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Your data matches 14 different statistics following compositions of up to 3 maps.
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Matching statistic: St000266
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(load all 3 compositions to match this statistic)
Values
([],1)
=> 1
([],2)
=> 1
([(0,1)],2)
=> 1
([],3)
=> 1
([(1,2)],3)
=> 1
([(0,2),(1,2)],3)
=> 1
([(0,1),(0,2),(1,2)],3)
=> 4
([],4)
=> 1
([(2,3)],4)
=> 1
([(1,3),(2,3)],4)
=> 1
([(0,3),(1,3),(2,3)],4)
=> 1
([(0,3),(1,2)],4)
=> 1
([(0,3),(1,2),(2,3)],4)
=> 1
([(1,2),(1,3),(2,3)],4)
=> 4
([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> 5
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 14
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 38
([],5)
=> 1
([(3,4)],5)
=> 1
([(2,4),(3,4)],5)
=> 1
([(1,4),(2,4),(3,4)],5)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
([(1,4),(2,3)],5)
=> 1
([(1,4),(2,3),(3,4)],5)
=> 1
([(0,1),(2,4),(3,4)],5)
=> 1
([(2,3),(2,4),(3,4)],5)
=> 4
([(0,4),(1,4),(2,3),(3,4)],5)
=> 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 4
([(1,3),(1,4),(2,3),(2,4)],5)
=> 5
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 5
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 14
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 4
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 14
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 19
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 46
([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> 4
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 4
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 16
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 6
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 18
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 48
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 14
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 38
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 38
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 124
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 52
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 134
Description
The number of spanning subgraphs of a graph with the same connected components.
A subgraph or factor of a graph is spanning, if it has the same vertex set [1]. The present statistic additionally requires the subgraph to have the same components. It can be obtained by evaluating the Tutte polynomial at the points $x=1$ and $y=2$, see [2,3].
By mistake, [2] refers to this statistic as the number of spanning subgraphs, which would be $2^m$, where $m$ is the number of edges. Equivalently, this would be the evaluation of the Tutte polynomial at $x=y=2$.
Matching statistic: St001645
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(load all 3 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([],2)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([],3)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1
([(1,2)],3)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 4
([],4)
=> ([],4)
=> ([],1)
=> ([],1)
=> 1
([(2,3)],4)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1
([(1,3),(2,3)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,2)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,2),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,5,14,38}
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,5,14,38}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {4,4,5,14,38}
([],5)
=> ([],5)
=> ([],1)
=> ([],1)
=> 1
([(3,4)],5)
=> ([],4)
=> ([],1)
=> ([],1)
=> 1
([(2,4),(3,4)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1
([(1,4),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,4),(2,3)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1
([(1,4),(2,3),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(2,3),(2,4),(3,4)],5)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 5
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? ∊ {4,4,4,4,4,4,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([],6)
=> ([],6)
=> ([],1)
=> ([],1)
=> 1
([(4,5)],6)
=> ([],5)
=> ([],1)
=> ([],1)
=> 1
([(3,5),(4,5)],6)
=> ([],4)
=> ([],1)
=> ([],1)
=> 1
([(2,5),(3,5),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(2,5),(3,4)],6)
=> ([],4)
=> ([],1)
=> ([],1)
=> 1
([(2,5),(3,4),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(3,5),(4,5)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1
([(3,4),(3,5),(4,5)],6)
=> ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,4),(2,3)],6)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? ∊ {4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 5
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 5
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 5
Description
The pebbling number of a connected graph.
