Identifier
Mp00146:
Dyck paths
—to tunnel matching⟶
Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Images
=>
Cc0005;cc-rep-0Cc0012;cc-rep-1
[1,0]=>[(1,2)]=>[2,1]=>[2,1]
[1,0,1,0]=>[(1,2),(3,4)]=>[2,1,4,3]=>[2,1,4,3]
[1,1,0,0]=>[(1,4),(2,3)]=>[4,3,2,1]=>[3,2,4,1]
[1,0,1,0,1,0]=>[(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[1,0,1,1,0,0]=>[(1,2),(3,6),(4,5)]=>[2,1,6,5,4,3]=>[2,1,5,4,6,3]
[1,1,0,0,1,0]=>[(1,4),(2,3),(5,6)]=>[4,3,2,1,6,5]=>[3,2,4,1,6,5]
[1,1,0,1,0,0]=>[(1,6),(2,3),(4,5)]=>[6,3,2,5,4,1]=>[3,2,5,4,6,1]
[1,1,1,0,0,0]=>[(1,6),(2,5),(3,4)]=>[6,5,4,3,2,1]=>[4,3,5,2,6,1]
[1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,6,8,5]
[1,0,1,1,0,0,1,0]=>[(1,2),(3,6),(4,5),(7,8)]=>[2,1,6,5,4,3,8,7]=>[2,1,5,4,6,3,8,7]
[1,0,1,1,0,1,0,0]=>[(1,2),(3,8),(4,5),(6,7)]=>[2,1,8,5,4,7,6,3]=>[2,1,5,4,7,6,8,3]
[1,0,1,1,1,0,0,0]=>[(1,2),(3,8),(4,7),(5,6)]=>[2,1,8,7,6,5,4,3]=>[2,1,6,5,7,4,8,3]
[1,1,0,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,8)]=>[4,3,2,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]
[1,1,0,0,1,1,0,0]=>[(1,4),(2,3),(5,8),(6,7)]=>[4,3,2,1,8,7,6,5]=>[3,2,4,1,7,6,8,5]
[1,1,0,1,0,0,1,0]=>[(1,6),(2,3),(4,5),(7,8)]=>[6,3,2,5,4,1,8,7]=>[3,2,5,4,6,1,8,7]
[1,1,0,1,0,1,0,0]=>[(1,8),(2,3),(4,5),(6,7)]=>[8,3,2,5,4,7,6,1]=>[3,2,5,4,7,6,8,1]
[1,1,0,1,1,0,0,0]=>[(1,8),(2,3),(4,7),(5,6)]=>[8,3,2,7,6,5,4,1]=>[3,2,6,5,7,4,8,1]
[1,1,1,0,0,0,1,0]=>[(1,6),(2,5),(3,4),(7,8)]=>[6,5,4,3,2,1,8,7]=>[4,3,5,2,6,1,8,7]
[1,1,1,0,0,1,0,0]=>[(1,8),(2,5),(3,4),(6,7)]=>[8,5,4,3,2,7,6,1]=>[4,3,5,2,7,6,8,1]
[1,1,1,0,1,0,0,0]=>[(1,8),(2,7),(3,4),(5,6)]=>[8,7,4,3,6,5,2,1]=>[4,3,6,5,7,2,8,1]
[1,1,1,1,0,0,0,0]=>[(1,8),(2,7),(3,6),(4,5)]=>[8,7,6,5,4,3,2,1]=>[5,4,6,3,7,2,8,1]
[1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[1,0,1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,6),(7,10),(8,9)]=>[2,1,4,3,6,5,10,9,8,7]=>[2,1,4,3,6,5,9,8,10,7]
[1,0,1,0,1,1,0,0,1,0]=>[(1,2),(3,4),(5,8),(6,7),(9,10)]=>[2,1,4,3,8,7,6,5,10,9]=>[2,1,4,3,7,6,8,5,10,9]
[1,0,1,0,1,1,0,1,0,0]=>[(1,2),(3,4),(5,10),(6,7),(8,9)]=>[2,1,4,3,10,7,6,9,8,5]=>[2,1,4,3,7,6,9,8,10,5]
[1,0,1,0,1,1,1,0,0,0]=>[(1,2),(3,4),(5,10),(6,9),(7,8)]=>[2,1,4,3,10,9,8,7,6,5]=>[2,1,4,3,8,7,9,6,10,5]
[1,0,1,1,0,0,1,0,1,0]=>[(1,2),(3,6),(4,5),(7,8),(9,10)]=>[2,1,6,5,4,3,8,7,10,9]=>[2,1,5,4,6,3,8,7,10,9]
[1,0,1,1,0,0,1,1,0,0]=>[(1,2),(3,6),(4,5),(7,10),(8,9)]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,5,4,6,3,9,8,10,7]
[1,0,1,1,0,1,0,0,1,0]=>[(1,2),(3,8),(4,5),(6,7),(9,10)]=>[2,1,8,5,4,7,6,3,10,9]=>[2,1,5,4,7,6,8,3,10,9]
[1,0,1,1,0,1,0,1,0,0]=>[(1,2),(3,10),(4,5),(6,7),(8,9)]=>[2,1,10,5,4,7,6,9,8,3]=>[2,1,5,4,7,6,9,8,10,3]
[1,0,1,1,0,1,1,0,0,0]=>[(1,2),(3,10),(4,5),(6,9),(7,8)]=>[2,1,10,5,4,9,8,7,6,3]=>[2,1,5,4,8,7,9,6,10,3]
[1,0,1,1,1,0,0,0,1,0]=>[(1,2),(3,8),(4,7),(5,6),(9,10)]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,6,5,7,4,8,3,10,9]
