Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000945
(load all 12 compositions to match this statistic)
Mapping
St000945: 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)]
 => 16
[(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)]
 => 16
[(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)]
 => 16
[(1,6),(2,7),(3,4),(5,8)]
 => 8
[(1,5),(2,7),(3,4),(6,8)]
 => 16
[(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 number of matchings in the dihedral orbit of a perfect matching. The dihedral orbit is induced by the dihedral symmetry of the underlying circular arrangement of points. In other words, this is the number of matchings that can be obtained by rotating or reflecting the given perfect matching.
Matching statistic: St000163
(load all 5 compositions to match this statistic)
Mapping
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00221: Set partitions —conjugate⟶ Set partitions
St000163: Set partitions ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 60%
Values
[(1,2)]
 => {{1,2}}
 => {{1},{2}}
 => 1
[(1,2),(3,4)]
 => {{1,2},{3,4}}
 => {{1,3},{2},{4}}
 => 2
[(1,3),(2,4)]
 => {{1,3},{2,4}}
 => {{1,3},{2,4}}
 => 1
[(1,4),(2,3)]
 => {{1,4},{2,3}}
 => {{1},{2,4},{3}}
 => 2
[(1,2),(3,4),(5,6)]
 => {{1,2},{3,4},{5,6}}
 => {{1,3,5},{2},{4},{6}}
 => 2
[(1,3),(2,4),(5,6)]
 => {{1,3},{2,4},{5,6}}
 => {{1,3,5},{2},{4,6}}
 => 6
[(1,4),(2,3),(5,6)]
 => {{1,4},{2,3},{5,6}}
 => {{1,3},{2},{4,6},{5}}
 => 3
[(1,5),(2,3),(4,6)]
 => {{1,5},{2,3},{4,6}}
 => {{1,3},{2,4,6},{5}}
 => 6
[(1,6),(2,3),(4,5)]
 => {{1,6},{2,3},{4,5}}
 => {{1},{2,4,6},{3},{5}}
 => 2
[(1,6),(2,4),(3,5)]
 => {{1,6},{2,4},{3,5}}
 => {{1},{2,4,6},{3,5}}
 => 6
[(1,5),(2,4),(3,6)]
 => {{1,5},{2,4},{3,6}}
 => {{1,4},{2,6},{3,5}}
 => 3
[(1,4),(2,5),(3,6)]
 => {{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}}
 => {{1,3},{2,5},{4,6}}
 => 3
[(1,2),(3,5),(4,6)]
 => {{1,2},{3,5},{4,6}}
 => {{1,3,5},{2,4},{6}}
 => 6
[(1,2),(3,6),(4,5)]
 => {{1,2},{3,6},{4,5}}
 => {{1,5},{2,4},{3},{6}}
 => 3
