => [4,1,6,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,19),(1,20),(2,15),(2,16),(2,19),(2,20),(3,9),(3,12),(3,13),(3,19),(4,8),(4,11),(4,13),(4,15),(4,20),(5,7),(5,11),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,16),(6,17),(7,21),(7,25),(7,26),(7,27),(8,21),(8,24),(8,26),(9,24),(9,25),(9,26),(11,18),(11,21),(11,25),(12,18),(12,25),(12,27),(13,18),(13,26),(13,27),(14,21),(14,27),(15,24),(15,25),(15,27),(16,24),(16,26),(17,24),(17,26),(17,27),(18,23),(19,24),(19,27),(20,21),(20,25),(20,26),(20,27),(21,22),(21,23),(22,10),(23,10),(24,22),(25,22),(25,23),(26,22),(26,23),(27,22),(27,23)],28)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,0,1,0,0,1,0]
=> [6,1,4,2,3,5] => [4,5,3,6,1,2] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,15),(2,6),(2,8),(2,18),(3,12),(3,13),(3,15),(4,10),(4,13),(4,15),(5,2),(5,10),(5,11),(5,12),(6,16),(6,17),(7,16),(7,17),(8,16),(10,14),(10,18),(11,8),(11,18),(12,6),(12,14),(12,18),(13,7),(13,14),(14,17),(15,7),(15,18),(16,9),(17,9),(18,16),(18,17)],19)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => [4,5,6,3,1,2] => ([(0,3),(0,4),(0,5),(1,14),(2,6),(2,7),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,13),(7,13),(7,14),(9,1),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(12,14),(13,8),(14,8)],15)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => [4,6,3,1,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,15),(1,16),(2,8),(2,11),(2,16),(2,18),(3,8),(3,10),(3,15),(3,17),(4,9),(4,13),(4,14),(4,17),(4,18),(5,10),(5,12),(5,13),(5,16),(5,18),(6,11),(6,12),(6,14),(6,15),(6,17),(8,21),(8,25),(9,23),(9,24),(10,21),(10,23),(10,25),(11,21),(11,24),(11,25),(12,23),(12,24),(12,25),(13,19),(13,23),(13,25),(14,19),(14,24),(14,25),(15,24),(15,25),(16,23),(16,25),(17,19),(17,21),(17,23),(17,24),(18,19),(18,21),(18,23),(18,24),(19,20),(19,22),(20,7),(21,20),(21,22),(22,7),(23,20),(23,22),(24,20),(24,22),(25,22)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5] => [5,1,3,6,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(1,12),(1,18),(1,20),(2,11),(2,13),(2,17),(2,18),(3,14),(3,15),(3,17),(3,18),(3,20),(4,9),(4,13),(4,15),(4,20),(5,7),(5,9),(5,12),(5,17),(6,7),(6,10),(6,11),(6,14),(6,20),(7,24),(7,25),(7,26),(9,19),(9,26),(10,24),(10,25),(11,21),(11,24),(11,25),(12,24),(12,26),(13,19),(13,21),(14,16),(14,24),(14,25),(15,16),(15,19),(15,21),(16,22),(16,23),(17,19),(17,25),(17,26),(18,21),(18,24),(18,26),(19,23),(20,16),(20,21),(20,25),(20,26),(21,22),(21,23),(22,8),(23,8),(24,22),(25,22),(25,23),(26,22),(26,23)],27)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => [5,1,6,4,3,2] => ([(0,2),(0,3),(0,4),(0,6),(1,15),(1,17),(2,12),(2,13),(3,7),(3,12),(4,8),(4,12),(4,13),(5,1),(5,10),(5,11),(5,14),(6,5),(6,7),(6,8),(6,13),(7,10),(7,16),(8,11),(8,14),(8,16),(10,15),(10,17),(11,15),(11,17),(12,16),(13,14),(13,16),(14,15),(14,17),(15,9),(16,17),(17,9)],18)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => [5,6,3,4,1,2] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(1,12),(2,6),(2,7),(2,12),(3,5),(3,7),(3,12),(5,9),(5,10),(6,9),(6,11),(7,9),(7,10),(7,11),(8,4),(9,13),(10,8),(10,13),(11,8),(11,13),(12,10),(12,11),(13,4)],14)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => [6,1,3,4,5,2] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,0,1,0,1,0,1,0]
