Your data matches 6 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000945
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
Mapping
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00221: Set partitions —conjugate⟶ Set partitions
St000163: Set partitions ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 86%
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}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,4),(5,6),(7,8)]
 => {{1,3},{2,4},{5,6},{7,8}}
 => {{1,3,5,7},{2},{4},{6,8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,3),(5,6),(7,8)]
 => {{1,4},{2,3},{5,6},{7,8}}
 => {{1,3,5},{2},{4},{6,8},{7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,3),(4,6),(7,8)]
 => {{1,5},{2,3},{4,6},{7,8}}
 => {{1,3,5},{2},{4,6,8},{7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,3),(4,5),(7,8)]
 => {{1,6},{2,3},{4,5},{7,8}}
 => {{1,3},{2},{4,6,8},{5},{7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,3),(4,5),(6,8)]
 => {{1,7},{2,3},{4,5},{6,8}}
 => {{1,3},{2,4,6,8},{5},{7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,3),(4,5),(6,7)]
 => {{1,8},{2,3},{4,5},{6,7}}
 => {{1},{2,4,6,8},{3},{5},{7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,4),(3,5),(6,7)]
 => {{1,8},{2,4},{3,5},{6,7}}
 => {{1},{2,4,6,8},{3},{5,7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(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}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,4),(3,6),(7,8)]
 => {{1,5},{2,4},{3,6},{7,8}}
 => {{1,3,6},{2},{4,8},{5,7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,5),(3,6),(7,8)]
 => {{1,4},{2,5},{3,6},{7,8}}
 => {{1,3,6},{2},{4,7},{5,8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,5),(4,6),(7,8)]
 => {{1,3},{2,5},{4,6},{7,8}}
 => {{1,3,5},{2},{4,7},{6,8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,5),(4,6),(7,8)]
 => {{1,2},{3,5},{4,6},{7,8}}
 => {{1,3,5,7},{2},{4,6},{8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,6),(4,5),(7,8)]
 => {{1,2},{3,6},{4,5},{7,8}}
 => {{1,3,7},{2},{4,6},{5},{8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,6),(4,5),(7,8)]
 => {{1,3},{2,6},{4,5},{7,8}}
 => {{1,3,7},{2},{4,6,8},{5}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,6),(3,5),(7,8)]
 => {{1,4},{2,6},{3,5},{7,8}}
 => {{1,3,7},{2},{4,6},{5,8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,6),(3,4),(7,8)]
 => {{1,5},{2,6},{3,4},{7,8}}
 => {{1,3,5,7},{2},{4,8},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,5),(3,4),(7,8)]
 => {{1,6},{2,5},{3,4},{7,8}}
 => {{1,3},{2},{4,8},{5,7},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,5),(3,4),(6,8)]
 => {{1,7},{2,5},{3,4},{6,8}}
 => {{1,3},{2,4,8},{5,7},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,5),(3,4),(6,7)]
 => {{1,8},{2,5},{3,4},{6,7}}
 => {{1},{2,4,8},{3},{5,7},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,6),(3,4),(5,7)]
 => {{1,8},{2,6},{3,4},{5,7}}
 => {{1},{2,4,8},{3,5,7},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,6),(3,4),(5,8)]
 => {{1,7},{2,6},{3,4},{5,8}}
 => {{1,4},{2,8},{3,5,7},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,7),(3,4),(5,8)]
 => {{1,6},{2,7},{3,4},{5,8}}
 => {{1,4},{2,5,7},{3,8},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,7),(3,4),(6,8)]
 => {{1,5},{2,7},{3,4},{6,8}}
 => {{1,3},{2,5,7},{4,8},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(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}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,7),(4,5),(6,8)]
 => {{1,2},{3,7},{4,5},{6,8}}
 => {{1,3,7},{2,4,6},{5},{8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,8),(4,5),(6,7)]
 => {{1,2},{3,8},{4,5},{6,7}}
 => {{1,7},{2,4,6},{3},{5},{8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,8),(4,5),(6,7)]
 => {{1,3},{2,8},{4,5},{6,7}}
 => {{1,7},{2,4,6,8},{3},{5}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,8),(3,5),(6,7)]
 => {{1,4},{2,8},{3,5},{6,7}}
 => {{1,7},{2,4,6},{3},{5,8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,8),(3,4),(6,7)]
 => {{1,5},{2,8},{3,4},{6,7}}
 => {{1,5,7},{2,4,8},{3},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,8),(3,4),(5,7)]
 => {{1,6},{2,8},{3,4},{5,7}}
 => {{1,5,7},{2,4},{3,8},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,8),(3,4),(5,6)]
 => {{1,7},{2,8},{3,4},{5,6}}
 => {{1,3,5,7},{2,8},{4},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,7),(3,4),(5,6)]
 => {{1,8},{2,7},{3,4},{5,6}}
 => {{1},{2,8},{3,5,7},{4},{6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,7),(3,5),(4,6)]
 => {{1,8},{2,7},{3,5},{4,6}}
