Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001047
(load all 2 compositions to match this statistic)
Mapping
St001047: 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)]
 => 1
[(1,4),(2,5),(3,6)]
 => 2
[(1,3),(2,5),(4,6)]
 => 1
[(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)]
 => 1
[(1,6),(2,4),(3,5),(7,8)]
 => 1
[(1,5),(2,4),(3,6),(7,8)]
 => 1
[(1,4),(2,5),(3,6),(7,8)]
 => 2
[(1,3),(2,5),(4,6),(7,8)]
 => 1
[(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)]
 => 1
[(1,6),(2,7),(3,4),(5,8)]
 => 2
[(1,5),(2,7),(3,4),(6,8)]
 => 1
[(1,4),(2,7),(3,5),(6,8)]
 => 2
[(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)]
 => 1
[(1,4),(2,8),(3,5),(6,7)]
 => 2
Description
The maximal number of arcs crossing a given arc of a perfect matching. This is also the largest difference between height and weight of a down step in the histoire d'Hermite corresponding to the perfect matching.
Matching statistic: St001046
(load all 2 compositions to match this statistic)
Mapping
Mp00116: Perfect matchings —Kasraoui-Zeng⟶ Perfect matchings
St001046: Perfect matchings ⟶ ℤResult quality: 87% ●values known / values provided: 87%●distinct values known / distinct values provided: 100%
Values
[(1,2)]
 => [(1,2)]
 => 0
[(1,2),(3,4)]
 => [(1,2),(3,4)]
 => 0
[(1,3),(2,4)]
 => [(1,4),(2,3)]
 => 1
[(1,4),(2,3)]
 => [(1,3),(2,4)]
 => 0
[(1,2),(3,4),(5,6)]
 => [(1,2),(3,4),(5,6)]
 => 0
[(1,3),(2,4),(5,6)]
 => [(1,4),(2,3),(5,6)]
 => 1
[(1,4),(2,3),(5,6)]
 => [(1,3),(2,4),(5,6)]
 => 0
[(1,5),(2,3),(4,6)]
 => [(1,3),(2,6),(4,5)]
 => 1
[(1,6),(2,3),(4,5)]
 => [(1,3),(2,5),(4,6)]
 => 0
[(1,6),(2,4),(3,5)]
 => [(1,5),(2,4),(3,6)]
 => 1
[(1,5),(2,4),(3,6)]
 => [(1,6),(2,4),(3,5)]
 => 1
[(1,4),(2,5),(3,6)]
 => [(1,6),(2,5),(3,4)]
 => 2
[(1,3),(2,5),(4,6)]
 => [(1,6),(2,3),(4,5)]
 => 1
[(1,2),(3,5),(4,6)]
 => [(1,2),(3,6),(4,5)]
 => 1
[(1,2),(3,6),(4,5)]
 => [(1,2),(3,5),(4,6)]
 => 0
[(1,3),(2,6),(4,5)]
 => [(1,5),(2,3),(4,6)]
 => 1
[(1,4),(2,6),(3,5)]
 => [(1,5),(2,6),(3,4)]
 => 2
[(1,5),(2,6),(3,4)]
 => [(1,4),(2,6),(3,5)]
 => 1
[(1,6),(2,5),(3,4)]
 => [(1,4),(2,5),(3,6)]
 => 0
[(1,2),(3,4),(5,6),(7,8)]
 => [(1,2),(3,4),(5,6),(7,8)]
 => 0
[(1,3),(2,4),(5,6),(7,8)]
 => [(1,4),(2,3),(5,6),(7,8)]
 => 1
[(1,4),(2,3),(5,6),(7,8)]
 => [(1,3),(2,4),(5,6),(7,8)]
 => 0
[(1,5),(2,3),(4,6),(7,8)]
 => [(1,3),(2,6),(4,5),(7,8)]
 => 1
[(1,6),(2,3),(4,5),(7,8)]
 => [(1,3),(2,5),(4,6),(7,8)]
 => 0
[(1,7),(2,3),(4,5),(6,8)]
 => [(1,3),(2,5),(4,8),(6,7)]
 => 1
[(1,8),(2,3),(4,5),(6,7)]
 => [(1,3),(2,5),(4,7),(6,8)]
 => 0
[(1,8),(2,4),(3,5),(6,7)]
 => [(1,5),(2,4),(3,7),(6,8)]
 => 1
[(1,7),(2,4),(3,5),(6,8)]
 => [(1,5),(2,4),(3,8),(6,7)]
 => 1
[(1,6),(2,4),(3,5),(7,8)]
 => [(1,5),(2,4),(3,6),(7,8)]
 => 1
[(1,5),(2,4),(3,6),(7,8)]
 => [(1,6),(2,4),(3,5),(7,8)]
 => 1
[(1,4),(2,5),(3,6),(7,8)]
 => [(1,6),(2,5),(3,4),(7,8)]
 => 2
[(1,3),(2,5),(4,6),(7,8)]
 => [(1,6),(2,3),(4,5),(7,8)]
 => 1
[(1,2),(3,5),(4,6),(7,8)]
 => [(1,2),(3,6),(4,5),(7,8)]
 => 1
[(1,2),(3,6),(4,5),(7,8)]
 => [(1,2),(3,5),(4,6),(7,8)]
 => 0
[(1,3),(2,6),(4,5),(7,8)]
 => [(1,5),(2,3),(4,6),(7,8)]
 => 1
[(1,4),(2,6),(3,5),(7,8)]
 => [(1,5),(2,6),(3,4),(7,8)]
 => 2
[(1,5),(2,6),(3,4),(7,8)]
 => [(1,4),(2,6),(3,5),(7,8)]
 => 1
[(1,6),(2,5),(3,4),(7,8)]
 => [(1,4),(2,5),(3,6),(7,8)]
 => 0
[(1,7),(2,5),(3,4),(6,8)]