=> [2,6,1,3,4,5] => [1,4,5,6,2,3] => ([(0,3),(0,4),(0,5),(1,14),(2,6),(2,8),(2,14),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,13),(6,15),(8,13),(8,15),(9,12),(9,14),(10,8),(10,12),(11,6),(11,12),(11,14),(12,13),(12,15),(13,7),(14,15),(15,7)],16)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => [1,4,6,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,19),(2,10),(2,13),(2,19),(2,20),(3,9),(3,13),(3,18),(3,20),(4,12),(4,14),(4,18),(4,19),(4,20),(5,11),(5,14),(5,18),(5,19),(5,20),(6,8),(6,9),(6,10),(6,11),(6,12),(8,21),(8,22),(9,15),(9,21),(9,25),(10,15),(10,22),(10,25),(11,16),(11,21),(11,22),(11,25),(12,16),(12,21),(12,22),(12,25),(13,15),(13,25),(14,16),(14,17),(14,25),(15,24),(16,23),(16,24),(17,23),(18,17),(18,21),(18,25),(19,17),(19,22),(19,25),(20,17),(20,25),(21,23),(21,24),(22,23),(22,24),(23,7),(24,7),(25,23),(25,24)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => [1,5,2,6,4,3] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,17),(1,19),(2,7),(2,18),(2,22),(3,9),(3,11),(3,19),(4,10),(4,12),(4,17),(4,19),(5,11),(5,12),(5,13),(5,19),(6,2),(6,9),(6,10),(6,13),(6,17),(7,20),(7,21),(9,16),(9,18),(9,22),(10,15),(10,18),(10,22),(11,14),(11,16),(12,14),(12,15),(12,22),(13,7),(13,15),(13,16),(13,22),(14,21),(15,20),(15,21),(16,20),(16,21),(17,18),(17,22),(18,20),(19,14),(19,22),(20,8),(21,8),(22,20),(22,21)],23)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,6,1,5,3,4] => [1,5,6,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(1,9),(2,9),(2,10),(2,12),(3,8),(3,10),(3,11),(4,7),(4,11),(4,12),(5,17),(7,14),(7,15),(8,13),(8,14),(9,13),(9,15),(10,13),(10,16),(11,5),(11,14),(11,16),(12,5),(12,15),(12,16),(13,18),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,6),(18,6)],19)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => [1,6,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,0,0,1,0,1,0]
=> [6,3,1,2,4,5] => [4,2,5,6,1,3] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,16),(1,18),(2,7),(2,17),(2,19),(3,11),(3,12),(3,16),(3,18),(4,10),(4,13),(4,18),(5,9),(5,10),(5,12),(5,18),(6,2),(6,9),(6,11),(6,13),(6,16),(7,20),(9,15),(9,17),(9,19),(9,22),(10,14),(10,19),(11,15),(11,17),(11,19),(11,22),(12,14),(12,15),(12,22),(13,7),(13,19),(13,22),(14,21),(15,20),(15,21),(16,17),(16,22),(17,20),(17,21),(18,14),(18,22),(19,20),(19,21),(20,8),(21,8),(22,20),(22,21)],23)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,0,0,1,1,0,0]
=> [5,3,1,2,6,4] => [4,2,6,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(1,13),(1,16),(1,17),(2,9),(2,13),(2,15),(2,17),(3,12),(3,14),(3,15),(3,17),(4,11),(4,14),(4,16),(4,17),(5,8),(5,11),(5,12),(5,15),(5,16),(6,8),(6,9),(6,10),(6,15),(6,16),(8,19),(8,20),(9,19),(9,22),(9,23),(10,20),(10,22),(10,23),(11,19),(11,22),(11,24),(12,20),(12,22),(12,24),(13,22),(13,23),(14,22),(14,24),(15,19),(15,20),(15,23),(15,24),(16,19),(16,20),(16,23),(16,24),(17,23),(17,24),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,21),(23,18),(23,21),(24,18),(24,21)],25)