[1,0,1,1,1,0,0,1,0,0]=>[(1,2),(3,10),(4,7),(5,6),(8,9)]=>[2,1,10,7,6,5,4,9,8,3]=>[2,1,6,5,7,4,9,8,10,3]
[1,0,1,1,1,0,1,0,0,0]=>[(1,2),(3,10),(4,9),(5,6),(7,8)]=>[2,1,10,9,6,5,8,7,4,3]=>[2,1,6,5,8,7,9,4,10,3]
[1,0,1,1,1,1,0,0,0,0]=>[(1,2),(3,10),(4,9),(5,8),(6,7)]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,7,6,8,5,9,4,10,3]
[1,1,0,0,1,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,8),(9,10)]=>[4,3,2,1,6,5,8,7,10,9]=>[3,2,4,1,6,5,8,7,10,9]
[1,1,0,0,1,0,1,1,0,0]=>[(1,4),(2,3),(5,6),(7,10),(8,9)]=>[4,3,2,1,6,5,10,9,8,7]=>[3,2,4,1,6,5,9,8,10,7]
[1,1,0,0,1,1,0,0,1,0]=>[(1,4),(2,3),(5,8),(6,7),(9,10)]=>[4,3,2,1,8,7,6,5,10,9]=>[3,2,4,1,7,6,8,5,10,9]
[1,1,0,0,1,1,0,1,0,0]=>[(1,4),(2,3),(5,10),(6,7),(8,9)]=>[4,3,2,1,10,7,6,9,8,5]=>[3,2,4,1,7,6,9,8,10,5]
[1,1,0,0,1,1,1,0,0,0]=>[(1,4),(2,3),(5,10),(6,9),(7,8)]=>[4,3,2,1,10,9,8,7,6,5]=>[3,2,4,1,8,7,9,6,10,5]
[1,1,0,1,0,0,1,0,1,0]=>[(1,6),(2,3),(4,5),(7,8),(9,10)]=>[6,3,2,5,4,1,8,7,10,9]=>[3,2,5,4,6,1,8,7,10,9]
[1,1,0,1,0,0,1,1,0,0]=>[(1,6),(2,3),(4,5),(7,10),(8,9)]=>[6,3,2,5,4,1,10,9,8,7]=>[3,2,5,4,6,1,9,8,10,7]
[1,1,0,1,0,1,0,0,1,0]=>[(1,8),(2,3),(4,5),(6,7),(9,10)]=>[8,3,2,5,4,7,6,1,10,9]=>[3,2,5,4,7,6,8,1,10,9]
[1,1,0,1,0,1,0,1,0,0]=>[(1,10),(2,3),(4,5),(6,7),(8,9)]=>[10,3,2,5,4,7,6,9,8,1]=>[3,2,5,4,7,6,9,8,10,1]
[1,1,0,1,0,1,1,0,0,0]=>[(1,10),(2,3),(4,5),(6,9),(7,8)]=>[10,3,2,5,4,9,8,7,6,1]=>[3,2,5,4,8,7,9,6,10,1]
[1,1,0,1,1,0,0,0,1,0]=>[(1,8),(2,3),(4,7),(5,6),(9,10)]=>[8,3,2,7,6,5,4,1,10,9]=>[3,2,6,5,7,4,8,1,10,9]
[1,1,0,1,1,0,0,1,0,0]=>[(1,10),(2,3),(4,7),(5,6),(8,9)]=>[10,3,2,7,6,5,4,9,8,1]=>[3,2,6,5,7,4,9,8,10,1]
[1,1,0,1,1,0,1,0,0,0]=>[(1,10),(2,3),(4,9),(5,6),(7,8)]=>[10,3,2,9,6,5,8,7,4,1]=>[3,2,6,5,8,7,9,4,10,1]
[1,1,0,1,1,1,0,0,0,0]=>[(1,10),(2,3),(4,9),(5,8),(6,7)]=>[10,3,2,9,8,7,6,5,4,1]=>[3,2,7,6,8,5,9,4,10,1]
[1,1,1,0,0,0,1,0,1,0]=>[(1,6),(2,5),(3,4),(7,8),(9,10)]=>[6,5,4,3,2,1,8,7,10,9]=>[4,3,5,2,6,1,8,7,10,9]
[1,1,1,0,0,0,1,1,0,0]=>[(1,6),(2,5),(3,4),(7,10),(8,9)]=>[6,5,4,3,2,1,10,9,8,7]=>[4,3,5,2,6,1,9,8,10,7]
[1,1,1,0,0,1,0,0,1,0]=>[(1,8),(2,5),(3,4),(6,7),(9,10)]=>[8,5,4,3,2,7,6,1,10,9]=>[4,3,5,2,7,6,8,1,10,9]
[1,1,1,0,0,1,0,1,0,0]=>[(1,10),(2,5),(3,4),(6,7),(8,9)]=>[10,5,4,3,2,7,6,9,8,1]=>[4,3,5,2,7,6,9,8,10,1]
[1,1,1,0,0,1,1,0,0,0]=>[(1,10),(2,5),(3,4),(6,9),(7,8)]=>[10,5,4,3,2,9,8,7,6,1]=>[4,3,5,2,8,7,9,6,10,1]
[1,1,1,0,1,0,0,0,1,0]=>[(1,8),(2,7),(3,4),(5,6),(9,10)]=>[8,7,4,3,6,5,2,1,10,9]=>[4,3,6,5,7,2,8,1,10,9]
[1,1,1,0,1,0,0,1,0,0]=>[(1,10),(2,7),(3,4),(5,6),(8,9)]=>[10,7,4,3,6,5,2,9,8,1]=>[4,3,6,5,7,2,9,8,10,1]
[1,1,1,0,1,0,1,0,0,0]=>[(1,10),(2,9),(3,4),(5,6),(7,8)]=>[10,9,4,3,6,5,8,7,2,1]=>[4,3,6,5,8,7,9,2,10,1]
[1,1,1,0,1,1,0,0,0,0]=>[(1,10),(2,9),(3,4),(5,8),(6,7)]=>[10,9,4,3,8,7,6,5,2,1]=>[4,3,7,6,8,5,9,2,10,1]
[1,1,1,1,0,0,0,0,1,0]=>[(1,8),(2,7),(3,6),(4,5),(9,10)]=>[8,7,6,5,4,3,2,1,10,9]=>[5,4,6,3,7,2,8,1,10,9]