 => [(1,4),(2,5),(3,8),(6,7)]
 => 1
[(1,8),(2,5),(3,4),(6,7)]
 => [(1,4),(2,5),(3,7),(6,8)]
 => 0
[(1,8),(2,6),(3,4),(5,7)]
 => [(1,4),(2,7),(3,6),(5,8)]
 => 1
[(1,7),(2,6),(3,4),(5,8)]
 => [(1,4),(2,8),(3,6),(5,7)]
 => 1
[(1,6),(2,7),(3,4),(5,8)]
 => [(1,4),(2,8),(3,7),(5,6)]
 => 2
[(1,5),(2,7),(3,4),(6,8)]
 => [(1,4),(2,8),(3,5),(6,7)]
 => 1
[(1,4),(2,7),(3,5),(6,8)]
 => [(1,5),(2,8),(3,4),(6,7)]
 => 2
[(1,3),(2,7),(4,5),(6,8)]
 => [(1,5),(2,3),(4,8),(6,7)]
 => 1
[(1,2),(3,7),(4,5),(6,8)]
 => [(1,2),(3,5),(4,8),(6,7)]
 => 1
[(1,2),(3,8),(4,5),(6,7)]
 => [(1,2),(3,5),(4,7),(6,8)]
 => 0
[(1,3),(2,8),(4,5),(6,7)]
 => [(1,5),(2,3),(4,7),(6,8)]
 => 1
[(1,4),(2,8),(3,5),(6,7)]
 => [(1,5),(2,7),(3,4),(6,8)]
 => 2
[(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)]
 => [(1,2),(3,5),(4,10),(6,11),(7,12),(8,13),(9,14)]
 => ? = 0
[(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)]
 => [(1,2),(3,6),(4,9),(5,11),(7,12),(8,13),(10,14)]
 => ? = 0
[(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)]
 => [(1,2),(3,6),(4,10),(5,11),(7,12),(8,13),(9,14)]
 => ? = 0
[(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)]
 => [(1,2),(3,7),(4,8),(5,11),(6,12),(9,13),(10,14)]
 => ? = 0
[(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)]
 => [(1,2),(3,7),(4,9),(5,10),(6,12),(8,13),(11,14)]
 => ? = 0
[(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)]
 => [(1,2),(3,7),(4,9),(5,11),(6,12),(8,13),(10,14)]
 => ? = 0
[(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)]
 => [(1,2),(3,7),(4,10),(5,11),(6,12),(8,13),(9,14)]
 => ? = 0
[(1,2),(3,14),(4,11),(5,10),(6,9),(7,8),(12,13)]
 => [(1,2),(3,8),(4,9),(5,10),(6,11),(7,13),(12,14)]
 => ? = 0
[(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)]
 => [(1,2),(3,8),(4,9),(5,10),(6,12),(7,13),(11,14)]
 => ? = 0
[(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)]
 => [(1,2),(3,8),(4,9),(5,11),(6,12),(7,13),(10,14)]
 => ? = 0
[(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)]
 => [(1,2),(3,8),(4,10),(5,11),(6,12),(7,13),(9,14)]
 => ? = 0
[(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)]
 => [(1,2),(3,9),(4,10),(5,11),(6,12),(7,13),(8,14)]
 => ? = 0
[(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)]
 => [(1,3),(2,4),(5,10),(6,11),(7,12),(8,13),(9,14)]
 => ? = 0
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8),(13,14)]
 => [(1,3),(2,8),(4,9),(5,10),(6,11),(7,12),(13,14)]
 => ? = 0
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9),(13,14)]
 => [(1,4),(2,7),(3,9),(5,10),(6,11),(8,12),(13,14)]
 => ? = 0
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8),(13,14)]
 => [(1,4),(2,8),(3,9),(5,10),(6,11),(7,12),(13,14)]
 => ? = 0
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9),(13,14)]
 => [(1,5),(2,6),(3,9),(4,10),(7,11),(8,12),(13,14)]
 => ? = 0
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10),(13,14)]
 => [(1,5),(2,7),(3,8),(4,10),(6,11),(9,12),(13,14)]
 => ? = 0
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9),(13,14)]
 => [(1,5),(2,7),(3,9),(4,10),(6,11),(8,12),(13,14)]
 => ? = 0
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)]
 => [(1,5),(2,8),(3,9),(4,10),(6,11),(7,12),(13,14)]
 => ? = 0
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)]
 => [(1,6),(2,7),(3,8),(4,9),(5,10),(11,13),(12,14)]
 => ? = 0
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)]