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => [4,5,2,6,1,3] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,16),(1,18),(2,8),(2,17),(2,19),(2,22),(3,11),(3,12),(3,18),(4,13),(4,14),(4,16),(4,18),(5,10),(5,11),(5,13),(5,16),(6,2),(6,10),(6,12),(6,14),(6,18),(7,20),(8,20),(8,21),(10,15),(10,19),(10,22),(11,15),(11,22),(12,15),(12,17),(12,19),(13,7),(13,19),(13,22),(14,8),(14,17),(14,19),(14,22),(15,21),(16,7),(16,22),(17,20),(17,21),(18,17),(18,22),(19,20),(19,21),(20,9),(21,9),(22,20),(22,21)],23)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,0,1,1,0,0,0]
=> [5,4,1,2,6,3] => [4,6,2,1,5,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(1,18),(1,21),(2,11),(2,13),(2,15),(3,12),(3,14),(3,15),(4,8),(4,10),(4,12),(4,15),(5,9),(5,10),(5,13),(5,15),(6,1),(6,8),(6,9),(6,11),(6,14),(8,17),(8,18),(8,19),(8,20),(9,17),(9,18),(9,19),(9,20),(10,20),(10,21),(11,17),(11,19),(12,18),(12,20),(13,17),(13,21),(14,18),(14,19),(14,21),(15,19),(15,20),(15,21),(16,7),(17,16),(17,22),(18,16),(18,22),(19,16),(19,22),(20,16),(20,22),(21,22),(22,7)],23)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,1,0,0,0,1,0]
=> [4,3,1,6,2,5] => [5,2,1,6,4,3] => ([(0,3),(0,4),(0,5),(0,6),(1,12),(1,19),(2,16),(2,19),(3,8),(3,13),(4,7),(4,9),(4,13),(5,2),(5,9),(5,10),(5,13),(6,1),(6,7),(6,8),(6,10),(7,14),(7,17),(7,19),(8,17),(8,19),(9,14),(9,16),(9,19),(10,12),(10,14),(10,16),(10,17),(12,15),(12,18),(13,16),(13,17),(14,15),(14,18),(15,11),(16,15),(16,18),(17,15),(17,18),(18,11),(19,18)],20)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,1,0,0,1,0,0]
=> [6,3,1,5,2,4] => [5,2,6,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,15),(1,16),(2,8),(2,11),(2,16),(2,18),(3,8),(3,10),(3,15),(3,17),(4,9),(4,13),(4,14),(4,17),(4,18),(5,10),(5,12),(5,13),(5,16),(5,18),(6,11),(6,12),(6,14),(6,15),(6,17),(8,21),(8,25),(9,23),(9,24),(10,21),(10,23),(10,25),(11,21),(11,24),(11,25),(12,23),(12,24),(12,25),(13,19),(13,23),(13,25),(14,19),(14,24),(14,25),(15,24),(15,25),(16,23),(16,25),(17,19),(17,21),(17,23),(17,24),(18,19),(18,21),(18,23),(18,24),(19,20),(19,22),(20,7),(21,20),(21,22),(22,7),(23,20),(23,22),(24,20),(24,22),(25,22)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,1,0,1,0,0,0]
=> [6,4,1,5,2,3] => [5,6,2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,10),(1,15),(1,16),(2,11),(2,15),(2,16),(3,13),(3,15),(3,16),(4,12),(4,15),(4,16),(5,8),(5,9),(5,14),(5,20),(6,5),(6,10),(6,11),(6,12),(6,13),(8,17),(8,19),(9,17),(9,19),(10,18),(10,20),(11,14),(11,18),(11,20),(12,8),(12,18),(12,20),(13,9),(13,18),(13,20),(14,17),(14,19),(15,14),(15,20),(16,14),(16,18),(17,7),(18,19),(19,7),(20,17),(20,19)],21)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,0,1,1,1,0,0,0,0]
=> [4,3,1,5,6,2] => [6,2,1,4,5,3] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,15),(1,18),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,9),(4,10),(4,13),(5,1),(5,8),(5,11),(5,13),(6,19),(6,20),(8,14),(8,18),(9,14),(9,16),(10,16),(10,17),(11,15),(11,17),(11,18),(12,15),(12,16),(12,18),(13,6),(13,14),(13,17),(14,19),(15,20),(16,19),(16,20),(17,19),(17,20),(18,19),(18,20),(19,7),(20,7)],21)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,0,0,1,0,1,0]
