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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000780
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(load all 12 compositions to match this statistic)
St000780: Perfect matchings ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[(1,2)]
=> 1
[(1,2),(3,4)]
=> 2
[(1,3),(2,4)]
=> 1
[(1,4),(2,3)]
=> 2
[(1,2),(3,4),(5,6)]
=> 2
[(1,3),(2,4),(5,6)]
=> 6
[(1,4),(2,3),(5,6)]
=> 3
[(1,5),(2,3),(4,6)]
=> 6
[(1,6),(2,3),(4,5)]
=> 2
[(1,6),(2,4),(3,5)]
=> 6
[(1,5),(2,4),(3,6)]
=> 3
[(1,4),(2,5),(3,6)]
=> 1
[(1,3),(2,5),(4,6)]
=> 3
[(1,2),(3,5),(4,6)]
=> 6
[(1,2),(3,6),(4,5)]
=> 3
[(1,3),(2,6),(4,5)]
=> 6
[(1,4),(2,6),(3,5)]
=> 3
[(1,5),(2,6),(3,4)]
=> 6
[(1,6),(2,5),(3,4)]
=> 3
[(1,2),(3,4),(5,6),(7,8)]
=> 2
[(1,3),(2,4),(5,6),(7,8)]
=> 8
[(1,4),(2,3),(5,6),(7,8)]
=> 8
[(1,5),(2,3),(4,6),(7,8)]
=> 8
[(1,6),(2,3),(4,5),(7,8)]
=> 8
[(1,7),(2,3),(4,5),(6,8)]
=> 8
[(1,8),(2,3),(4,5),(6,7)]
=> 2
[(1,8),(2,4),(3,5),(6,7)]
=> 8
[(1,7),(2,4),(3,5),(6,8)]
=> 4
[(1,6),(2,4),(3,5),(7,8)]
=> 8
[(1,5),(2,4),(3,6),(7,8)]
=> 8
[(1,4),(2,5),(3,6),(7,8)]
=> 8
[(1,3),(2,5),(4,6),(7,8)]
=> 8
[(1,2),(3,5),(4,6),(7,8)]
=> 8
[(1,2),(3,6),(4,5),(7,8)]
=> 8
[(1,3),(2,6),(4,5),(7,8)]
=> 8
[(1,4),(2,6),(3,5),(7,8)]
=> 8
[(1,5),(2,6),(3,4),(7,8)]
=> 4
[(1,6),(2,5),(3,4),(7,8)]
=> 4
[(1,7),(2,5),(3,4),(6,8)]
=> 8
[(1,8),(2,5),(3,4),(6,7)]
=> 8
[(1,8),(2,6),(3,4),(5,7)]
=> 8
[(1,7),(2,6),(3,4),(5,8)]
=> 8
[(1,6),(2,7),(3,4),(5,8)]
=> 8
[(1,5),(2,7),(3,4),(6,8)]
=> 8
[(1,4),(2,7),(3,5),(6,8)]
=> 8
[(1,3),(2,7),(4,5),(6,8)]
=> 8
[(1,2),(3,7),(4,5),(6,8)]
=> 8
[(1,2),(3,8),(4,5),(6,7)]
=> 8
[(1,3),(2,8),(4,5),(6,7)]
=> 8
[(1,4),(2,8),(3,5),(6,7)]
=> 8
Description
The size of the orbit under rotation of a perfect matching.
The number of orbits is given in [1].