 => [(1,6),(2,7),(3,8),(4,9),(5,11),(10,12),(13,14)]
 => ? = 0
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)]
 => [(1,6),(2,7),(3,8),(4,10),(5,11),(9,12),(13,14)]
 => ? = 0
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)]
 => [(1,6),(2,7),(3,9),(4,10),(5,11),(8,12),(13,14)]
 => ? = 0
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)]
 => [(1,6),(2,8),(3,9),(4,10),(5,11),(7,12),(13,14)]
 => ? = 0
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)]
 => [(1,7),(2,8),(3,9),(4,10),(5,11),(6,12),(13,14)]
 => ? = 0
[(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)]
 => [(1,2),(3,7),(4,11),(5,12),(6,13),(8,14),(9,15),(10,16)]
 => ? = 0
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)]
 => [(1,2),(3,8),(4,10),(5,12),(6,13),(7,14),(9,15),(11,16)]
 => ? = 0
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)]
 => [(1,2),(3,8),(4,11),(5,12),(6,13),(7,14),(9,15),(10,16)]
 => ? = 0
[(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)]
 => [(1,2),(3,9),(4,10),(5,11),(6,13),(7,14),(8,15),(12,16)]
 => ? = 0
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)]
 => [(1,2),(3,9),(4,10),(5,12),(6,13),(7,14),(8,15),(11,16)]
 => ? = 0
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)]
 => [(1,2),(3,9),(4,11),(5,12),(6,13),(7,14),(8,15),(10,16)]
 => ? = 0
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)]
 => [(1,2),(3,10),(4,11),(5,12),(6,13),(7,14),(8,15),(9,16)]
 => ? = 0
[(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9),(15,16)]
 => [(1,5),(2,9),(3,10),(4,11),(6,12),(7,13),(8,14),(15,16)]
 => ? = 0
[(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10),(15,16)]
 => [(1,6),(2,8),(3,10),(4,11),(5,12),(7,13),(9,14),(15,16)]
 => ? = 0
[(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9),(15,16)]
 => [(1,6),(2,9),(3,10),(4,11),(5,12),(7,13),(8,14),(15,16)]
 => ? = 0
[(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11),(15,16)]
 => [(1,7),(2,8),(3,9),(4,11),(5,12),(6,13),(10,14),(15,16)]
 => ? = 0
[(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10),(15,16)]
 => [(1,7),(2,8),(3,10),(4,11),(5,12),(6,13),(9,14),(15,16)]
 => ? = 0
[(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9),(15,16)]
 => [(1,7),(2,9),(3,10),(4,11),(5,12),(6,13),(8,14),(15,16)]
 => ? = 0
[(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)]
 => [(1,8),(2,9),(3,10),(4,11),(5,12),(6,13),(7,14),(15,16)]
 => ? = 0
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)]
 => ?
 => ? = 1
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)]
 => ?
 => ? = 1
[(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)]
 => ?
 => ? = 1
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)]
 => ?
 => ? = 2
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)]
 => ?
 => ? = 1
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)]
 => ?
 => ? = 1
[(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)]
 => ?
 => ? = 1
[(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)]
 => ?
 => ? = 1
[(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)]
 => ?
 => ? = 2
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)]
 => ?
 => ? = 2
Description
The maximal number of arcs nesting a given arc of a perfect matching. This is also the largest weight of a down step in the histoire d'Hermite corresponding to the perfect matching.