=> [2,3,6,1,4,5] => [1,2,5,6,3,4] => ([(0,2),(0,3),(0,4),(1,8),(1,9),(2,1),(2,10),(2,11),(3,6),(3,7),(3,11),(4,6),(4,7),(4,10),(6,14),(7,12),(7,14),(8,13),(8,15),(9,13),(9,15),(10,8),(10,12),(10,14),(11,9),(11,12),(11,14),(12,13),(12,15),(13,5),(14,15),(15,5)],16)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => [1,2,6,3,5,4] => ([(0,1),(0,2),(0,4),(0,5),(1,9),(1,16),(2,10),(2,16),(3,6),(3,7),(3,15),(4,9),(4,11),(4,16),(5,3),(5,10),(5,11),(5,16),(6,13),(7,13),(7,14),(9,12),(10,6),(10,15),(11,7),(11,12),(11,15),(12,14),(13,8),(14,8),(15,13),(15,14),(16,12),(16,15)],17)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,0,1,0,0,1,0]
=> [2,6,4,1,3,5] => [1,5,3,6,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,17),(1,18),(2,12),(2,14),(2,18),(2,19),(3,11),(3,14),(3,17),(3,19),(4,10),(4,13),(4,17),(4,18),(4,19),(5,9),(5,13),(5,17),(5,18),(5,19),(6,8),(6,9),(6,10),(6,11),(6,12),(8,21),(8,22),(9,20),(9,21),(9,22),(9,25),(10,20),(10,21),(10,22),(10,25),(11,15),(11,20),(11,21),(12,15),(12,20),(12,22),(13,16),(13,25),(14,15),(14,25),(15,24),(16,23),(17,16),(17,21),(17,25),(18,16),(18,22),(18,25),(19,16),(19,20),(19,25),(20,23),(20,24),(21,23),(21,24),(22,23),(22,24),(23,7),(24,7),(25,23),(25,24)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,0,1,0,1,0,0]
=> [2,6,5,1,3,4] => [1,5,6,3,2,4] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,15),(1,18),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,9),(4,10),(4,13),(5,1),(5,8),(5,11),(5,13),(6,19),(6,20),(8,14),(8,18),(9,14),(9,16),(10,16),(10,17),(11,15),(11,17),(11,18),(12,15),(12,16),(12,18),(13,6),(13,14),(13,17),(14,19),(15,20),(16,19),(16,20),(17,19),(17,20),(18,19),(18,20),(19,7),(20,7)],21)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,0,1,1,0,0,0]
=> [2,5,4,1,6,3] => [1,6,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(1,11),(1,12),(2,8),(2,9),(2,12),(3,6),(3,7),(3,9),(3,11),(4,6),(4,7),(4,8),(4,10),(6,14),(6,19),(7,13),(7,15),(7,19),(8,13),(8,19),(9,13),(9,16),(9,19),(10,14),(10,15),(10,19),(11,14),(11,15),(11,16),(12,16),(12,19),(13,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,5),(18,5),(19,17),(19,18)],20)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,0,1,0,0,0,1,0]
=> [6,3,4,1,2,5] => [5,2,3,6,1,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,24),(1,25),(2,9),(2,11),(2,13),(2,15),(3,8),(3,10),(3,13),(3,14),(4,8),(4,11),(4,12),(4,16),(5,9),(5,10),(5,12),(5,17),(6,1),(6,14),(6,15),(6,16),(6,17),(8,20),(8,24),(9,20),(9,25),(10,20),(10,23),(10,25),(11,20),(11,23),(11,24),(12,19),(12,20),(13,18),(13,24),(13,25),(14,18),(14,23),(14,24),(15,18),(15,23),(15,25),(16,19),(16,23),(16,24),(16,25),(17,19),(17,23),(17,24),(17,25),(18,22),(19,21),(19,22),(20,21),(21,7),(22,7),(23,21),(23,22),(24,21),(24,22),(25,21),(25,22)],26)
=> ? ∊ {11,11,13,13,13,13,13,18,18,20,22,23,23,24,24,24,24,26,27,27,32,32,32,33,33,37,37,43,43,43,43,52,56,56,57,66,66,76,76,90,132} + 1
[1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 7 = 6 + 1
Description
The number of facets in the chain polytope of the poset.
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