Processing math: 100%

Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001832
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Mapping
St001832: 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)]
 => 1
[(1,3),(2,4)]
 => 2
[(1,4),(2,3)]
 => 1
[(1,2),(3,4),(5,6)]
 => 1
[(1,3),(2,4),(5,6)]
 => 2
[(1,4),(2,3),(5,6)]
 => 1
[(1,5),(2,3),(4,6)]
 => 2
[(1,6),(2,3),(4,5)]
 => 1
[(1,6),(2,4),(3,5)]
 => 2
[(1,5),(2,4),(3,6)]
 => 4
[(1,4),(2,5),(3,6)]
 => 5
[(1,3),(2,5),(4,6)]
 => 4
[(1,2),(3,5),(4,6)]
 => 2
[(1,2),(3,6),(4,5)]
 => 1
[(1,3),(2,6),(4,5)]
 => 2
[(1,4),(2,6),(3,5)]
 => 4
[(1,5),(2,6),(3,4)]
 => 2
[(1,6),(2,5),(3,4)]
 => 1
[(1,2),(3,4),(5,6),(7,8)]
 => 1
[(1,3),(2,4),(5,6),(7,8)]
 => 2
[(1,4),(2,3),(5,6),(7,8)]
 => 1
[(1,5),(2,3),(4,6),(7,8)]
 => 2
[(1,6),(2,3),(4,5),(7,8)]
 => 1
[(1,7),(2,3),(4,5),(6,8)]
 => 2
[(1,8),(2,3),(4,5),(6,7)]
 => 1
[(1,8),(2,4),(3,5),(6,7)]
 => 2
[(1,7),(2,4),(3,5),(6,8)]
 => 4
[(1,6),(2,4),(3,5),(7,8)]
 => 2
[(1,5),(2,4),(3,6),(7,8)]
 => 4
[(1,4),(2,5),(3,6),(7,8)]
 => 5
[(1,3),(2,5),(4,6),(7,8)]
 => 4
[(1,2),(3,5),(4,6),(7,8)]
 => 2
[(1,2),(3,6),(4,5),(7,8)]
 => 1
[(1,3),(2,6),(4,5),(7,8)]
 => 2
[(1,4),(2,6),(3,5),(7,8)]
 => 4
[(1,5),(2,6),(3,4),(7,8)]
 => 2
[(1,6),(2,5),(3,4),(7,8)]
 => 1
[(1,7),(2,5),(3,4),(6,8)]
 => 2
[(1,8),(2,5),(3,4),(6,7)]
 => 1
[(1,8),(2,6),(3,4),(5,7)]
 => 2
[(1,7),(2,6),(3,4),(5,8)]
 => 4
[(1,6),(2,7),(3,4),(5,8)]
 => 5
[(1,5),(2,7),(3,4),(6,8)]
 => 4
[(1,4),(2,7),(3,5),(6,8)]
 => 8
[(1,3),(2,7),(4,5),(6,8)]
 => 4
[(1,2),(3,7),(4,5),(6,8)]
 => 2
[(1,2),(3,8),(4,5),(6,7)]
 => 1
[(1,3),(2,8),(4,5),(6,7)]
 => 2
[(1,4),(2,8),(3,5),(6,7)]
 => 4
Description
The number of non-crossing perfect matchings in the chord expansion of a perfect matching. Given a perfect matching, we obtain a formal sum of non-crossing perfect matchings by replacing recursively every matching M that has a crossing (a,c),(b,d) with a<b<c<d with the sum of the two matchings (M∖{(a,c),(b,d)})∪{(a,b),(c,d)} and (M∖{(a,c),(b,d)})∪{(a,d),(b,c)}. This statistic is the number of distinct non-crossing perfect matchings in the formal sum.