Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000754
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Mapping
St000754: 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)]
 => 0
[(1,4),(2,3)]
 => 1
[(1,2),(3,4),(5,6)]
 => 0
[(1,3),(2,4),(5,6)]
 => 0
[(1,4),(2,3),(5,6)]
 => 1
[(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)]
 => 0
[(1,4),(2,5),(3,6)]
 => 0
[(1,3),(2,5),(4,6)]
 => 0
[(1,2),(3,5),(4,6)]
 => 0
[(1,2),(3,6),(4,5)]
 => 1
[(1,3),(2,6),(4,5)]
 => 1
[(1,4),(2,6),(3,5)]
 => 0
[(1,5),(2,6),(3,4)]
 => 0
[(1,6),(2,5),(3,4)]
 => 1
[(1,2),(3,4),(5,6),(7,8)]
 => 0
[(1,3),(2,4),(5,6),(7,8)]
 => 0
[(1,4),(2,3),(5,6),(7,8)]
 => 1
[(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)]
 => 0
[(1,8),(2,3),(4,5),(6,7)]
 => 1
[(1,8),(2,4),(3,5),(6,7)]
 => 0
[(1,7),(2,4),(3,5),(6,8)]
 => 1
[(1,6),(2,4),(3,5),(7,8)]
 => 1
[(1,5),(2,4),(3,6),(7,8)]
 => 0
[(1,4),(2,5),(3,6),(7,8)]
 => 0
[(1,3),(2,5),(4,6),(7,8)]
 => 0
[(1,2),(3,5),(4,6),(7,8)]
 => 0
[(1,2),(3,6),(4,5),(7,8)]
 => 1
[(1,3),(2,6),(4,5),(7,8)]
 => 1
[(1,4),(2,6),(3,5),(7,8)]
 => 0
[(1,5),(2,6),(3,4),(7,8)]
 => 0
[(1,6),(2,5),(3,4),(7,8)]
 => 1
[(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)]
 => 2
[(1,5),(2,7),(3,4),(6,8)]
 => 0
[(1,4),(2,7),(3,5),(6,8)]
 => 0
[(1,3),(2,7),(4,5),(6,8)]
 => 1
[(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)]
 => 0
[(1,4),(2,8),(3,5),(6,7)]
 => 1
Description
The Grundy value for the game of removing nestings in a perfect matching. A move consists of choosing a nesting, that is two pairs $(a,d)$ and $(b,c)$ with $a < b < c < d$ and replacing them with the two pairs $(a,b)$ and $(c,d)$. The player facing a non-nesting matching looses.