Identifier
-
Mp00116:
Perfect matchings
—Kasraoui-Zeng⟶
Perfect matchings
St000041: Perfect matchings ⟶ ℤ
Values
=>
Cc0012;cc-rep-0
Cc0012;cc-rep
[(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)]=>2
[(1,4),(2,5),(3,6)]=>[(1,6),(2,5),(3,4)]=>3
[(1,3),(2,5),(4,6)]=>[(1,6),(2,3),(4,5)]=>2
[(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)]=>2
[(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)]=>2
[(1,4),(2,5),(3,6),(7,8)]=>[(1,6),(2,5),(3,4),(7,8)]=>3
[(1,3),(2,5),(4,6),(7,8)]=>[(1,6),(2,3),(4,5),(7,8)]=>2
[(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)]=>2
[(1,6),(2,7),(3,4),(5,8)]=>[(1,4),(2,8),(3,7),(5,6)]=>3
[(1,5),(2,7),(3,4),(6,8)]=>[(1,4),(2,8),(3,5),(6,7)]=>2
[(1,4),(2,7),(3,5),(6,8)]=>[(1,5),(2,8),(3,4),(6,7)]=>3
[(1,3),(2,7),(4,5),(6,8)]=>[(1,5),(2,3),(4,8),(6,7)]=>2
[(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
[(1,5),(2,8),(3,4),(6,7)]=>[(1,4),(2,7),(3,5),(6,8)]=>1
[(1,6),(2,8),(3,4),(5,7)]=>[(1,4),(2,7),(3,8),(5,6)]=>2
[(1,7),(2,8),(3,4),(5,6)]=>[(1,4),(2,6),(3,8),(5,7)]=>1
[(1,8),(2,7),(3,4),(5,6)]=>[(1,4),(2,6),(3,7),(5,8)]=>0
[(1,8),(2,7),(3,5),(4,6)]=>[(1,6),(2,5),(3,7),(4,8)]=>1
[(1,7),(2,8),(3,5),(4,6)]=>[(1,6),(2,5),(3,8),(4,7)]=>2
[(1,6),(2,8),(3,5),(4,7)]=>[(1,7),(2,5),(3,8),(4,6)]=>3
[(1,5),(2,8),(3,6),(4,7)]=>[(1,7),(2,6),(3,8),(4,5)]=>4
[(1,4),(2,8),(3,6),(5,7)]=>[(1,7),(2,6),(3,4),(5,8)]=>3
[(1,3),(2,8),(4,6),(5,7)]=>[(1,7),(2,3),(4,6),(5,8)]=>2
[(1,2),(3,8),(4,6),(5,7)]=>[(1,2),(3,7),(4,6),(5,8)]=>1
[(1,2),(3,7),(4,6),(5,8)]=>[(1,2),(3,8),(4,6),(5,7)]=>2
[(1,3),(2,7),(4,6),(5,8)]=>[(1,8),(2,3),(4,6),(5,7)]=>3
[(1,4),(2,7),(3,6),(5,8)]=>[(1,8),(2,6),(3,4),(5,7)]=>4
[(1,5),(2,7),(3,6),(4,8)]=>[(1,8),(2,6),(3,7),(4,5)]=>5
[(1,6),(2,7),(3,5),(4,8)]=>[(1,8),(2,5),(3,7),(4,6)]=>4
[(1,7),(2,6),(3,5),(4,8)]=>[(1,8),(2,5),(3,6),(4,7)]=>3
[(1,8),(2,6),(3,5),(4,7)]=>[(1,7),(2,5),(3,6),(4,8)]=>2
[(1,8),(2,5),(3,6),(4,7)]=>[(1,7),(2,6),(3,5),(4,8)]=>3
[(1,7),(2,5),(3,6),(4,8)]=>[(1,8),(2,6),(3,5),(4,7)]=>4
[(1,6),(2,5),(3,7),(4,8)]=>[(1,8),(2,7),(3,5),(4,6)]=>5
[(1,5),(2,6),(3,7),(4,8)]=>[(1,8),(2,7),(3,6),(4,5)]=>6
[(1,4),(2,6),(3,7),(5,8)]=>[(1,8),(2,7),(3,4),(5,6)]=>5
[(1,3),(2,6),(4,7),(5,8)]=>[(1,8),(2,3),(4,7),(5,6)]=>4
[(1,2),(3,6),(4,7),(5,8)]=>[(1,2),(3,8),(4,7),(5,6)]=>3
[(1,2),(3,5),(4,7),(6,8)]=>[(1,2),(3,8),(4,5),(6,7)]=>2
[(1,3),(2,5),(4,7),(6,8)]=>[(1,8),(2,3),(4,5),(6,7)]=>3
[(1,4),(2,5),(3,7),(6,8)]=>[(1,8),(2,5),(3,4),(6,7)]=>4
[(1,5),(2,4),(3,7),(6,8)]=>[(1,8),(2,4),(3,5),(6,7)]=>3
[(1,6),(2,4),(3,7),(5,8)]=>[(1,8),(2,4),(3,7),(5,6)]=>4
[(1,7),(2,4),(3,6),(5,8)]=>[(1,8),(2,4),(3,6),(5,7)]=>3
[(1,8),(2,4),(3,6),(5,7)]=>[(1,7),(2,4),(3,6),(5,8)]=>2
[(1,8),(2,3),(4,6),(5,7)]=>[(1,3),(2,7),(4,6),(5,8)]=>1
[(1,7),(2,3),(4,6),(5,8)]=>[(1,3),(2,8),(4,6),(5,7)]=>2
[(1,6),(2,3),(4,7),(5,8)]=>[(1,3),(2,8),(4,7),(5,6)]=>3
[(1,5),(2,3),(4,7),(6,8)]=>[(1,3),(2,8),(4,5),(6,7)]=>2
[(1,4),(2,3),(5,7),(6,8)]=>[(1,3),(2,4),(5,8),(6,7)]=>1
[(1,3),(2,4),(5,7),(6,8)]=>[(1,4),(2,3),(5,8),(6,7)]=>2
[(1,2),(3,4),(5,7),(6,8)]=>[(1,2),(3,4),(5,8),(6,7)]=>1
[(1,2),(3,4),(5,8),(6,7)]=>[(1,2),(3,4),(5,7),(6,8)]=>0
[(1,3),(2,4),(5,8),(6,7)]=>[(1,4),(2,3),(5,7),(6,8)]=>1
[(1,4),(2,3),(5,8),(6,7)]=>[(1,3),(2,4),(5,7),(6,8)]=>0
[(1,5),(2,3),(4,8),(6,7)]=>[(1,3),(2,7),(4,5),(6,8)]=>1
[(1,6),(2,3),(4,8),(5,7)]=>[(1,3),(2,7),(4,8),(5,6)]=>2
[(1,7),(2,3),(4,8),(5,6)]=>[(1,3),(2,6),(4,8),(5,7)]=>1
[(1,8),(2,3),(4,7),(5,6)]=>[(1,3),(2,6),(4,7),(5,8)]=>0
[(1,8),(2,4),(3,7),(5,6)]=>[(1,6),(2,4),(3,7),(5,8)]=>1
[(1,7),(2,4),(3,8),(5,6)]=>[(1,6),(2,4),(3,8),(5,7)]=>2
[(1,6),(2,4),(3,8),(5,7)]=>[(1,7),(2,4),(3,8),(5,6)]=>3
[(1,5),(2,4),(3,8),(6,7)]=>[(1,7),(2,4),(3,5),(6,8)]=>2