[(1,3),(2,6),(4,5)]
 => {{1,3},{2,6},{4,5}}
 => {{1,5},{2,4,6},{3}}
 => 6
[(1,4),(2,6),(3,5)]
 => {{1,4},{2,6},{3,5}}
 => {{1,5},{2,4},{3,6}}
 => 3
[(1,5),(2,6),(3,4)]
 => {{1,5},{2,6},{3,4}}
 => {{1,3,5},{2,6},{4}}
 => 6
[(1,6),(2,5),(3,4)]
 => {{1,6},{2,5},{3,4}}
 => {{1},{2,6},{3,5},{4}}
 => 3
[(1,2),(3,4),(5,6),(7,8)]
 => {{1,2},{3,4},{5,6},{7,8}}
 => {{1,3,5,7},{2},{4},{6},{8}}
 => ? = 2
[(1,3),(2,4),(5,6),(7,8)]
 => {{1,3},{2,4},{5,6},{7,8}}
 => {{1,3,5,7},{2},{4},{6,8}}
 => ? = 8
[(1,4),(2,3),(5,6),(7,8)]
 => {{1,4},{2,3},{5,6},{7,8}}
 => {{1,3,5},{2},{4},{6,8},{7}}
 => ? = 8
[(1,5),(2,3),(4,6),(7,8)]
 => {{1,5},{2,3},{4,6},{7,8}}
 => {{1,3,5},{2},{4,6,8},{7}}
 => ? = 8
[(1,6),(2,3),(4,5),(7,8)]
 => {{1,6},{2,3},{4,5},{7,8}}
 => {{1,3},{2},{4,6,8},{5},{7}}
 => ? = 8
[(1,7),(2,3),(4,5),(6,8)]
 => {{1,7},{2,3},{4,5},{6,8}}
 => {{1,3},{2,4,6,8},{5},{7}}
 => ? = 8
[(1,8),(2,3),(4,5),(6,7)]
 => {{1,8},{2,3},{4,5},{6,7}}
 => {{1},{2,4,6,8},{3},{5},{7}}
 => ? = 2
[(1,8),(2,4),(3,5),(6,7)]
 => {{1,8},{2,4},{3,5},{6,7}}
 => {{1},{2,4,6,8},{3},{5,7}}
 => ? = 8
[(1,7),(2,4),(3,5),(6,8)]
 => {{1,7},{2,4},{3,5},{6,8}}
 => {{1,3},{2,8},{4,6},{5,7}}
 => 4
[(1,6),(2,4),(3,5),(7,8)]
 => {{1,6},{2,4},{3,5},{7,8}}
 => {{1,3},{2},{4,6,8},{5,7}}
 => ? = 8
[(1,5),(2,4),(3,6),(7,8)]
 => {{1,5},{2,4},{3,6},{7,8}}
 => {{1,3,6},{2},{4,8},{5,7}}
 => ? = 16
[(1,4),(2,5),(3,6),(7,8)]
 => {{1,4},{2,5},{3,6},{7,8}}
 => {{1,3,6},{2},{4,7},{5,8}}
 => ? = 8
[(1,3),(2,5),(4,6),(7,8)]
 => {{1,3},{2,5},{4,6},{7,8}}
 => {{1,3,5},{2},{4,7},{6,8}}
 => ? = 8
[(1,2),(3,5),(4,6),(7,8)]
 => {{1,2},{3,5},{4,6},{7,8}}
 => {{1,3,5,7},{2},{4,6},{8}}
 => ? = 8
[(1,2),(3,6),(4,5),(7,8)]
 => {{1,2},{3,6},{4,5},{7,8}}
 => {{1,3,7},{2},{4,6},{5},{8}}
 => ? = 8
[(1,3),(2,6),(4,5),(7,8)]
 => {{1,3},{2,6},{4,5},{7,8}}
 => {{1,3,7},{2},{4,6,8},{5}}
 => ? = 8
[(1,4),(2,6),(3,5),(7,8)]
 => {{1,4},{2,6},{3,5},{7,8}}
 => {{1,3,7},{2},{4,6},{5,8}}
 => ? = 16
[(1,5),(2,6),(3,4),(7,8)]
 => {{1,5},{2,6},{3,4},{7,8}}
 => {{1,3,5,7},{2},{4,8},{6}}