Matching statistic: St001877
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> ? = 1
([],2)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1}
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1}
([],3)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1}
([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1}
([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1}
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([],4)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,5,14,38}
([(2,3)],4)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,5,14,38}
([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,5,14,38}
([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,5,14,38}
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,5,14,38}
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,5,14,38}
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,5,14,38}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,5,14,38}
([],5)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,16),(2,8),(2,11),(2,16),(3,7),(3,10),(3,16),(4,6),(4,10),(4,11),(4,12),(5,6),(5,7),(5,8),(5,9),(6,13),(6,14),(6,15),(7,13),(7,17),(8,14),(8,17),(9,15),(9,17),(10,13),(10,18),(11,14),(11,18),(12,15),(12,18),(13,19),(14,19),(15,19),(16,17),(16,18),(17,19),(18,19)],20)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(1,14),(1,15),(1,17),(2,10),(2,11),(2,12),(2,17),(3,7),(3,8),(3,9),(3,17),(4,9),(4,12),(4,15),(4,16),(5,8),(5,11),(5,14),(5,16),(6,7),(6,10),(6,13),(6,16),(7,18),(7,21),(8,19),(8,21),(9,20),(9,21),(10,18),(10,22),(11,19),(11,22),(12,20),(12,22),(13,18),(13,23),(14,19),(14,23),(15,20),(15,23),(16,21),(16,22),(16,23),(17,18),(17,19),(17,20),(18,24),(19,24),(20,24),(21,24),(22,24),(23,24)],25)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,14),(1,15),(2,9),(2,10),(2,11),(2,15),(3,7),(3,8),(3,11),(3,14),(4,6),(4,8),(4,10),(4,13),(5,6),(5,7),(5,9),(5,12),(6,16),(6,19),(6,22),(7,16),(7,17),(7,20),(8,16),(8,18),(8,21),(9,17),(9,19),(9,23),(10,18),(10,19),(10,24),(11,17),(11,18),(11,25),(12,20),(12,22),(12,23),(13,21),(13,22),(13,24),(14,20),(14,21),(14,25),(15,23),(15,24),(15,25),(16,26),(17,26),(18,26),(19,26),(20,26),(21,26),(22,26),(23,26),(24,26),(25,26)],27)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,16),(1,17),(1,18),(1,25),(2,13),(2,14),(2,15),(2,25),(3,10),(3,11),(3,12),(3,25),(4,8),(4,9),(4,12),(4,15),(4,18),(5,7),(5,9),(5,11),(5,14),(5,17),(6,7),(6,8),(6,10),(6,13),(6,16),(7,21),(7,24),(7,29),(8,19),(8,22),(8,29),(9,20),(9,23),(9,29),(10,26),(10,29),(11,27),(11,29),(12,28),(12,29),(13,19),(13,21),(13,26),(14,20),(14,21),(14,27),(15,19),(15,20),(15,28),(16,22),(16,24),(16,26),(17,23),(17,24),(17,27),(18,22),(18,23),(18,28),(19,30),(20,30),(21,30),(22,30),(23,30),(24,30),(25,26),(25,27),(25,28),(26,30),(27,30),(28,30),(29,30)],31)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(1,11),(1,24),(1,26),(2,8),(2,9),(2,24),(2,25),(3,16),(3,17),(3,18),(3,19),(3,24),(4,9),(4,14),(4,15),(4,17),(4,26),(5,8),(5,12),(5,13),(5,16),(5,26),(6,11),(6,13),(6,15),(6,19),(6,25),(7,10),(7,12),(7,14),(7,18),(7,25),(8,27),(8,31),(9,28),(9,31),(10,29),(10,32),(11,30),(11,32),(12,20),(12,27),(12,29),(13,21),(13,27),(13,30),(14,22),(14,28),(14,29),(15,23),(15,28),(15,30),(16,20),(16,21),(16,31),(17,22),(17,23),(17,31),(18,20),(18,22),(18,32),(19,21),(19,23),(19,32),(20,33),(21,33),(22,33),(23,33),(24,31),(24,32),(25,27),(25,28),(25,32),(26,29),(26,30),(26,31),(27,33),(28,33),(29,33),(30,33),(31,33),(32,33)],34)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(1,20),(1,21),(2,9),(2,14),(2,15),(2,21),(3,8),(3,12),(3,13),(3,21),(4,11),(4,13),(4,15),(4,20),(5,10),(5,12),(5,14),(5,20),(6,7),(6,8),(6,9),(6,10),(6,11),(7,22),(7,23),(8,16),(8,17),(8,22),(9,18),(9,19),(9,22),(10,16),(10,18),(10,23),(11,17),(11,19),(11,23),(12,16),(12,24),(13,17),(13,24),(14,18),(14,24),(15,19),(15,24),(16,25),(17,25),(18,25),(19,25),(20,23),(20,24),(21,22),(21,24),(22,25),(23,25),(24,25)],26)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