[1,1,1,1,0,0,0,1,0,0]=>[(1,10),(2,7),(3,6),(4,5),(8,9)]=>[10,7,6,5,4,3,2,9,8,1]=>[5,4,6,3,7,2,9,8,10,1]
[1,1,1,1,0,0,1,0,0,0]=>[(1,10),(2,9),(3,6),(4,5),(7,8)]=>[10,9,6,5,4,3,8,7,2,1]=>[5,4,6,3,8,7,9,2,10,1]
[1,1,1,1,0,1,0,0,0,0]=>[(1,10),(2,9),(3,8),(4,5),(6,7)]=>[10,9,8,5,4,7,6,3,2,1]=>[5,4,7,6,8,3,9,2,10,1]
[1,1,1,1,1,0,0,0,0,0]=>[(1,10),(2,9),(3,8),(4,7),(5,6)]=>[10,9,8,7,6,5,4,3,2,1]=>[6,5,7,4,8,3,9,2,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>[2,1,4,3,6,5,8,7,11,10,12,9]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>[2,1,4,3,6,5,9,8,10,7,12,11]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>[2,1,4,3,6,5,12,9,8,11,10,7]=>[2,1,4,3,6,5,9,8,11,10,12,7]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,1,4,3,6,5,10,9,11,8,12,7]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>[2,1,4,3,7,6,8,5,10,9,12,11]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>[2,1,4,3,7,6,8,5,11,10,12,9]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>[2,1,4,3,10,7,6,9,8,5,12,11]=>[2,1,4,3,7,6,9,8,10,5,12,11]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>[2,1,4,3,12,7,6,9,8,11,10,5]=>[2,1,4,3,7,6,9,8,11,10,12,5]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>[2,1,4,3,12,7,6,11,10,9,8,5]=>[2,1,4,3,7,6,10,9,11,8,12,5]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,1,4,3,8,7,9,6,10,5,12,11]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>[2,1,4,3,12,9,8,7,6,11,10,5]=>[2,1,4,3,8,7,9,6,11,10,12,5]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>[2,1,4,3,12,11,8,7,10,9,6,5]=>[2,1,4,3,8,7,10,9,11,6,12,5]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,4,3,9,8,10,7,11,6,12,5]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>[2,1,5,4,6,3,8,7,10,9,12,11]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>[2,1,5,4,6,3,8,7,11,10,12,9]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>[2,1,5,4,6,3,9,8,10,7,12,11]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>[2,1,6,5,4,3,12,9,8,11,10,7]=>[2,1,5,4,6,3,9,8,11,10,12,7]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>[2,1,5,4,6,3,10,9,11,8,12,7]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>[2,1,8,5,4,7,6,3,10,9,12,11]=>[2,1,5,4,7,6,8,3,10,9,12,11]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>[2,1,8,5,4,7,6,3,12,11,10,9]=>[2,1,5,4,7,6,8,3,11,10,12,9]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>[2,1,10,5,4,7,6,9,8,3,12,11]=>[2,1,5,4,7,6,9,8,10,3,12,11]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>[2,1,12,5,4,7,6,9,8,11,10,3]=>[2,1,5,4,7,6,9,8,11,10,12,3]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>[2,1,12,5,4,7,6,11,10,9,8,3]=>[2,1,5,4,7,6,10,9,11,8,12,3]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>[2,1,10,5,4,9,8,7,6,3,12,11]=>[2,1,5,4,8,7,9,6,10,3,12,11]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>[2,1,12,5,4,9,8,7,6,11,10,3]=>[2,1,5,4,8,7,9,6,11,10,12,3]