[(1,4),(2,5),(3,8),(6,7)]=>[(1,7),(2,5),(3,4),(6,8)]=>3
[(1,3),(2,5),(4,8),(6,7)]=>[(1,7),(2,3),(4,5),(6,8)]=>2
[(1,2),(3,5),(4,8),(6,7)]=>[(1,2),(3,7),(4,5),(6,8)]=>1
[(1,2),(3,6),(4,8),(5,7)]=>[(1,2),(3,7),(4,8),(5,6)]=>2
[(1,3),(2,6),(4,8),(5,7)]=>[(1,7),(2,3),(4,8),(5,6)]=>3
[(1,4),(2,6),(3,8),(5,7)]=>[(1,7),(2,8),(3,4),(5,6)]=>4
[(1,5),(2,6),(3,8),(4,7)]=>[(1,7),(2,8),(3,6),(4,5)]=>5
[(1,6),(2,5),(3,8),(4,7)]=>[(1,7),(2,8),(3,5),(4,6)]=>4
[(1,7),(2,5),(3,8),(4,6)]=>[(1,6),(2,8),(3,5),(4,7)]=>3
[(1,8),(2,5),(3,7),(4,6)]=>[(1,6),(2,7),(3,5),(4,8)]=>2
[(1,8),(2,6),(3,7),(4,5)]=>[(1,5),(2,7),(3,6),(4,8)]=>1
[(1,7),(2,6),(3,8),(4,5)]=>[(1,5),(2,8),(3,6),(4,7)]=>2
[(1,6),(2,7),(3,8),(4,5)]=>[(1,5),(2,8),(3,7),(4,6)]=>3
[(1,5),(2,7),(3,8),(4,6)]=>[(1,6),(2,8),(3,7),(4,5)]=>4
[(1,4),(2,7),(3,8),(5,6)]=>[(1,6),(2,8),(3,4),(5,7)]=>3
[(1,3),(2,7),(4,8),(5,6)]=>[(1,6),(2,3),(4,8),(5,7)]=>2
[(1,2),(3,7),(4,8),(5,6)]=>[(1,2),(3,6),(4,8),(5,7)]=>1
[(1,2),(3,8),(4,7),(5,6)]=>[(1,2),(3,6),(4,7),(5,8)]=>0
[(1,3),(2,8),(4,7),(5,6)]=>[(1,6),(2,3),(4,7),(5,8)]=>1
[(1,4),(2,8),(3,7),(5,6)]=>[(1,6),(2,7),(3,4),(5,8)]=>2
[(1,5),(2,8),(3,7),(4,6)]=>[(1,6),(2,7),(3,8),(4,5)]=>3
[(1,6),(2,8),(3,7),(4,5)]=>[(1,5),(2,7),(3,8),(4,6)]=>2
[(1,7),(2,8),(3,6),(4,5)]=>[(1,5),(2,6),(3,8),(4,7)]=>1
[(1,8),(2,7),(3,6),(4,5)]=>[(1,5),(2,6),(3,7),(4,8)]=>0
[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>0
[(1,3),(2,4),(5,6),(7,8),(9,10)]=>[(1,4),(2,3),(5,6),(7,8),(9,10)]=>1
[(1,4),(2,3),(5,6),(7,8),(9,10)]=>[(1,3),(2,4),(5,6),(7,8),(9,10)]=>0
[(1,6),(2,3),(4,5),(7,8),(9,10)]=>[(1,3),(2,5),(4,6),(7,8),(9,10)]=>0
[(1,8),(2,3),(4,5),(6,7),(9,10)]=>[(1,3),(2,5),(4,7),(6,8),(9,10)]=>0
[(1,10),(2,3),(4,5),(6,7),(8,9)]=>[(1,3),(2,5),(4,7),(6,9),(8,10)]=>0
[(1,4),(2,5),(3,6),(7,8),(9,10)]=>[(1,6),(2,5),(3,4),(7,8),(9,10)]=>3
[(1,3),(2,5),(4,6),(7,8),(9,10)]=>[(1,6),(2,3),(4,5),(7,8),(9,10)]=>2
[(1,2),(3,5),(4,6),(7,8),(9,10)]=>[(1,2),(3,6),(4,5),(7,8),(9,10)]=>1
[(1,2),(3,6),(4,5),(7,8),(9,10)]=>[(1,2),(3,5),(4,6),(7,8),(9,10)]=>0
[(1,6),(2,5),(3,4),(7,8),(9,10)]=>[(1,4),(2,5),(3,6),(7,8),(9,10)]=>0
[(1,8),(2,5),(3,4),(6,7),(9,10)]=>[(1,4),(2,5),(3,7),(6,8),(9,10)]=>0
[(1,10),(2,5),(3,4),(6,7),(8,9)]=>[(1,4),(2,5),(3,7),(6,9),(8,10)]=>0
[(1,2),(3,8),(4,5),(6,7),(9,10)]=>[(1,2),(3,5),(4,7),(6,8),(9,10)]=>0
[(1,8),(2,7),(3,4),(5,6),(9,10)]=>[(1,4),(2,6),(3,7),(5,8),(9,10)]=>0
[(1,10),(2,7),(3,4),(5,6),(8,9)]=>[(1,4),(2,6),(3,7),(5,9),(8,10)]=>0
[(1,2),(3,10),(4,5),(6,7),(8,9)]=>[(1,2),(3,5),(4,7),(6,9),(8,10)]=>0
[(1,10),(2,9),(3,4),(5,6),(7,8)]=>[(1,4),(2,6),(3,8),(5,9),(7,10)]=>0
[(1,5),(2,6),(3,7),(4,8),(9,10)]=>[(1,8),(2,7),(3,6),(4,5),(9,10)]=>6
[(1,4),(2,6),(3,7),(5,8),(9,10)]=>[(1,8),(2,7),(3,4),(5,6),(9,10)]=>5
[(1,3),(2,6),(4,7),(5,8),(9,10)]=>[(1,8),(2,3),(4,7),(5,6),(9,10)]=>4
[(1,2),(3,6),(4,7),(5,8),(9,10)]=>[(1,2),(3,8),(4,7),(5,6),(9,10)]=>3
[(1,2),(3,5),(4,7),(6,8),(9,10)]=>[(1,2),(3,8),(4,5),(6,7),(9,10)]=>2
[(1,3),(2,5),(4,7),(6,8),(9,10)]=>[(1,8),(2,3),(4,5),(6,7),(9,10)]=>3
[(1,4),(2,5),(3,7),(6,8),(9,10)]=>[(1,8),(2,5),(3,4),(6,7),(9,10)]=>4
[(1,3),(2,4),(5,7),(6,8),(9,10)]=>[(1,4),(2,3),(5,8),(6,7),(9,10)]=>2
[(1,2),(3,4),(5,7),(6,8),(9,10)]=>[(1,2),(3,4),(5,8),(6,7),(9,10)]=>1
[(1,2),(3,4),(5,8),(6,7),(9,10)]=>[(1,2),(3,4),(5,7),(6,8),(9,10)]=>0
[(1,4),(2,3),(5,8),(6,7),(9,10)]=>[(1,3),(2,4),(5,7),(6,8),(9,10)]=>0
[(1,8),(2,3),(4,7),(5,6),(9,10)]=>[(1,3),(2,6),(4,7),(5,8),(9,10)]=>0
[(1,10),(2,3),(4,7),(5,6),(8,9)]=>[(1,3),(2,6),(4,7),(5,9),(8,10)]=>0
[(1,2),(3,8),(4,7),(5,6),(9,10)]=>[(1,2),(3,6),(4,7),(5,8),(9,10)]=>0
[(1,8),(2,7),(3,6),(4,5),(9,10)]=>[(1,5),(2,6),(3,7),(4,8),(9,10)]=>0