(1,16),(1,21),(1,23),(2,8),(2,16),(2,20),(2,22),(3,10),(3,15),(3,20),(3,23),(4,11),(4,15),(4,21),(4,22),(5,13),(5,14),(5,22),(5,23),(6,12),(6,14),(6,20),(6,21),(7,8),(7,9),(7,10),(7,11),(7,12),(7,13),(8,17),(8,24),(8,26),(9,17),(9,25),(9,27),(10,18),(10,24),(10,27),(11,18),(11,25),(11,26),(12,19),(12,24),(12,25),(13,19),(13,26),(13,27),(14,19),(14,28),(15,18),(15,28),(16,17),(16,28),(17,29),(18,29),(19,29),(20,24),(20,28),(21,25),(21,28),(22,26),(22,28),(23,27),(23,28),(24,29),(25,29),(26,29),(27,29),(28,29)],30)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,9),(1,26),(1,27),(1,28),(2,9),(2,10),(2,11),(2,29),(2,30),(3,13),(3,17),(3,21),(3,28),(3,30),(4,12),(4,16),(4,21),(4,27),(4,29),(5,15),(5,18),(5,20),(5,27),(5,30),(6,14),(6,19),(6,20),(6,28),(6,29),(7,11),(7,16),(7,17),(7,18),(7,19),(7,26),(8,10),(8,12),(8,13),(8,14),(8,15),(8,26),(9,35),(9,38),(10,31),(10,32),(10,35),(11,33),(11,34),(11,35),(12,22),(12,31),(12,36),(13,22),(13,32),(13,37),(14,23),(14,31),(14,37),(15,23),(15,32),(15,36),(16,24),(16,33),(16,36),(17,24),(17,34),(17,37),(18,25),(18,34),(18,36),(19,25),(19,33),(19,37),(20,23),(20,25),(20,38),(21,22),(21,24),(21,38),(22,39),(23,39),(24,39),(25,39),(26,35),(26,36),(26,37),(27,36),(27,38),(28,37),(28,38),(29,31),(29,33),(29,38),(30,32),(30,34),(30,38),(31,39),(32,39),(33,39),(34,39),(35,39),(36,39),(37,39),(38,39)],40)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(4,7),(5,9),(6,9),(7,9),(8,9)],10)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,11),(1,13),(2,9),(2,10),(2,12),(3,8),(3,10),(3,13),(4,8),(4,11),(4,12),(5,7),(5,12),(5,13),(6,7),(6,10),(6,11),(7,14),(8,14),(9,14),(10,14),(11,14),(12,14),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(1,13),(1,14),(1,20),(1,28),(1,29),(1,31),(2,11),(2,12),(2,19),(2,26),(2,27),(2,31),(3,16),(3,18),(3,22),(3,27),(3,29),(3,30),(4,15),(4,17),(4,21),(4,26),(4,28),(4,30),(5,11),(5,15),(5,24),(5,29),(5,32),(5,34),(6,12),(6,16),(6,25),(6,28),(6,32),(6,35),(7,13),(7,17),(7,25),(7,27),(7,33),(7,34),(8,14),(8,18),(8,24),(8,26),(8,33),(8,35),(9,21),(9,22),(9,23),(9,31),(9,34),(9,35),(10,19),(10,20),(10,23),(10,30),(10,32),(10,33),(11,36),(11,40),(11,50),(12,36),(12,41),(12,49),(13,37),(13,42),(13,50),(14,37),(14,43),(14,49),(15,38),(15,40),(15,48),(16,39),(16,41),(16,48),(17,38),(17,42),(17,47),(18,39),(18,43),(18,47),(19,36),(19,44),(19,47),(20,37),(20,44),(20,48),(21,38),(21,45),(21,49),(22,39),(22,45),(22,50),(23,44),(23,45),(23,46),(24,40),(24,43),(24,46),(25,41),(25,42),(25,46),(26,40),(26,47),(26,49),(27,41),(27,47),(27,50),(28,42),(28,48),(28,49),(29,43),(29,48),(29,50),(30,45),(30,47),(30,48),(31,44),(31,49),(31,50),(32,36),(32,46),(32,48),(33,37),(33,46),(33,47),(34,38),(34,46),(34,50),(35,39),(35,46),(35,49),(36,51),(37,51),(38,51),(39,51),(40,51),(41,51),(42,51),(43,51),(44,51),(45,51),(46,51),(47,51),(48,51),(49,51),(50,51)],52)
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([],6)
=> ([],1)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4)],6)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
([(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,2),(3,5),(4,5)],6)
=> ([(1,4),(2,3)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
([(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
Description
Number of indecomposable injective modules with projective dimension 2.
Matching statistic: St000618
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000618: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000618: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 1
([],2)
=> [1,1]
=> [1]
=> []
=> ? ∊ {1,1}
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? ∊ {1,1}
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? ∊ {1,1,4}
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([(0,1),(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
Description
The number of self-evacuating tableaux of given shape.
This is the same as the number of standard domino tableaux of the given shape.