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>[2,1,12,5,4,11,8,7,10,9,6,3]=>[2,1,5,4,8,7,10,9,11,6,12,3]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>[2,1,12,5,4,11,10,9,8,7,6,3]=>[2,1,5,4,9,8,10,7,11,6,12,3]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,6,5,7,4,8,3,10,9,12,11]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>[2,1,6,5,7,4,8,3,11,10,12,9]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>[2,1,10,7,6,5,4,9,8,3,12,11]=>[2,1,6,5,7,4,9,8,10,3,12,11]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>[2,1,12,7,6,5,4,9,8,11,10,3]=>[2,1,6,5,7,4,9,8,11,10,12,3]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>[2,1,12,7,6,5,4,11,10,9,8,3]=>[2,1,6,5,7,4,10,9,11,8,12,3]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>[2,1,10,9,6,5,8,7,4,3,12,11]=>[2,1,6,5,8,7,9,4,10,3,12,11]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>[2,1,12,9,6,5,8,7,4,11,10,3]=>[2,1,6,5,8,7,9,4,11,10,12,3]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>[2,1,12,11,6,5,8,7,10,9,4,3]=>[2,1,6,5,8,7,10,9,11,4,12,3]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>[2,1,12,11,6,5,10,9,8,7,4,3]=>[2,1,6,5,9,8,10,7,11,4,12,3]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,7,6,8,5,9,4,10,3,12,11]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>[2,1,12,9,8,7,6,5,4,11,10,3]=>[2,1,7,6,8,5,9,4,11,10,12,3]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>[2,1,12,11,8,7,6,5,10,9,4,3]=>[2,1,7,6,8,5,10,9,11,4,12,3]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>[2,1,12,11,10,7,6,9,8,5,4,3]=>[2,1,7,6,9,8,10,5,11,4,12,3]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,8,7,9,6,10,5,11,4,12,3]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>[3,2,4,1,6,5,8,7,10,9,12,11]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>[3,2,4,1,6,5,8,7,11,10,12,9]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>[3,2,4,1,6,5,9,8,10,7,12,11]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]=>[4,3,2,1,6,5,12,9,8,11,10,7]=>[3,2,4,1,6,5,9,8,11,10,12,7]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>[3,2,4,1,6,5,10,9,11,8,12,7]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>[3,2,4,1,7,6,8,5,10,9,12,11]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>[3,2,4,1,7,6,8,5,11,10,12,9]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>[4,3,2,1,10,7,6,9,8,5,12,11]=>[3,2,4,1,7,6,9,8,10,5,12,11]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]=>[4,3,2,1,12,7,6,9,8,11,10,5]=>[3,2,4,1,7,6,9,8,11,10,12,5]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]=>[4,3,2,1,12,7,6,11,10,9,8,5]=>[3,2,4,1,7,6,10,9,11,8,12,5]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>[3,2,4,1,8,7,9,6,10,5,12,11]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]=>[4,3,2,1,12,9,8,7,6,11,10,5]=>[3,2,4,1,8,7,9,6,11,10,12,5]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]=>[4,3,2,1,12,11,8,7,10,9,6,5]=