Matching statistic: St000163
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(load all 13 compositions to match this statistic)
Mp00092: Perfect matchings —to set partition⟶ Set partitions
St000163: Set partitions ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 100%
St000163: Set partitions ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 100%
Values
[(1,2)]
=> {{1,2}}
=> 1
[(1,2),(3,4)]
=> {{1,2},{3,4}}
=> 2
[(1,3),(2,4)]
=> {{1,3},{2,4}}
=> 1
[(1,4),(2,3)]
=> {{1,4},{2,3}}
=> 2
[(1,2),(3,4),(5,6)]
=> {{1,2},{3,4},{5,6}}
=> 2
[(1,3),(2,4),(5,6)]
=> {{1,3},{2,4},{5,6}}
=> 6
[(1,4),(2,3),(5,6)]
=> {{1,4},{2,3},{5,6}}
=> 3
[(1,5),(2,3),(4,6)]
=> {{1,5},{2,3},{4,6}}
=> 6
[(1,6),(2,3),(4,5)]
=> {{1,6},{2,3},{4,5}}
=> 2
[(1,6),(2,4),(3,5)]
=> {{1,6},{2,4},{3,5}}
=> 6
[(1,5),(2,4),(3,6)]
=> {{1,5},{2,4},{3,6}}
=> 3
[(1,4),(2,5),(3,6)]
=> {{1,4},{2,5},{3,6}}
=> 1
[(1,3),(2,5),(4,6)]
=> {{1,3},{2,5},{4,6}}
=> 3
[(1,2),(3,5),(4,6)]
=> {{1,2},{3,5},{4,6}}
=> 6
[(1,2),(3,6),(4,5)]
=> {{1,2},{3,6},{4,5}}
=> 3
[(1,3),(2,6),(4,5)]
=> {{1,3},{2,6},{4,5}}
=> 6
[(1,4),(2,6),(3,5)]
=> {{1,4},{2,6},{3,5}}
=> 3
[(1,5),(2,6),(3,4)]
=> {{1,5},{2,6},{3,4}}
=> 6
[(1,6),(2,5),(3,4)]
=> {{1,6},{2,5},{3,4}}
=> 3
[(1,2),(3,4),(5,6),(7,8)]
=> {{1,2},{3,4},{5,6},{7,8}}
=> 2
[(1,3),(2,4),(5,6),(7,8)]
=> {{1,3},{2,4},{5,6},{7,8}}
=> 8
[(1,4),(2,3),(5,6),(7,8)]
=> {{1,4},{2,3},{5,6},{7,8}}
=> 8
[(1,5),(2,3),(4,6),(7,8)]
=> {{1,5},{2,3},{4,6},{7,8}}
=> 8
[(1,6),(2,3),(4,5),(7,8)]
=> {{1,6},{2,3},{4,5},{7,8}}
=> 8
[(1,7),(2,3),(4,5),(6,8)]
=> {{1,7},{2,3},{4,5},{6,8}}
=> 8
[(1,8),(2,3),(4,5),(6,7)]
=> {{1,8},{2,3},{4,5},{6,7}}
=> 2
[(1,8),(2,4),(3,5),(6,7)]
=> {{1,8},{2,4},{3,5},{6,7}}
=> 8
[(1,7),(2,4),(3,5),(6,8)]
=> {{1,7},{2,4},{3,5},{6,8}}
=> 4
[(1,6),(2,4),(3,5),(7,8)]
=> {{1,6},{2,4},{3,5},{7,8}}
=> 8
[(1,5),(2,4),(3,6),(7,8)]
=> {{1,5},{2,4},{3,6},{7,8}}
=> 8
[(1,4),(2,5),(3,6),(7,8)]
=> {{1,4},{2,5},{3,6},{7,8}}
=> 8
[(1,3),(2,5),(4,6),(7,8)]
=> {{1,3},{2,5},{4,6},{7,8}}
=> 8
[(1,2),(3,5),(4,6),(7,8)]
=> {{1,2},{3,5},{4,6},{7,8}}
=> 8
[(1,2),(3,6),(4,5),(7,8)]
=> {{1,2},{3,6},{4,5},{7,8}}
=> 8
[(1,3),(2,6),(4,5),(7,8)]
=> {{1,3},{2,6},{4,5},{7,8}}
=> 8
[(1,4),(2,6),(3,5),(7,8)]
=> {{1,4},{2,6},{3,5},{7,8}}
=> 8
[(1,5),(2,6),(3,4),(7,8)]
=> {{1,5},{2,6},{3,4},{7,8}}
=> 4
[(1,6),(2,5),(3,4),(7,8)]
=> {{1,6},{2,5},{3,4},{7,8}}
=> 4
[(1,7),(2,5),(3,4),(6,8)]