 => {{1},{2,8},{3,5,7},{4,6}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(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}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,7),(4,6),(5,8)]
 => {{1,2},{3,7},{4,6},{5,8}}
 => {{1,4,7},{2,6},{3,5},{8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(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}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,5),(3,6),(4,7)]
 => {{1,8},{2,5},{3,6},{4,7}}
 => {{1},{2,5,8},{3,6},{4,7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(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}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,5),(4,7),(6,8)]
 => {{1,2},{3,5},{4,7},{6,8}}
 => {{1,3,7},{2,5},{4,6},{8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(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}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,3),(4,6),(5,7)]
 => {{1,8},{2,3},{4,6},{5,7}}
 => {{1},{2,4,6,8},{3,5},{7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,3),(4,6),(5,8)]
 => {{1,7},{2,3},{4,6},{5,8}}
 => {{1,4},{2,6,8},{3,5},{7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,3),(4,7),(5,8)]
 => {{1,6},{2,3},{4,7},{5,8}}
 => {{1,4},{2,5},{3,6,8},{7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,3),(4,7),(6,8)]
 => {{1,5},{2,3},{4,7},{6,8}}
 => {{1,3},{2,5},{4,6,8},{7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,3),(5,7),(6,8)]
 => {{1,4},{2,3},{5,7},{6,8}}
 => {{1,3,5},{2,4},{6,8},{7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(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}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,4),(5,8),(6,7)]
 => {{1,2},{3,4},{5,8},{6,7}}
 => {{1,5,7},{2,4},{3},{6},{8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,4),(5,8),(6,7)]
 => {{1,3},{2,4},{5,8},{6,7}}
 => {{1,5,7},{2,4},{3},{6,8}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,3),(5,8),(6,7)]
 => {{1,4},{2,3},{5,8},{6,7}}
 => {{1,5},{2,4},{3},{6,8},{7}}
 => ? ∊ {2,2,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(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.
Matching statistic: St001880
(load all 3 compositions to match this statistic)
Mapping
Mp00150: Perfect matchings —to Dyck path⟶ Dyck paths
Mp00123: Dyck paths —Barnabei-Castronuovo involution⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 29%
Values
[(1,2)]
 => [1,0]
 => [1,0]
 => ([],1)
 => ? = 1
[(1,2),(3,4)]
 => [1,0,1,0]
 => [1,0,1,0]
 => ([(0,1)],2)
 => ? ∊ {1,2,2}
[(1,3),(2,4)]
 => [1,1,0,0]
 => [1,1,0,0]
 => ([],2)
 => ? ∊ {1,2,2}
[(1,4),(2,3)]
 => [1,1,0,0]
 => [1,1,0,0]
 => ([],2)
 => ? ∊ {1,2,2}
[(1,2),(3,4),(5,6)]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => ([(1,2)],3)
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,3),(2,4),(5,6)]
 => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,4),(2,3),(5,6)]
 => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,5),(2,3),(4,6)]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ([(0,2),(2,1)],3)
 => 3
[(1,6),(2,3),(4,5)]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ([(0,2),(2,1)],3)
 => 3
[(1,6),(2,4),(3,5)]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => ([],3)
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,5),(2,4),(3,6)]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => ([],3)
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,4),(2,5),(3,6)]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => ([],3)
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,3),(2,5),(4,6)]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ([(0,2),(2,1)],3)
 => 3
[(1,2),(3,5),(4,6)]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => ([(0,1),(0,2)],3)
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,2),(3,6),(4,5)]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => ([(0,1),(0,2)],3)
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,3),(2,6),(4,5)]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ([(0,2),(2,1)],3)
 => 3
[(1,4),(2,6),(3,5)]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => ([],3)
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,5),(2,6),(3,4)]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => ([],3)
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,6),(2,5),(3,4)]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => ([],3)
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,2),(3,4),(5,6),(7,8)]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[(1,3),(2,4),(5,6),(7,8)]
 => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ([(0,3),(3,1),(3,2)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,3),(5,6),(7,8)]
 => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ([(0,3),(3,1),(3,2)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,3),(4,6),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,3),(4,5),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,3),(4,5),(6,8)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ([(0,3),(1,2),(1,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,3),(4,5),(6,7)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ([(0,3),(1,2),(1,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,4),(3,5),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,4),(3,5),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,4),(3,5),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,4),(3,6),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,5),(3,6),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,5),(4,6),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,5),(4,6),(7,8)]
 => [1,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => ([(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,6),(4,5),(7,8)]
 => [1,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => ([(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,6),(4,5),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,6),(3,5),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,6),(3,4),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,5),(3,4),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,5),(3,4),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,5),(3,4),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,6),(3,4),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,7),(2,6),(3,4),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,6),(2,7),(3,4),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,5),(2,7),(3,4),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,7),(3,5),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,7),(4,5),(6,8)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ([(0,3),(1,2),(1,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,7),(4,5),(6,8)]
 => [1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0]
 => ([(1,2),(1,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,8),(4,5),(6,7)]
 => [1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0]
 => ([(1,2),(1,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,8),(4,5),(6,7)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ([(0,3),(1,2),(1,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,8),(3,5),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,8),(3,4),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,8),(3,4),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,7),(2,8),(3,4),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,8),(2,7),(3,4),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,8),(2,7),(3,5),(4,6)]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => ([],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,8),(3,5),(4,6)]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => ([],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,8),(3,5),(4,7)]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => ([],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,8),(3,6),(4,7)]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => ([],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,8),(3,6),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,3),(2,8),(4,6),(5,7)]
 => [1,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(3,1)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,8),(4,6),(5,7)]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,7),(4,6),(5,8)]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3)],4)
 => ? ∊ {1,2,2,2,2,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,7),(3,6),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,4),(2,6),(3,7),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,6),(2,4),(3,7),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,7),(2,4),(3,6),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,8),(2,4),(3,6),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,8),(2,4),(3,7),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,7),(2,4),(3,8),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,6),(2,4),(3,8),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,4),(2,6),(3,8),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,4),(2,7),(3,8),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[(1,4),(2,8),(3,7),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St000264
Mapping
Mp00150: Perfect matchings —to Dyck path⟶ Dyck paths
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 15%●distinct values known / distinct values provided: 14%