>[3,2,4,1,8,7,10,9,11,6,12,5]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[3,2,4,1,9,8,10,7,11,6,12,5]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>[6,3,2,5,4,1,8,7,10,9,12,11]=>[3,2,5,4,6,1,8,7,10,9,12,11]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]=>[6,3,2,5,4,1,8,7,12,11,10,9]=>[3,2,5,4,6,1,8,7,11,10,12,9]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>[6,3,2,5,4,1,10,9,8,7,12,11]=>[3,2,5,4,6,1,9,8,10,7,12,11]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]=>[6,3,2,5,4,1,12,9,8,11,10,7]=>[3,2,5,4,6,1,9,8,11,10,12,7]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]=>[6,3,2,5,4,1,12,11,10,9,8,7]=>[3,2,5,4,6,1,10,9,11,8,12,7]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>[8,3,2,5,4,7,6,1,10,9,12,11]=>[3,2,5,4,7,6,8,1,10,9,12,11]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]=>[8,3,2,5,4,7,6,1,12,11,10,9]=>[3,2,5,4,7,6,8,1,11,10,12,9]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]=>[10,3,2,5,4,7,6,9,8,1,12,11]=>[3,2,5,4,7,6,9,8,10,1,12,11]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]=>[12,3,2,5,4,7,6,9,8,11,10,1]=>[3,2,5,4,7,6,9,8,11,10,12,1]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]=>[12,3,2,5,4,7,6,11,10,9,8,1]=>[3,2,5,4,7,6,10,9,11,8,12,1]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>[10,3,2,5,4,9,8,7,6,1,12,11]=>[3,2,5,4,8,7,9,6,10,1,12,11]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]=>[12,3,2,5,4,9,8,7,6,11,10,1]=>[3,2,5,4,8,7,9,6,11,10,12,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]=>[12,3,2,5,4,11,8,7,10,9,6,1]=>[3,2,5,4,8,7,10,9,11,6,12,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]=>[12,3,2,5,4,11,10,9,8,7,6,1]=>[3,2,5,4,9,8,10,7,11,6,12,1]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>[8,3,2,7,6,5,4,1,10,9,12,11]=>[3,2,6,5,7,4,8,1,10,9,12,11]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]=>[8,3,2,7,6,5,4,1,12,11,10,9]=>[3,2,6,5,7,4,8,1,11,10,12,9]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>[10,3,2,7,6,5,4,9,8,1,12,11]=>[3,2,6,5,7,4,9,8,10,1,12,11]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]=>[12,3,2,7,6,5,4,9,8,11,10,1]=>[3,2,6,5,7,4,9,8,11,10,12,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]=>[12,3,2,7,6,5,4,11,10,9,8,1]=>[3,2,6,5,7,4,10,9,11,8,12,1]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>[10,3,2,9,6,5,8,7,4,1,12,11]=>[3,2,6,5,8,7,9,4,10,1,12,11]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]=>[12,3,2,9,6,5,8,7,4,11,10,1]=>[3,2,6,5,8,7,9,4,11,10,12,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]=>[12,3,2,11,6,5,8,7,10,9,4,1]=>[3,2,6,5,8,7,10,9,11,4,12,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]=>[12,3,2,11,6,5,10,9,8,7,4,1]=>[3,2,6,5,9,8,10,7,11,4,12,1]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>[10,3,2,9,8,7,6,5,4,1,12,11]=>[3,2,7,6,8,5,9,4,10,1,12,11]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