[(1,10),(2,7),(3,6),(4,5),(8,9)]=>[(1,5),(2,6),(3,7),(4,9),(8,10)]=>0
[(1,2),(3,10),(4,7),(5,6),(8,9)]=>[(1,2),(3,6),(4,7),(5,9),(8,10)]=>0
[(1,10),(2,9),(3,6),(4,5),(7,8)]=>[(1,5),(2,6),(3,8),(4,9),(7,10)]=>0
[(1,2),(3,4),(5,10),(6,7),(8,9)]=>[(1,2),(3,4),(5,7),(6,9),(8,10)]=>0
[(1,4),(2,3),(5,10),(6,7),(8,9)]=>[(1,3),(2,4),(5,7),(6,9),(8,10)]=>0
[(1,10),(2,3),(4,9),(5,6),(7,8)]=>[(1,3),(2,6),(4,8),(5,9),(7,10)]=>0
[(1,2),(3,10),(4,9),(5,6),(7,8)]=>[(1,2),(3,6),(4,8),(5,9),(7,10)]=>0
[(1,10),(2,9),(3,8),(4,5),(6,7)]=>[(1,5),(2,7),(3,8),(4,9),(6,10)]=>0
[(1,2),(3,7),(4,8),(5,9),(6,10)]=>[(1,2),(3,10),(4,9),(5,8),(6,7)]=>6
[(1,3),(2,7),(4,8),(5,9),(6,10)]=>[(1,10),(2,3),(4,9),(5,8),(6,7)]=>7
[(1,4),(2,7),(3,8),(5,9),(6,10)]=>[(1,10),(2,9),(3,4),(5,8),(6,7)]=>8
[(1,5),(2,7),(3,8),(4,9),(6,10)]=>[(1,10),(2,9),(3,8),(4,5),(6,7)]=>9
[(1,6),(2,7),(3,8),(4,9),(5,10)]=>[(1,10),(2,9),(3,8),(4,7),(5,6)]=>10
[(1,5),(2,6),(3,8),(4,9),(7,10)]=>[(1,10),(2,9),(3,6),(4,5),(7,8)]=>8
[(1,4),(2,6),(3,8),(5,9),(7,10)]=>[(1,10),(2,9),(3,4),(5,6),(7,8)]=>7
[(1,3),(2,6),(4,8),(5,9),(7,10)]=>[(1,10),(2,3),(4,9),(5,6),(7,8)]=>6
[(1,2),(3,6),(4,8),(5,9),(7,10)]=>[(1,2),(3,10),(4,9),(5,6),(7,8)]=>5
[(1,2),(3,5),(4,8),(6,9),(7,10)]=>[(1,2),(3,10),(4,5),(6,9),(7,8)]=>4
[(1,3),(2,5),(4,8),(6,9),(7,10)]=>[(1,10),(2,3),(4,5),(6,9),(7,8)]=>5
[(1,4),(2,5),(3,8),(6,9),(7,10)]=>[(1,10),(2,5),(3,4),(6,9),(7,8)]=>6
[(1,3),(2,4),(5,8),(6,9),(7,10)]=>[(1,4),(2,3),(5,10),(6,9),(7,8)]=>4
[(1,2),(3,4),(5,8),(6,9),(7,10)]=>[(1,2),(3,4),(5,10),(6,9),(7,8)]=>3
[(1,2),(3,4),(5,7),(6,9),(8,10)]=>[(1,2),(3,4),(5,10),(6,7),(8,9)]=>2
[(1,3),(2,4),(5,7),(6,9),(8,10)]=>[(1,4),(2,3),(5,10),(6,7),(8,9)]=>3
[(1,4),(2,5),(3,7),(6,9),(8,10)]=>[(1,10),(2,5),(3,4),(6,7),(8,9)]=>5
[(1,3),(2,5),(4,7),(6,9),(8,10)]=>[(1,10),(2,3),(4,5),(6,7),(8,9)]=>4
[(1,2),(3,5),(4,7),(6,9),(8,10)]=>[(1,2),(3,10),(4,5),(6,7),(8,9)]=>3
[(1,2),(3,6),(4,7),(5,9),(8,10)]=>[(1,2),(3,10),(4,7),(5,6),(8,9)]=>4
[(1,3),(2,6),(4,7),(5,9),(8,10)]=>[(1,10),(2,3),(4,7),(5,6),(8,9)]=>5
[(1,4),(2,6),(3,7),(5,9),(8,10)]=>[(1,10),(2,7),(3,4),(5,6),(8,9)]=>6
[(1,5),(2,6),(3,7),(4,9),(8,10)]=>[(1,10),(2,7),(3,6),(4,5),(8,9)]=>7
[(1,2),(3,5),(4,6),(7,9),(8,10)]=>[(1,2),(3,6),(4,5),(7,10),(8,9)]=>2
[(1,3),(2,5),(4,6),(7,9),(8,10)]=>[(1,6),(2,3),(4,5),(7,10),(8,9)]=>3
[(1,4),(2,5),(3,6),(7,9),(8,10)]=>[(1,6),(2,5),(3,4),(7,10),(8,9)]=>4
[(1,3),(2,4),(5,6),(7,9),(8,10)]=>[(1,4),(2,3),(5,6),(7,10),(8,9)]=>2
[(1,2),(3,4),(5,6),(7,9),(8,10)]=>[(1,2),(3,4),(5,6),(7,10),(8,9)]=>1
[(1,2),(3,4),(5,6),(7,10),(8,9)]=>[(1,2),(3,4),(5,6),(7,9),(8,10)]=>0
[(1,4),(2,3),(5,6),(7,10),(8,9)]=>[(1,3),(2,4),(5,6),(7,9),(8,10)]=>0
[(1,6),(2,3),(4,5),(7,10),(8,9)]=>[(1,3),(2,5),(4,6),(7,9),(8,10)]=>0
[(1,10),(2,3),(4,5),(6,9),(7,8)]=>[(1,3),(2,5),(4,8),(6,9),(7,10)]=>0
[(1,2),(3,6),(4,5),(7,10),(8,9)]=>[(1,2),(3,5),(4,6),(7,9),(8,10)]=>0
[(1,6),(2,5),(3,4),(7,10),(8,9)]=>[(1,4),(2,5),(3,6),(7,9),(8,10)]=>0
[(1,10),(2,5),(3,4),(6,9),(7,8)]=>[(1,4),(2,5),(3,8),(6,9),(7,10)]=>0
[(1,2),(3,10),(4,5),(6,9),(7,8)]=>[(1,2),(3,5),(4,8),(6,9),(7,10)]=>0
[(1,10),(2,9),(3,4),(5,8),(6,7)]=>[(1,4),(2,7),(3,8),(5,9),(6,10)]=>0
[(1,2),(3,4),(5,10),(6,9),(7,8)]=>[(1,2),(3,4),(5,8),(6,9),(7,10)]=>0
[(1,4),(2,3),(5,10),(6,9),(7,8)]=>[(1,3),(2,4),(5,8),(6,9),(7,10)]=>0
[(1,10),(2,3),(4,9),(5,8),(6,7)]=>[(1,3),(2,7),(4,8),(5,9),(6,10)]=>0
[(1,2),(3,10),(4,9),(5,8),(6,7)]=>[(1,2),(3,7),(4,8),(5,9),(6,10)]=>0
[(1,10),(2,9),(3,8),(4,7),(5,6)]=>[(1,6),(2,7),(3,8),(4,9),(5,10)]=>0
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)]=>0
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)]=>0
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]=>[(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)]=>0