 => ? = 4
[(1,6),(2,5),(3,4),(7,8)]
 => {{1,6},{2,5},{3,4},{7,8}}
 => {{1,3},{2},{4,8},{5,7},{6}}
 => ? = 4
[(1,7),(2,5),(3,4),(6,8)]
 => {{1,7},{2,5},{3,4},{6,8}}
 => {{1,3},{2,4,8},{5,7},{6}}
 => ? = 8
[(1,8),(2,5),(3,4),(6,7)]
 => {{1,8},{2,5},{3,4},{6,7}}
 => {{1},{2,4,8},{3},{5,7},{6}}
 => ? = 8
[(1,8),(2,6),(3,4),(5,7)]
 => {{1,8},{2,6},{3,4},{5,7}}
 => {{1},{2,4,8},{3,5,7},{6}}
 => ? = 8
[(1,7),(2,6),(3,4),(5,8)]
 => {{1,7},{2,6},{3,4},{5,8}}
 => {{1,4},{2,8},{3,5,7},{6}}
 => ? = 16
[(1,6),(2,7),(3,4),(5,8)]
 => {{1,6},{2,7},{3,4},{5,8}}
 => {{1,4},{2,5,7},{3,8},{6}}
 => ? = 8
[(1,5),(2,7),(3,4),(6,8)]
 => {{1,5},{2,7},{3,4},{6,8}}
 => {{1,3},{2,5,7},{4,8},{6}}
 => ? = 16
[(1,4),(2,7),(3,5),(6,8)]
 => {{1,4},{2,7},{3,5},{6,8}}
 => {{1,3},{2,7},{4,6},{5,8}}
 => 8
[(1,3),(2,7),(4,5),(6,8)]
 => {{1,3},{2,7},{4,5},{6,8}}
 => {{1,3},{2,7},{4,6,8},{5}}
 => ? = 8
[(1,2),(3,7),(4,5),(6,8)]
 => {{1,2},{3,7},{4,5},{6,8}}
 => {{1,3,7},{2,4,6},{5},{8}}
 => ? = 8
[(1,2),(3,8),(4,5),(6,7)]
 => {{1,2},{3,8},{4,5},{6,7}}
 => {{1,7},{2,4,6},{3},{5},{8}}
 => ? = 8
[(1,3),(2,8),(4,5),(6,7)]
 => {{1,3},{2,8},{4,5},{6,7}}
 => {{1,7},{2,4,6,8},{3},{5}}
 => ? = 8
[(1,4),(2,8),(3,5),(6,7)]
 => {{1,4},{2,8},{3,5},{6,7}}
 => {{1,7},{2,4,6},{3},{5,8}}
 => ? = 8
[(1,5),(2,8),(3,4),(6,7)]
 => {{1,5},{2,8},{3,4},{6,7}}
 => {{1,5,7},{2,4,8},{3},{6}}
 => ? = 8
[(1,6),(2,8),(3,4),(5,7)]
 => {{1,6},{2,8},{3,4},{5,7}}
 => {{1,5,7},{2,4},{3,8},{6}}
 => ? = 8
[(1,7),(2,8),(3,4),(5,6)]
 => {{1,7},{2,8},{3,4},{5,6}}
 => {{1,3,5,7},{2,8},{4},{6}}
 => ? = 8
[(1,8),(2,7),(3,4),(5,6)]
 => {{1,8},{2,7},{3,4},{5,6}}
 => {{1},{2,8},{3,5,7},{4},{6}}
 => ? = 8
[(1,8),(2,7),(3,5),(4,6)]
 => {{1,8},{2,7},{3,5},{4,6}}
 => {{1},{2,8},{3,5,7},{4,6}}
 => ? = 8
[(1,7),(2,8),(3,5),(4,6)]
 => {{1,7},{2,8},{3,5},{4,6}}
 => {{1,7},{2,8},{3,5},{4,6}}
 => 4
[(1,6),(2,8),(3,5),(4,7)]
 => {{1,6},{2,8},{3,5},{4,7}}
 => {{1,7},{2,5},{3,8},{4,6}}
 => 8
[(1,5),(2,8),(3,6),(4,7)]
 => {{1,5},{2,8},{3,6},{4,7}}
 => {{1,7},{2,5},{3,6},{4,8}}