Matching statistic: St000781
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 1
([],2)
=> [1,1]
=> [1]
=> []
=> ? ∊ {1,1}
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? ∊ {1,1}
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? ∊ {1,1,4}
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([(0,1),(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
Description
The number of proper colouring schemes of a Ferrers diagram.
A colouring of a Ferrers diagram is proper if no two cells in a row or in a column have the same colour. The minimal number of colours needed is the maximum of the length and the first part of the partition, because we can restrict a latin square to the shape. We can associate to each colouring the integer partition recording how often each colour is used, see [1].
This statistic is the number of distinct such integer partitions that occur.
Matching statistic: St001432
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001432: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001432: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 1
([],2)
=> [1,1]
=> [1]
=> []
=> ? ∊ {1,1}
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? ∊ {1,1}
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? ∊ {1,1,4}
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([(0,1),(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
Description
The order dimension of the partition.
Given a partition $\lambda$, let $I(\lambda)$ be the principal order ideal in the Young lattice generated by $\lambda$. The order dimension of a partition is defined as the order dimension of the poset $I(\lambda)$.
Matching statistic: St001627
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001627: Integer partitions ⟶ ℤResult quality: 4% ●values known / values provided: 11%●distinct values known / distinct values provided: 4%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001627: Integer partitions ⟶ ℤResult quality: 4% ●values known / values provided: 11%●distinct values known / distinct values provided: 4%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 1
([],2)
=> [1,1]
=> [1]
=> []
=> ? ∊ {1,1}
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? ∊ {1,1}
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? ∊ {1,1,4}
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([(0,1),(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 4
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 38
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 4
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
Description
The number of coloured connected graphs such that the multiplicities of colours are given by a partition.
In particular, the value on the partition $(n)$ is the number of unlabelled connected graphs on $n$ vertices, [[oeis:A001349]], whereas the value on the partition $(1^n)$ is the number of labelled connected graphs [[oeis:A001187]].
Matching statistic: St001780
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001780: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001780: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 1
([],2)
=> [1,1]
=> [1]
=> []
=> ? ∊ {1,1}
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? ∊ {1,1}
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? ∊ {1,1,4}
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([(0,1),(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
Description
The order of promotion on the set of standard tableaux of given shape.
Matching statistic: St001899
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001899: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001899: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 1
([],2)
=> [1,1]
=> [1]
=> []
=> ? ∊ {1,1}
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? ∊ {1,1}
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? ∊ {1,1,4}
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([(0,1),(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
Description
The total number of irreducible representations contained in the higher Lie character for an integer partition.
Matching statistic: St001900
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001900: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001900: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 11%●distinct values known / distinct values provided: 1%
Values
([],1)
=> [1]
=> []
=> ?
=> ? = 1
([],2)
=> [1,1]
=> [1]
=> []
=> ? ∊ {1,1}
([(0,1)],2)
=> [2]
=> []
=> ?
=> ? ∊ {1,1}
([],3)
=> [1,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2)],3)
=> [2,1]
=> [1]
=> []
=> ? ∊ {1,1,4}
([(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([(0,1),(0,2),(1,2)],3)
=> [3]
=> []
=> ?
=> ? ∊ {1,1,4}
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3)],4)
=> [2,1,1]
=> [1,1]
=> [1]
=> 1
([(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2)],4)
=> [2,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> []
=> ?
=> ? ∊ {1,1,1,1,4,4,5,14,38}
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1]
=> 1
([(1,4),(2,3),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [1,1]
=> [1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,3),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,4,4,4,4,4,4,5,5,6,14,14,14,16,18,19,38,38,46,48,52,124,134,314,728}
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(2,5),(3,4),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(1,2),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(3,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [6]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [5,1]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,7,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,18,18,18,18,19,19,19,20,22,23,24,38,38,38,38,38,38,46,46,46,48,48,48,48,52,52,52,52,56,56,60,62,64,64,65,66,66,70,71,124,124,124,124,134,134,134,146,152,156,160,162,164,164,170,172,176,180,182,186,198,205,314,314,314,392,400,404,420,432,438,440,448,462,476,478,484,728,728,988,1008,1042,1052,1094,1106,1132,1134,2284,2414,2478,2564,2656,5564,5758,12424,26704}
([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [2,2]
=> [2]
=> 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1]
=> 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [4,1,1]
=> [1,1]
=> [1]
=> 1
Description
The number of distinct irreducible representations contained in the higher Lie character for an integer partition.
The following 4 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001924The number of cells in an integer partition whose arm and leg length coincide. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type.
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