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>[(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)]=>0
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>[(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)]=>0
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>[(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)]=>0
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)]=>0
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]=>[(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)]=>0
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>[(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)]=>0
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)]=>0
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>[(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)]=>0
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)]=>0
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]=>[(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)]=>0
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]=>[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)]=>0
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>[(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)]=>0
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>[(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)]=>0
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]=>[(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)]=>0
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>[(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)]=>0
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]=>[(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)]=>0
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>[(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)]=>0
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>[(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)]=>0
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]=>[(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)]=>0
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>[(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)]=>0
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>[(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)]=>0
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>[(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)]=>0
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>[(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)]=>0
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]=>[(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)]=>0
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]=>[(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)]=>0
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>[(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)]=>0
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>[(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)]=>0
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]=>[(1,3),(2,5),(4,7),(6,10),(8,11),(9,12)]=>0
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>[(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)]=>0
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>[(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)]=>0
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>[(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)]=>0
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>[(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)]=>0
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>[(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)]=>0
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]=>[(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)]=>0
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]=>[(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)]=>0
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>[(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)]=>0
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>[(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)]=>0
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]=>[(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)]=>0
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>[(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)]=>0
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>[(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)]=>0
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>[(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)]=>0
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]=>[(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)]=>0
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>[(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)]=>0
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>[(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)]=>0
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>[(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)]=>0
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>0
[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]=>[(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)]=>0
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>[(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)]=>0
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)]=>0
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>[(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)]=>0
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)]=>0
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]=>[(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)]=>0
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]=>[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)]=>0
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>[(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)]=>0
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>[(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)]=>0
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]=>[(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)]=>0
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>[(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)]=>0
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>[(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)]=>0
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>[(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)]=>0
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)]=>0
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]=>[(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)]=>0
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)]=>0
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)]=>0
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>[(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)]=>0
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>[(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)]=>0
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]=>[(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)]=>0
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]=>[(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)]=>0
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>[(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)]=>0