 => 8
[(1,4),(2,8),(3,6),(5,7)]
 => {{1,4},{2,8},{3,6},{5,7}}
 => {{1,7},{2,4},{3,6},{5,8}}
 => 8
[(1,3),(2,8),(4,6),(5,7)]
 => {{1,3},{2,8},{4,6},{5,7}}
 => {{1,7},{2,4},{3,5},{6,8}}
 => 4
[(1,2),(3,8),(4,6),(5,7)]
 => {{1,2},{3,8},{4,6},{5,7}}
 => {{1,7},{2,4,6},{3,5},{8}}
 => ? = 8
[(1,2),(3,7),(4,6),(5,8)]
 => {{1,2},{3,7},{4,6},{5,8}}
 => {{1,4,7},{2,6},{3,5},{8}}
 => ? = 16
[(1,3),(2,7),(4,6),(5,8)]
 => {{1,3},{2,7},{4,6},{5,8}}
 => {{1,4},{2,7},{3,5},{6,8}}
 => 8
[(1,4),(2,7),(3,6),(5,8)]
 => {{1,4},{2,7},{3,6},{5,8}}
 => {{1,4},{2,7},{3,6},{5,8}}
 => 2
[(1,5),(2,7),(3,6),(4,8)]
 => {{1,5},{2,7},{3,6},{4,8}}
 => {{1,5},{2,7},{3,6},{4,8}}
 => 4
[(1,6),(2,7),(3,5),(4,8)]
 => {{1,6},{2,7},{3,5},{4,8}}
 => {{1,5},{2,7},{3,8},{4,6}}
 => 8
[(1,7),(2,6),(3,5),(4,8)]
 => {{1,7},{2,6},{3,5},{4,8}}
 => {{1,5},{2,8},{3,7},{4,6}}
 => 4
[(1,8),(2,6),(3,5),(4,7)]
 => {{1,8},{2,6},{3,5},{4,7}}
 => {{1},{2,5,8},{3,7},{4,6}}
 => ? = 16
[(1,8),(2,5),(3,6),(4,7)]
 => {{1,8},{2,5},{3,6},{4,7}}
 => {{1},{2,5,8},{3,6},{4,7}}
 => ? = 8
[(1,7),(2,5),(3,6),(4,8)]
 => {{1,7},{2,5},{3,6},{4,8}}
 => {{1,5},{2,8},{3,6},{4,7}}
 => 8
[(1,6),(2,5),(3,7),(4,8)]
 => {{1,6},{2,5},{3,7},{4,8}}
 => {{1,5},{2,6},{3,8},{4,7}}
 => 4
[(1,5),(2,6),(3,7),(4,8)]
 => {{1,5},{2,6},{3,7},{4,8}}
 => {{1,5},{2,6},{3,7},{4,8}}
 => 1
[(1,4),(2,6),(3,7),(5,8)]
 => {{1,4},{2,6},{3,7},{5,8}}
 => {{1,4},{2,6},{3,7},{5,8}}
 => 4
[(1,3),(2,6),(4,7),(5,8)]
 => {{1,3},{2,6},{4,7},{5,8}}
 => {{1,4},{2,5},{3,7},{6,8}}
 => 8
[(1,2),(3,6),(4,7),(5,8)]
 => {{1,2},{3,6},{4,7},{5,8}}
 => {{1,4,7},{2,5},{3,6},{8}}
 => ? = 8
[(1,2),(3,5),(4,7),(6,8)]
 => {{1,2},{3,5},{4,7},{6,8}}
 => {{1,3,7},{2,5},{4,6},{8}}
 => ? = 8
[(1,3),(2,5),(4,7),(6,8)]
 => {{1,3},{2,5},{4,7},{6,8}}
 => {{1,3},{2,5},{4,7},{6,8}}
 => 8
[(1,4),(2,5),(3,7),(6,8)]
 => {{1,4},{2,5},{3,7},{6,8}}
 => {{1,3},{2,6},{4,7},{5,8}}
 => 8
[(1,5),(2,4),(3,7),(6,8)]
 => {{1,5},{2,4},{3,7},{6,8}}
 => {{1,3},{2,6},{4,8},{5,7}}
 => 4
[(1,6),(2,4),(3,7),(5,8)]