=> {{1,7},{2,5},{3,4},{6,8}}
=> 8
[(1,8),(2,5),(3,4),(6,7)]
=> {{1,8},{2,5},{3,4},{6,7}}
=> 8
[(1,8),(2,6),(3,4),(5,7)]
=> {{1,8},{2,6},{3,4},{5,7}}
=> 8
[(1,7),(2,6),(3,4),(5,8)]
=> {{1,7},{2,6},{3,4},{5,8}}
=> 8
[(1,6),(2,7),(3,4),(5,8)]
=> {{1,6},{2,7},{3,4},{5,8}}
=> 8
[(1,5),(2,7),(3,4),(6,8)]
=> {{1,5},{2,7},{3,4},{6,8}}
=> 8
[(1,4),(2,7),(3,5),(6,8)]
=> {{1,4},{2,7},{3,5},{6,8}}
=> 8
[(1,3),(2,7),(4,5),(6,8)]
=> {{1,3},{2,7},{4,5},{6,8}}
=> 8
[(1,2),(3,7),(4,5),(6,8)]
=> {{1,2},{3,7},{4,5},{6,8}}
=> 8
[(1,2),(3,8),(4,5),(6,7)]
=> {{1,2},{3,8},{4,5},{6,7}}
=> 8
[(1,3),(2,8),(4,5),(6,7)]
=> {{1,3},{2,8},{4,5},{6,7}}
=> 8
[(1,4),(2,8),(3,5),(6,7)]
=> {{1,4},{2,8},{3,5},{6,7}}
=> 8
[(1,3),(2,4),(5,6),(7,8),(9,10)]
=> {{1,3},{2,4},{5,6},{7,8},{9,10}}
=> ? = 10
[(1,5),(2,3),(4,6),(7,8),(9,10)]
=> {{1,5},{2,3},{4,6},{7,8},{9,10}}
=> ? = 10
[(1,7),(2,3),(4,5),(6,8),(9,10)]
=> {{1,7},{2,3},{4,5},{6,8},{9,10}}
=> ? = 10
[(1,9),(2,3),(4,5),(6,7),(8,10)]
=> {{1,9},{2,3},{4,5},{6,7},{8,10}}
=> ? = 10
[(1,10),(2,4),(3,5),(6,7),(8,9)]
=> {{1,10},{2,4},{3,5},{6,7},{8,9}}
=> ? = 10
[(1,9),(2,4),(3,5),(6,7),(8,10)]
=> {{1,9},{2,4},{3,5},{6,7},{8,10}}
=> ? = 10
[(1,8),(2,4),(3,5),(6,7),(9,10)]
=> {{1,8},{2,4},{3,5},{6,7},{9,10}}
=> ? = 10
[(1,7),(2,4),(3,5),(6,8),(9,10)]
=> {{1,7},{2,4},{3,5},{6,8},{9,10}}
=> ? = 10
[(1,6),(2,4),(3,5),(7,8),(9,10)]
=> {{1,6},{2,4},{3,5},{7,8},{9,10}}
=> ? = 10
[(1,5),(2,4),(3,6),(7,8),(9,10)]
=> {{1,5},{2,4},{3,6},{7,8},{9,10}}
=> ? = 10
[(1,4),(2,5),(3,6),(7,8),(9,10)]
=> {{1,4},{2,5},{3,6},{7,8},{9,10}}
=> ? = 10
[(1,3),(2,5),(4,6),(7,8),(9,10)]
=> {{1,3},{2,5},{4,6},{7,8},{9,10}}
=> ? = 10
[(1,2),(3,5),(4,6),(7,8),(9,10)]
=> {{1,2},{3,5},{4,6},{7,8},{9,10}}
=> ? = 10
[(1,3),(2,6),(4,5),(7,8),(9,10)]
=> {{1,3},{2,6},{4,5},{7,8},{9,10}}
=> ? = 10
[(1,4),(2,6),(3,5),(7,8),(9,10)]
=> {{1,4},{2,6},{3,5},{7,8},{9,10}}
=> ? = 10
[(1,5),(2,6),(3,4),(7,8),(9,10)]
=> {{1,5},{2,6},{3,4},{7,8},{9,10}}
=> ? = 10
[(1,7),(2,5),(3,4),(6,8),(9,10)]
=> {{1,7},{2,5},{3,4},{6,8},{9,10}}
=> ? = 10
[(1,9),(2,5),(3,4),(6,7),(8,10)]
=> {{1,9},{2,5},{3,4},{6,7},{8,10}}
=> ? = 10
[(1,10),(2,6),(3,4),(5,7),(8,9)]
=> {{1,10},{2,6},{3,4},{5,7},{8,9}}
=> ? = 10
[(1,9),(2,6),(3,4),(5,7),(8,10)]
=> {{1,9},{2,6},{3,4},{5,7},{8,10}}
=> ? = 10
[(1,8),(2,6),(3,4),(5,7),(9,10)]
=> {{1,8},{2,6},{3,4},{5,7},{9,10}}
=> ? = 10
[(1,7),(2,6),(3,4),(5,8),(9,10)]