Values
[(1,2)]
 => [1,0]
 => [1] => ([],1)
 => ? = 1
[(1,2),(3,4)]
 => [1,0,1,0]
 => [1,2] => ([],2)
 => ? ∊ {1,2,2}
[(1,3),(2,4)]
 => [1,1,0,0]
 => [2,1] => ([(0,1)],2)
 => ? ∊ {1,2,2}
[(1,4),(2,3)]
 => [1,1,0,0]
 => [2,1] => ([(0,1)],2)
 => ? ∊ {1,2,2}
[(1,2),(3,4),(5,6)]
 => [1,0,1,0,1,0]
 => [1,2,3] => ([],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,3),(2,4),(5,6)]
 => [1,1,0,0,1,0]
 => [2,1,3] => ([(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,4),(2,3),(5,6)]
 => [1,1,0,0,1,0]
 => [2,1,3] => ([(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,5),(2,3),(4,6)]
 => [1,1,0,1,0,0]
 => [2,3,1] => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,6),(2,3),(4,5)]
 => [1,1,0,1,0,0]
 => [2,3,1] => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,6),(2,4),(3,5)]
 => [1,1,1,0,0,0]
 => [3,1,2] => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,5),(2,4),(3,6)]
 => [1,1,1,0,0,0]
 => [3,1,2] => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,4),(2,5),(3,6)]
 => [1,1,1,0,0,0]
 => [3,1,2] => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,3),(2,5),(4,6)]
 => [1,1,0,1,0,0]
 => [2,3,1] => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,2),(3,5),(4,6)]
 => [1,0,1,1,0,0]
 => [1,3,2] => ([(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,2),(3,6),(4,5)]
 => [1,0,1,1,0,0]
 => [1,3,2] => ([(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,3),(2,6),(4,5)]
 => [1,1,0,1,0,0]
 => [2,3,1] => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,4),(2,6),(3,5)]
 => [1,1,1,0,0,0]
 => [3,1,2] => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,5),(2,6),(3,4)]
 => [1,1,1,0,0,0]
 => [3,1,2] => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,6),(2,5),(3,4)]
 => [1,1,1,0,0,0]
 => [3,1,2] => ([(0,2),(1,2)],3)
 => ? ∊ {1,2,2,3,3,3,3,3,3,6,6,6,6,6,6}
[(1,2),(3,4),(5,6),(7,8)]
 => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => ([],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,4),(5,6),(7,8)]
 => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => ([(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,3),(5,6),(7,8)]
 => [1,1,0,0,1,0,1,0]
 => [2,1,3,4] => ([(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,3),(4,6),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,3),(4,5),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,3),(4,5),(6,8)]
 => [1,1,0,1,0,1,0,0]
 => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,3),(4,5),(6,7)]
 => [1,1,0,1,0,1,0,0]
 => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,4),(3,5),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,4),(3,5),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,4),(3,5),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,4),(3,6),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,5),(3,6),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,5),(4,6),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,5),(4,6),(7,8)]
 => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,6),(4,5),(7,8)]
 => [1,0,1,1,0,0,1,0]
 => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,6),(4,5),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,6),(3,5),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,6),(3,4),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,5),(3,4),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,5),(3,4),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,5),(3,4),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,6),(3,4),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,7),(2,6),(3,4),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,6),(2,7),(3,4),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,5),(2,7),(3,4),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,7),(3,5),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,7),(4,5),(6,8)]
 => [1,1,0,1,0,1,0,0]
 => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,7),(4,5),(6,8)]
 => [1,0,1,1,0,1,0,0]
 => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,8),(4,5),(6,7)]
 => [1,0,1,1,0,1,0,0]
 => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,8),(4,5),(6,7)]
 => [1,1,0,1,0,1,0,0]
 => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,8),(3,5),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,8),(3,4),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,8),(3,4),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,7),(2,8),(3,4),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,8),(2,7),(3,4),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,8),(2,7),(3,5),(4,6)]
 => [1,1,1,1,0,0,0,0]
 => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,8),(3,5),(4,6)]