]=>[12,3,2,9,8,7,6,5,4,11,10,1]=>[3,2,7,6,8,5,9,4,11,10,12,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]=>[12,3,2,11,8,7,6,5,10,9,4,1]=>[3,2,7,6,8,5,10,9,11,4,12,1]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]=>[12,3,2,11,10,7,6,9,8,5,4,1]=>[3,2,7,6,9,8,10,5,11,4,12,1]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]=>[12,3,2,11,10,9,8,7,6,5,4,1]=>[3,2,8,7,9,6,10,5,11,4,12,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>[4,3,5,2,6,1,8,7,10,9,12,11]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>[4,3,5,2,6,1,8,7,11,10,12,9]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>[4,3,5,2,6,1,9,8,10,7,12,11]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>[6,5,4,3,2,1,12,9,8,11,10,7]=>[4,3,5,2,6,1,9,8,11,10,12,7]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[4,3,5,2,6,1,10,9,11,8,12,7]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>[8,5,4,3,2,7,6,1,10,9,12,11]=>[4,3,5,2,7,6,8,1,10,9,12,11]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>[8,5,4,3,2,7,6,1,12,11,10,9]=>[4,3,5,2,7,6,8,1,11,10,12,9]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]=>[10,5,4,3,2,7,6,9,8,1,12,11]=>[4,3,5,2,7,6,9,8,10,1,12,11]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>[12,5,4,3,2,7,6,9,8,11,10,1]=>[4,3,5,2,7,6,9,8,11,10,12,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]=>[12,5,4,3,2,7,6,11,10,9,8,1]=>[4,3,5,2,7,6,10,9,11,8,12,1]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]=>[10,5,4,3,2,9,8,7,6,1,12,11]=>[4,3,5,2,8,7,9,6,10,1,12,11]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>[12,5,4,3,2,9,8,7,6,11,10,1]=>[4,3,5,2,8,7,9,6,11,10,12,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]=>[12,5,4,3,2,11,8,7,10,9,6,1]=>[4,3,5,2,8,7,10,9,11,6,12,1]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]=>[12,5,4,3,2,11,10,9,8,7,6,1]=>[4,3,5,2,9,8,10,7,11,6,12,1]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>[8,7,4,3,6,5,2,1,10,9,12,11]=>[4,3,6,5,7,2,8,1,10,9,12,11]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>[8,7,4,3,6,5,2,1,12,11,10,9]=>[4,3,6,5,7,2,8,1,11,10,12,9]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]=>[10,7,4,3,6,5,2,9,8,1,12,11]=>[4,3,6,5,7,2,9,8,10,1,12,11]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>[12,7,4,3,6,5,2,9,8,11,10,1]=>[4,3,6,5,7,2,9,8,11,10,12,1]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]=>[12,7,4,3,6,5,2,11,10,9,8,1]=>[4,3,6,5,7,2,10,9,11,8,12,1]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]=>[10,9,4,3,6,5,8,7,2,1,12,11]=>[4,3,6,5,8,7,9,2,10,1,12,11]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>[12,9,4,3,6,5,8,7,2,11,10,1]=>[4,3,6,5,8,7,9,2,11,10,12,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>[12,11,4,3,6,5,8,7,10,9,2,1]=>[4,3,6,5,8,7,10,9,11,2,12,1]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>[12,11,4,3,6,5,10,9,8,7,2,1]=>[4,3,6,5,9,8,10,7,11,2,12