Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001299
(load all 6 compositions to match this statistic)
Mapping
St001299: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => 1
[1,0,1,0]
 => 2
[1,1,0,0]
 => 1
[1,0,1,0,1,0]
 => 6
[1,0,1,1,0,0]
 => 2
[1,1,0,0,1,0]
 => 2
[1,1,0,1,0,0]
 => 2
[1,1,1,0,0,0]
 => 1
[1,0,1,0,1,0,1,0]
 => 24
[1,0,1,0,1,1,0,0]
 => 6
[1,0,1,1,0,0,1,0]
 => 4
[1,0,1,1,0,1,0,0]
 => 6
[1,0,1,1,1,0,0,0]
 => 2
[1,1,0,0,1,0,1,0]
 => 6
[1,1,0,0,1,1,0,0]
 => 2
[1,1,0,1,0,0,1,0]
 => 6
[1,1,0,1,0,1,0,0]
 => 6
[1,1,0,1,1,0,0,0]
 => 2
[1,1,1,0,0,0,1,0]
 => 2
[1,1,1,0,0,1,0,0]
 => 2
[1,1,1,0,1,0,0,0]
 => 2
[1,1,1,1,0,0,0,0]
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => 120
[1,0,1,0,1,0,1,1,0,0]
 => 24
[1,0,1,0,1,1,0,0,1,0]
 => 12
[1,0,1,0,1,1,0,1,0,0]
 => 24
[1,0,1,0,1,1,1,0,0,0]
 => 6
[1,0,1,1,0,0,1,0,1,0]
 => 12
[1,0,1,1,0,0,1,1,0,0]
 => 4
[1,0,1,1,0,1,0,0,1,0]
 => 24
[1,0,1,1,0,1,0,1,0,0]
 => 24
[1,0,1,1,0,1,1,0,0,0]
 => 6
[1,0,1,1,1,0,0,0,1,0]
 => 4
[1,0,1,1,1,0,0,1,0,0]
 => 4
[1,0,1,1,1,0,1,0,0,0]
 => 6
[1,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,0,0,1,0,1,0,1,0]
 => 24
[1,1,0,0,1,0,1,1,0,0]
 => 6
[1,1,0,0,1,1,0,0,1,0]
 => 4
[1,1,0,0,1,1,0,1,0,0]
 => 6
[1,1,0,0,1,1,1,0,0,0]
 => 2
[1,1,0,1,0,0,1,0,1,0]
 => 24
[1,1,0,1,0,0,1,1,0,0]
 => 6
[1,1,0,1,0,1,0,0,1,0]
 => 24
[1,1,0,1,0,1,0,1,0,0]
 => 18
[1,1,0,1,0,1,1,0,0,0]
 => 6
[1,1,0,1,1,0,0,0,1,0]
 => 4
[1,1,0,1,1,0,0,1,0,0]
 => 6
[1,1,0,1,1,0,1,0,0,0]
 => 6
[1,1,0,1,1,1,0,0,0,0]
 => 2
Description
The product of all non-zero projective dimensions of simple modules of the corresponding Nakayama algebra.
Matching statistic: St001330
Mapping
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 15%
Values
[1,0]
 => [1,1,0,0]
 => [2] => ([],2)
 => 1
[1,0,1,0]
 => [1,1,0,1,0,0]
 => [2,1] => ([(0,2),(1,2)],3)
 => 2
[1,1,0,0]
 => [1,1,1,0,0,0]
 => [3] => ([],3)
 => 1
[1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 6
[1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [2,2] => ([(1,3),(2,3)],4)
 => 2
[1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [4] => ([],4)
 => 1
[1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 24
[1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4
[1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6
[1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [2,3] => ([(2,4),(3,4)],5)
 => 2
[1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6
[1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 2
[1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6
[1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6
[1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 2
[1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [5] => ([],5)
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 120
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 24
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 12
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 24
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 12
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 24
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 24
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,4] => ([(3,5),(4,5)],6)
 => 2
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 24
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 2
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 24
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 24
[1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 18
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4
[1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 2
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 2
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 2
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6
[1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 2
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
[1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [6] => ([],6)
 => 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 720
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 120
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 48
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 120
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 24
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 36
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
 => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 12
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 120
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 120
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
 => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 24
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 12
[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]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2
Description
The hat guessing number of a graph. Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors. Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Matching statistic: St001232
Mapping
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00296: Dyck paths —Knuth-Krattenthaler⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 15%
Values
[1,0]
 => [1,1,0,0]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
[1,0,1,0]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => [1,1,0,0,1,0]
 => 1
[1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 6
[1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2
[1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? = 24
[1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 6
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? = 4
[1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 6
[1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? = 6
[1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 2
[1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? = 6
[1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 6
[1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? = 2
[1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 2
[1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 120
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => ? = 24
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 12
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => ? = 24
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 6
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => ? = 12
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => ? = 4
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => ? = 24
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => ? = 24
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 6
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => ? = 4
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => ? = 4
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 6
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 24
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? = 6
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 4
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? = 6
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 2
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => ? = 24
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? = 6
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => ? = 24
[1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? = 18
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 6
[1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => ? = 4
[1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? = 6
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 6
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => ? = 6
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? = 2
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => ? = 6
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? = 6
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 2
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => ? = 6
[1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? = 6
[1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 6
[1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => ? = 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? = 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 720
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 2
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 2
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [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.