 => [1,1,1,1,0,0,0,0]
 => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {1,2,2,2,2,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,8),(3,6),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,4),(2,7),(3,6),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,4),(2,6),(3,7),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,6),(2,4),(3,7),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,7),(2,4),(3,6),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,8),(2,4),(3,6),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,8),(2,4),(3,7),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,7),(2,4),(3,8),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,6),(2,4),(3,8),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,4),(2,6),(3,8),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,4),(2,7),(3,8),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[(1,4),(2,8),(3,7),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.
Matching statistic: St001232
Mapping
Mp00150: Perfect matchings —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 57%
Values
[(1,2)]
 => [1,0]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
[(1,2),(3,4)]
 => [1,0,1,0]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ? = 1
[(1,3),(2,4)]
 => [1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2
[(1,4),(2,3)]
 => [1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2
[(1,2),(3,4),(5,6)]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,3),(2,4),(5,6)]
 => [1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,4),(2,3),(5,6)]
 => [1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,5),(2,3),(4,6)]
 => [1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[(1,6),(2,3),(4,5)]
 => [1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[(1,6),(2,4),(3,5)]
 => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,5),(2,4),(3,6)]
 => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,4),(2,5),(3,6)]
 => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,3),(2,5),(4,6)]
 => [1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[(1,2),(3,5),(4,6)]
 => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,2),(3,6),(4,5)]
 => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,3),(2,6),(4,5)]
 => [1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[(1,4),(2,6),(3,5)]
 => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,5),(2,6),(3,4)]
 => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,6),(2,5),(3,4)]
 => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,3,3,6,6,6,6,6,6}
[(1,2),(3,4),(5,6),(7,8)]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,4),(5,6),(7,8)]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,3),(5,6),(7,8)]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,3),(4,6),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,3),(4,5),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,3),(4,5),(6,8)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[(1,8),(2,3),(4,5),(6,7)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[(1,8),(2,4),(3,5),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,4),(3,5),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,4),(3,5),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,4),(3,6),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,5),(3,6),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,5),(4,6),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,5),(4,6),(7,8)]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,6),(4,5),(7,8)]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,6),(4,5),(7,8)]
 => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,6),(3,5),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,6),(3,4),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,5),(3,4),(7,8)]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,5),(3,4),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,5),(3,4),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,6),(3,4),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,6),(3,4),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,7),(3,4),(5,8)]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,7),(3,4),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,7),(3,5),(6,8)]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,7),(4,5),(6,8)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[(1,2),(3,7),(4,5),(6,8)]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,8),(4,5),(6,7)]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,8),(4,5),(6,7)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