,1]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]=>[10,9,4,3,8,7,6,5,2,1,12,11]=>[4,3,7,6,8,5,9,2,10,1,12,11]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>[12,9,4,3,8,7,6,5,2,11,10,1]=>[4,3,7,6,8,5,9,2,11,10,12,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>[12,11,4,3,8,7,6,5,10,9,2,1]=>[4,3,7,6,8,5,10,9,11,2,12,1]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>[12,11,4,3,10,7,6,9,8,5,2,1]=>[4,3,7,6,9,8,10,5,11,2,12,1]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[4,3,8,7,9,6,10,5,11,2,12,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[5,4,6,3,7,2,8,1,10,9,12,11]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[5,4,6,3,7,2,8,1,11,10,12,9]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>[10,7,6,5,4,3,2,9,8,1,12,11]=>[5,4,6,3,7,2,9,8,10,1,12,11]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]=>[12,7,6,5,4,3,2,9,8,11,10,1]=>[5,4,6,3,7,2,9,8,11,10,12,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>[12,7,6,5,4,3,2,11,10,9,8,1]=>[5,4,6,3,7,2,10,9,11,8,12,1]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>[10,9,6,5,4,3,8,7,2,1,12,11]=>[5,4,6,3,8,7,9,2,10,1,12,11]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>[12,9,6,5,4,3,8,7,2,11,10,1]=>[5,4,6,3,8,7,9,2,11,10,12,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>[12,11,6,5,4,3,8,7,10,9,2,1]=>[5,4,6,3,8,7,10,9,11,2,12,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[5,4,6,3,9,8,10,7,11,2,12,1]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>[10,9,8,5,4,7,6,3,2,1,12,11]=>[5,4,7,6,8,3,9,2,10,1,12,11]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>[12,9,8,5,4,7,6,3,2,11,10,1]=>[5,4,7,6,8,3,9,2,11,10,12,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>[12,11,8,5,4,7,6,3,10,9,2,1]=>[5,4,7,6,8,3,10,9,11,2,12,1]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>[12,11,10,5,4,7,6,9,8,3,2,1]=>[5,4,7,6,9,8,10,3,11,2,12,1]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>[12,11,10,5,4,9,8,7,6,3,2,1]=>[5,4,8,7,9,6,10,3,11,2,12,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[6,5,7,4,8,3,9,2,10,1,12,11]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]=>[12,9,8,7,6,5,4,3,2,11,10,1]=>[6,5,7,4,8,3,9,2,11,10,12,1]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>[12,11,8,7,6,5,4,3,10,9,2,1]=>[6,5,7,4,8,3,10,9,11,2,12,1]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>[12,11,10,7,6,5,4,9,8,3,2,1]=>[6,5,7,4,9,8,10,3,11,2,12,1]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[6,5,8,7,9,4,10,3,11,2,12,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[7,6,8,5,9,4,10,3,11,2,12,1]
Map
to tunnel matching
Description
Sends a Dyck path of semilength n to the noncrossing perfect matching given by matching an up-step with the corresponding down-step.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
searching the database
Sorry, this map was not found in the database.