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)]=>0
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]=>[(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)]=>0
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>[(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)]=>0
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>[(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)]=>0
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>[(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)]=>0
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)]=>0
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>[(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)]=>0
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]=>[(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)]=>0
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]=>[(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)]=>0
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>[(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)]=>0
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)]=>0
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]=>[(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)]=>0
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)]=>0
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>[(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)]=>0
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>[(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)]=>0
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]=>[(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)]=>0
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>[(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)]=>0
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>[(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)]=>0
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>[(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)]=>0
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)]=>0
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]=>[(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)]=>0
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>[(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)]=>0
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)]=>0
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>[(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)]=>0
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>[(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)]=>0
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]=>[(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)]=>0
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]=>[(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)]=>0
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>[(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)]=>0
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)]=>0
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]=>[(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)]=>0
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>[(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)]=>0
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>[(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)]=>0
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]=>[(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)]=>0
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)]=>0
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)]=>0
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]=>[(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)]=>0
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]=>[(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)]=>0
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)]=>0
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>[(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)]=>0
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]=>[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)]=>0
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>[(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)]=>0
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>[(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)]=>0
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)]=>0
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]=>[(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)]=>0
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>[(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)]=>0
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>[(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)]=>0
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]=>[(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)]=>0
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>[(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)]=>0
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>[(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)]=>0
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]=>[(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)]=>0
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]=>[(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)]=>0
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)]=>0
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)]=>0
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]=>[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)]=>0
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>[(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)]=>0
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>[(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)]=>0
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)]=>0
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]=>[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)]=>0
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]=>[(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)]=>0
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]=>[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)]=>0
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]=>[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)]=>0
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14)]=>0
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]=>0
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)]=>[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>15
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)]=>0
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)]=>0
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Description
The number of nestings of a perfect matching.
This is the number of pairs of edges $((a,b), (c,d))$ such that $a\le c\le d\le b$. i.e., the edge $(c,d)$ is nested inside $(a,b)$.
This is the number of pairs of edges $((a,b), (c,d))$ such that $a\le c\le d\le b$. i.e., the edge $(c,d)$ is nested inside $(a,b)$.
Map
Kasraoui-Zeng
Description
The Kasraoui-Zeng involution for perfect matchings.
This yields the perfect matching with the number of nestings and crossings exchanged.
This yields the perfect matching with the number of nestings and crossings exchanged.
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