 => {{1,6},{2,4},{3,7},{5,8}}
 => {{1,4},{2,6},{3,8},{5,7}}
 => 8
[(1,7),(2,4),(3,6),(5,8)]
 => {{1,7},{2,4},{3,6},{5,8}}
 => {{1,4},{2,8},{3,6},{5,7}}
 => 8
[(1,8),(2,4),(3,6),(5,7)]
 => {{1,8},{2,4},{3,6},{5,7}}
 => {{1},{2,4,8},{3,6},{5,7}}
 => ? = 8
[(1,8),(2,3),(4,6),(5,7)]
 => {{1,8},{2,3},{4,6},{5,7}}
 => {{1},{2,4,6,8},{3,5},{7}}
 => ? = 8
[(1,7),(2,3),(4,6),(5,8)]
 => {{1,7},{2,3},{4,6},{5,8}}
 => {{1,4},{2,6,8},{3,5},{7}}
 => ? = 8
[(1,6),(2,3),(4,7),(5,8)]
 => {{1,6},{2,3},{4,7},{5,8}}
 => {{1,4},{2,5},{3,6,8},{7}}
 => ? = 8
[(1,5),(2,3),(4,7),(6,8)]
 => {{1,5},{2,3},{4,7},{6,8}}
 => {{1,3},{2,5},{4,6,8},{7}}
 => ? = 16
[(1,4),(2,3),(5,7),(6,8)]
 => {{1,4},{2,3},{5,7},{6,8}}
 => {{1,3,5},{2,4},{6,8},{7}}
 => ? = 8
[(1,3),(2,4),(5,7),(6,8)]
 => {{1,3},{2,4},{5,7},{6,8}}
 => {{1,3},{2,4},{5,7},{6,8}}
 => 4
[(1,2),(3,4),(5,7),(6,8)]
 => {{1,2},{3,4},{5,7},{6,8}}
 => {{1,3,5,7},{2,4},{6},{8}}
 => ? = 8
[(1,2),(3,4),(5,8),(6,7)]
 => {{1,2},{3,4},{5,8},{6,7}}
 => {{1,5,7},{2,4},{3},{6},{8}}
 => ? = 8
[(1,3),(2,4),(5,8),(6,7)]
 => {{1,3},{2,4},{5,8},{6,7}}
 => {{1,5,7},{2,4},{3},{6,8}}
 => ? = 8
[(1,4),(2,3),(5,8),(6,7)]
 => {{1,4},{2,3},{5,8},{6,7}}
 => {{1,5},{2,4},{3},{6,8},{7}}
 => ? = 4
[(1,6),(2,4),(3,8),(5,7)]
 => {{1,6},{2,4},{3,8},{5,7}}
 => {{1,6},{2,4},{3,8},{5,7}}
 => 8
[(1,3),(2,6),(4,8),(5,7)]
 => {{1,3},{2,6},{4,8},{5,7}}
 => {{1,5},{2,4},{3,7},{6,8}}
 => 4
[(1,4),(2,6),(3,8),(5,7)]
 => {{1,4},{2,6},{3,8},{5,7}}
 => {{1,6},{2,4},{3,7},{5,8}}
 => 8
[(1,5),(2,6),(3,8),(4,7)]
 => {{1,5},{2,6},{3,8},{4,7}}
 => {{1,6},{2,5},{3,7},{4,8}}
 => 4
[(1,6),(2,5),(3,8),(4,7)]
 => {{1,6},{2,5},{3,8},{4,7}}
 => {{1,6},{2,5},{3,8},{4,7}}
 => 2
[(1,7),(2,5),(3,8),(4,6)]
 => {{1,7},{2,5},{3,8},{4,6}}
 => {{1,6},{2,8},{3,5},{4,7}}
 => 8
[(1,5),(2,7),(3,8),(4,6)]
 => {{1,5},{2,7},{3,8},{4,6}}
 => {{1,6},{2,7},{3,5},{4,8}}
 => 8
[(1,5),(2,8),(3,7),(4,6)]
 => {{1,5},{2,8},{3,7},{4,6}}
 => {{1,7},{2,6},{3,5},{4,8}}
 => 4
Description
The size of the orbit of the set partition under rotation.