[(1,4),(2,8),(3,5),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,8),(3,4),(6,7)]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,8),(3,4),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,8),(3,4),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,7),(3,4),(5,6)]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,7),(3,5),(4,6)]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,8),(3,5),(4,6)]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,8),(3,5),(4,7)]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,8),(3,6),(4,7)]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,8),(3,6),(5,7)]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,8),(4,6),(5,7)]
 => [1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,8),(4,6),(5,7)]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,5),(4,7),(6,8)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[(1,5),(2,3),(4,7),(6,8)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[(1,5),(2,3),(4,8),(6,7)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[(1,3),(2,5),(4,8),(6,7)]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001907
(load all 4 compositions to match this statistic)
Mapping
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001907: Signed permutations ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 57%
Values
[(1,2)]
 => [2,1] => [2,1] => [2,1] => 1
[(1,2),(3,4)]
 => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2
[(1,3),(2,4)]
 => [3,4,1,2] => [4,1,3,2] => [4,1,3,2] => 1
[(1,4),(2,3)]
 => [3,4,2,1] => [2,4,3,1] => [2,4,3,1] => 2
[(1,2),(3,4),(5,6)]
 => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[(1,3),(2,4),(5,6)]
 => [3,4,1,2,6,5] => [4,1,3,2,6,5] => [4,1,3,2,6,5] => ? ∊ {1,6,6,6,6,6,6}
[(1,4),(2,3),(5,6)]
 => [3,4,2,1,6,5] => [2,4,3,1,6,5] => [2,4,3,1,6,5] => 3
[(1,5),(2,3),(4,6)]
 => [3,5,2,6,1,4] => [6,5,3,1,2,4] => [6,5,3,1,2,4] => 2
[(1,6),(2,3),(4,5)]
 => [3,5,2,6,4,1] => [4,6,3,5,1,2] => [4,6,3,5,1,2] => 3
[(1,6),(2,4),(3,5)]
 => [4,5,6,2,3,1] => [3,6,2,4,5,1] => [3,6,2,4,5,1] => ? ∊ {1,6,6,6,6,6,6}
[(1,5),(2,4),(3,6)]
 => [4,5,6,2,1,3] => [2,6,1,4,5,3] => [2,6,1,4,5,3] => ? ∊ {1,6,6,6,6,6,6}
[(1,4),(2,5),(3,6)]
 => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [6,1,2,4,5,3] => ? ∊ {1,6,6,6,6,6,6}
[(1,3),(2,5),(4,6)]
 => [3,5,1,6,2,4] => [5,6,3,2,1,4] => [5,6,3,2,1,4] => 2
[(1,2),(3,5),(4,6)]
 => [2,1,5,6,3,4] => [2,1,6,3,5,4] => [2,1,6,3,5,4] => ? ∊ {1,6,6,6,6,6,6}
[(1,2),(3,6),(4,5)]
 => [2,1,5,6,4,3] => [2,1,4,6,5,3] => [2,1,4,6,5,3] => 3
[(1,3),(2,6),(4,5)]
 => [3,5,1,6,4,2] => [5,4,3,6,1,2] => [5,4,3,6,1,2] => 3
[(1,4),(2,6),(3,5)]
 => [4,5,6,1,3,2] => [6,3,1,4,5,2] => [6,3,1,4,5,2] => ? ∊ {1,6,6,6,6,6,6}
[(1,5),(2,6),(3,4)]
 => [4,5,6,3,1,2] => [3,1,6,4,5,2] => [3,1,6,4,5,2] => ? ∊ {1,6,6,6,6,6,6}
[(1,6),(2,5),(3,4)]
 => [4,5,6,3,2,1] => [2,3,6,4,5,1] => [2,3,6,4,5,1] => 3
[(1,2),(3,4),(5,6),(7,8)]
 => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[(1,3),(2,4),(5,6),(7,8)]
 => [3,4,1,2,6,5,8,7] => [4,1,3,2,6,5,8,7] => [4,1,3,2,6,5,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,3),(5,6),(7,8)]
 => [3,4,2,1,6,5,8,7] => [2,4,3,1,6,5,8,7] => [2,4,3,1,6,5,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,3),(4,6),(7,8)]
 => [3,5,2,6,1,4,8,7] => [6,5,3,1,2,4,8,7] => [6,5,3,1,2,4,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,3),(4,5),(7,8)]
 => [3,5,2,6,4,1,8,7] => [4,6,3,5,1,2,8,7] => [4,6,3,5,1,2,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,3),(4,5),(6,8)]
 => [3,5,2,7,4,8,1,6] => [8,5,3,7,2,1,4,6] => [8,5,3,7,2,1,4,6] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,3),(4,5),(6,7)]
 => [3,5,2,7,4,8,6,1] => [6,5,3,8,2,7,1,4] => [6,5,3,8,2,7,1,4] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,4),(3,5),(6,7)]
 => [4,5,7,2,3,8,6,1] => [6,8,1,4,5,7,3,2] => [6,8,1,4,5,7,3,2] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,4),(3,5),(6,8)]
 => [4,5,7,2,3,8,1,6] => [8,7,2,4,5,1,3,6] => [8,7,2,4,5,1,3,6] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,4),(3,5),(7,8)]
 => [4,5,6,2,3,1,8,7] => [3,6,2,4,5,1,8,7] => [3,6,2,4,5,1,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,4),(3,6),(7,8)]
 => [4,5,6,2,1,3,8,7] => [2,6,1,4,5,3,8,7] => [2,6,1,4,5,3,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,5),(3,6),(7,8)]
 => [4,5,6,1,2,3,8,7] => [6,1,2,4,5,3,8,7] => [6,1,2,4,5,3,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,5),(4,6),(7,8)]
 => [3,5,1,6,2,4,8,7] => [5,6,3,2,1,4,8,7] => [5,6,3,2,1,4,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,5),(4,6),(7,8)]