=> {{1,7},{2,6},{3,4},{5,8},{9,10}}
=> ? = 10
[(1,6),(2,7),(3,4),(5,8),(9,10)]
=> {{1,6},{2,7},{3,4},{5,8},{9,10}}
=> ? = 10
[(1,5),(2,7),(3,4),(6,8),(9,10)]
=> {{1,5},{2,7},{3,4},{6,8},{9,10}}
=> ? = 10
[(1,4),(2,7),(3,5),(6,8),(9,10)]
=> {{1,4},{2,7},{3,5},{6,8},{9,10}}
=> ? = 10
[(1,3),(2,7),(4,5),(6,8),(9,10)]
=> {{1,3},{2,7},{4,5},{6,8},{9,10}}
=> ? = 5
[(1,2),(3,7),(4,5),(6,8),(9,10)]
=> {{1,2},{3,7},{4,5},{6,8},{9,10}}
=> ? = 10
[(1,3),(2,8),(4,5),(6,7),(9,10)]
=> {{1,3},{2,8},{4,5},{6,7},{9,10}}
=> ? = 10
[(1,4),(2,8),(3,5),(6,7),(9,10)]
=> {{1,4},{2,8},{3,5},{6,7},{9,10}}
=> ? = 10
[(1,5),(2,8),(3,4),(6,7),(9,10)]
=> {{1,5},{2,8},{3,4},{6,7},{9,10}}
=> ? = 10
[(1,6),(2,8),(3,4),(5,7),(9,10)]
=> {{1,6},{2,8},{3,4},{5,7},{9,10}}
=> ? = 10
[(1,7),(2,8),(3,4),(5,6),(9,10)]
=> {{1,7},{2,8},{3,4},{5,6},{9,10}}
=> ? = 10
[(1,9),(2,7),(3,4),(5,6),(8,10)]
=> {{1,9},{2,7},{3,4},{5,6},{8,10}}
=> ? = 10
[(1,10),(2,8),(3,4),(5,6),(7,9)]
=> {{1,10},{2,8},{3,4},{5,6},{7,9}}
=> ? = 10
[(1,9),(2,8),(3,4),(5,6),(7,10)]
=> {{1,9},{2,8},{3,4},{5,6},{7,10}}
=> ? = 10
[(1,8),(2,9),(3,4),(5,6),(7,10)]
=> {{1,8},{2,9},{3,4},{5,6},{7,10}}
=> ? = 10
[(1,7),(2,9),(3,4),(5,6),(8,10)]
=> {{1,7},{2,9},{3,4},{5,6},{8,10}}
=> ? = 10
[(1,6),(2,9),(3,4),(5,7),(8,10)]
=> {{1,6},{2,9},{3,4},{5,7},{8,10}}
=> ? = 10
[(1,5),(2,9),(3,4),(6,7),(8,10)]
=> {{1,5},{2,9},{3,4},{6,7},{8,10}}
=> ? = 10
[(1,4),(2,9),(3,5),(6,7),(8,10)]
=> {{1,4},{2,9},{3,5},{6,7},{8,10}}
=> ? = 10
[(1,3),(2,9),(4,5),(6,7),(8,10)]
=> {{1,3},{2,9},{4,5},{6,7},{8,10}}
=> ? = 10
[(1,2),(3,9),(4,5),(6,7),(8,10)]
=> {{1,2},{3,9},{4,5},{6,7},{8,10}}
=> ? = 10
[(1,3),(2,10),(4,5),(6,7),(8,9)]
=> {{1,3},{2,10},{4,5},{6,7},{8,9}}
=> ? = 10
[(1,4),(2,10),(3,5),(6,7),(8,9)]
=> {{1,4},{2,10},{3,5},{6,7},{8,9}}
=> ? = 10
[(1,5),(2,10),(3,4),(6,7),(8,9)]
=> {{1,5},{2,10},{3,4},{6,7},{8,9}}
=> ? = 10
[(1,6),(2,10),(3,4),(5,7),(8,9)]
=> {{1,6},{2,10},{3,4},{5,7},{8,9}}
=> ? = 5
[(1,7),(2,10),(3,4),(5,6),(8,9)]
=> {{1,7},{2,10},{3,4},{5,6},{8,9}}
=> ? = 10
[(1,8),(2,10),(3,4),(5,6),(7,9)]
=> {{1,8},{2,10},{3,4},{5,6},{7,9}}
=> ? = 10
[(1,9),(2,10),(3,4),(5,6),(7,8)]
=> {{1,9},{2,10},{3,4},{5,6},{7,8}}
=> ? = 10
[(1,10),(2,9),(3,5),(4,6),(7,8)]
=> {{1,10},{2,9},{3,5},{4,6},{7,8}}
=> ? = 10
Description
The size of the orbit of the set partition under rotation.
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