Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000787
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Mapping
St000787: Perfect matchings ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[(1,2)]
 => 0
[(1,2),(3,4)]
 => 0
[(1,3),(2,4)]
 => 1
[(1,4),(2,3)]
 => 0
[(1,2),(3,4),(5,6)]
 => 0
[(1,3),(2,4),(5,6)]
 => 1
[(1,4),(2,3),(5,6)]
 => 0
[(1,5),(2,3),(4,6)]
 => 1
[(1,6),(2,3),(4,5)]
 => 0
[(1,6),(2,4),(3,5)]
 => 1
[(1,5),(2,4),(3,6)]
 => 2
[(1,4),(2,5),(3,6)]
 => 1
[(1,3),(2,5),(4,6)]
 => 2
[(1,2),(3,5),(4,6)]
 => 1
[(1,2),(3,6),(4,5)]
 => 0
[(1,3),(2,6),(4,5)]
 => 1
[(1,4),(2,6),(3,5)]
 => 2
[(1,5),(2,6),(3,4)]
 => 1
[(1,6),(2,5),(3,4)]
 => 0
[(1,2),(3,4),(5,6),(7,8)]
 => 0
[(1,3),(2,4),(5,6),(7,8)]
 => 1
[(1,4),(2,3),(5,6),(7,8)]
 => 0
[(1,5),(2,3),(4,6),(7,8)]
 => 1
[(1,6),(2,3),(4,5),(7,8)]
 => 0
[(1,7),(2,3),(4,5),(6,8)]
 => 1
[(1,8),(2,3),(4,5),(6,7)]
 => 0
[(1,8),(2,4),(3,5),(6,7)]
 => 1
[(1,7),(2,4),(3,5),(6,8)]
 => 2
[(1,6),(2,4),(3,5),(7,8)]
 => 1
[(1,5),(2,4),(3,6),(7,8)]
 => 2
[(1,4),(2,5),(3,6),(7,8)]
 => 1
[(1,3),(2,5),(4,6),(7,8)]
 => 2
[(1,2),(3,5),(4,6),(7,8)]
 => 1
[(1,2),(3,6),(4,5),(7,8)]
 => 0
[(1,3),(2,6),(4,5),(7,8)]
 => 1
[(1,4),(2,6),(3,5),(7,8)]
 => 2
[(1,5),(2,6),(3,4),(7,8)]
 => 1
[(1,6),(2,5),(3,4),(7,8)]
 => 0
[(1,7),(2,5),(3,4),(6,8)]
 => 1
[(1,8),(2,5),(3,4),(6,7)]
 => 0
[(1,8),(2,6),(3,4),(5,7)]
 => 1
[(1,7),(2,6),(3,4),(5,8)]
 => 2
[(1,6),(2,7),(3,4),(5,8)]
 => 1
[(1,5),(2,7),(3,4),(6,8)]
 => 2
[(1,4),(2,7),(3,5),(6,8)]
 => 3
[(1,3),(2,7),(4,5),(6,8)]
 => 2
[(1,2),(3,7),(4,5),(6,8)]
 => 1
[(1,2),(3,8),(4,5),(6,7)]
 => 0
[(1,3),(2,8),(4,5),(6,7)]
 => 1
[(1,4),(2,8),(3,5),(6,7)]
 => 2
Description
The number of flips required to make a perfect matching noncrossing. A crossing in a perfect matching is a pair of arcs $\{a,b\}$ and $\{c,d\}$ such that $a < c < b < d$. Replacing any such pair by either $\{a,c\}$ and $\{b,d\}$ or by $\{a,d\}$, $\{b,c\}$ produces a perfect matching with fewer crossings. This statistic is the minimal number of such flips required to turn a given matching into a noncrossing matching.