 => [2,1,5,6,3,4,8,7] => [2,1,6,3,5,4,8,7] => [2,1,6,3,5,4,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,6),(4,5),(7,8)]
 => [2,1,5,6,4,3,8,7] => [2,1,4,6,5,3,8,7] => [2,1,4,6,5,3,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,6),(4,5),(7,8)]
 => [3,5,1,6,4,2,8,7] => [5,4,3,6,1,2,8,7] => [5,4,3,6,1,2,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,6),(3,5),(7,8)]
 => [4,5,6,1,3,2,8,7] => [6,3,1,4,5,2,8,7] => [6,3,1,4,5,2,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,6),(3,4),(7,8)]
 => [4,5,6,3,1,2,8,7] => [3,1,6,4,5,2,8,7] => [3,1,6,4,5,2,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,5),(3,4),(7,8)]
 => [4,5,6,3,2,1,8,7] => [2,3,6,4,5,1,8,7] => [2,3,6,4,5,1,8,7] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,5),(3,4),(6,8)]
 => [4,5,7,3,2,8,1,6] => [8,3,7,4,5,1,2,6] => [8,3,7,4,5,1,2,6] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,5),(3,4),(6,7)]
 => [4,5,7,3,2,8,6,1] => [6,3,8,4,5,7,1,2] => [6,3,8,4,5,7,1,2] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,6),(3,4),(5,7)]
 => [4,6,7,3,8,2,5,1] => [5,8,7,4,2,6,3,1] => [5,8,7,4,2,6,3,1] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,6),(3,4),(5,8)]
 => [4,6,7,3,8,2,1,5] => [2,8,7,4,1,6,3,5] => [2,8,7,4,1,6,3,5] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,7),(3,4),(5,8)]
 => [4,6,7,3,8,1,2,5] => [8,1,7,4,2,6,3,5] => [8,1,7,4,2,6,3,5] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,7),(3,4),(6,8)]
 => [4,5,7,3,1,8,2,6] => [3,7,8,4,5,1,2,6] => [3,7,8,4,5,1,2,6] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,7),(3,5),(6,8)]
 => [4,5,7,1,3,8,2,6] => [7,8,1,4,5,2,3,6] => [7,8,1,4,5,2,3,6] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,7),(4,5),(6,8)]
 => [3,5,1,7,4,8,2,6] => [5,8,3,7,1,2,4,6] => [5,8,3,7,1,2,4,6] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,7),(4,5),(6,8)]
 => [2,1,5,7,4,8,3,6] => [2,1,8,7,5,3,4,6] => [2,1,8,7,5,3,4,6] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,8),(4,5),(6,7)]
 => [2,1,5,7,4,8,6,3] => [2,1,6,8,5,7,3,4] => [2,1,6,8,5,7,3,4] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,8),(4,5),(6,7)]
 => [3,5,1,7,4,8,6,2] => [5,6,3,8,1,7,2,4] => [5,6,3,8,1,7,2,4] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,8),(3,5),(6,7)]
 => [4,5,7,1,3,8,6,2] => [7,6,1,4,5,8,3,2] => [7,6,1,4,5,8,3,2] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,8),(3,4),(6,7)]
 => [4,5,7,3,1,8,6,2] => [3,7,6,4,5,8,2,1] => [3,7,6,4,5,8,2,1] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,8),(3,4),(5,7)]
 => [4,6,7,3,8,1,5,2] => [8,5,7,4,1,6,3,2] => [8,5,7,4,1,6,3,2] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,8),(3,4),(5,6)]
 => [4,6,7,3,8,5,1,2] => [5,1,8,4,7,6,2,3] => [5,1,8,4,7,6,2,3] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,7),(3,4),(5,6)]
 => [4,6,7,3,8,5,2,1] => [2,5,8,4,7,6,1,3] => [2,5,8,4,7,6,1,3] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,8),(2,7),(3,5),(4,6)]
 => [5,6,7,8,3,4,2,1] => [2,4,8,3,5,6,7,1] => [2,4,8,3,5,6,7,1] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,7),(2,8),(3,5),(4,6)]
 => [5,6,7,8,3,4,1,2] => [4,1,8,3,5,6,7,2] => [4,1,8,3,5,6,7,2] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,6),(2,8),(3,5),(4,7)]
 => [5,6,7,8,3,1,4,2] => [3,8,4,2,5,6,7,1] => [3,8,4,2,5,6,7,1] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,5),(2,8),(3,6),(4,7)]
 => [5,6,7,8,1,3,4,2] => [8,4,1,3,5,6,7,2] => [8,4,1,3,5,6,7,2] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,4),(2,8),(3,6),(5,7)]
 => [4,6,7,1,8,3,5,2] => [7,5,8,4,3,6,1,2] => [7,5,8,4,3,6,1,2] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,8),(4,6),(5,7)]
 => [3,6,1,7,8,4,5,2] => [6,5,3,8,4,1,7,2] => [6,5,3,8,4,1,7,2] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,8),(4,6),(5,7)]
 => [2,1,6,7,8,4,5,3] => [2,1,5,8,4,6,7,3] => [2,1,5,8,4,6,7,3] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,2),(3,7),(4,6),(5,8)]
 => [2,1,6,7,8,4,3,5] => [2,1,4,8,3,6,7,5] => [2,1,4,8,3,6,7,5] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
[(1,3),(2,7),(4,6),(5,8)]
 => [3,6,1,7,8,4,2,5] => [6,4,3,8,2,1,7,5] => [6,4,3,8,2,1,7,5] => ? ∊ {1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16}
Description
The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. For a signed permutation $\sigma$, this equals $$ \left\lfloor \dfrac{fexc(\sigma)+1}{2} \right\rfloor = exc(\sigma) + \left\lfloor \dfrac{neg(\sigma)+1}{2} \right\rfloor, $$ where $$fexc(\sigma) = 2exc(\sigma) + neg(\sigma),$$ $$exc(\sigma) = |\{i \in [n-1] \,:\, \sigma(i) > i\}|,$$ $$neg(\sigma) = |\{i \in [n] \,:\, \sigma(i) < 0\}|.$$ This statistic has the same distribution as the descent statistic [[St001427]].