Identifier
Mp00086:
Permutations
—first fundamental transformation⟶
Permutations
Mp00209: Permutations —pattern poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00209: Permutations —pattern poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
Images
=>
Cc0014;cc-rep-2Cc0029;cc-rep-3
[1]=>[1]=>([],1)=>([],1)
[1,2]=>[1,2]=>([(0,1)],2)=>([(0,1)],2)
[2,1]=>[2,1]=>([(0,1)],2)=>([(0,1)],2)
[1,2,3]=>[1,2,3]=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3)
[1,3,2]=>[1,3,2]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],1)
[2,1,3]=>[2,1,3]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],1)
[2,3,1]=>[3,2,1]=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3)
[3,1,2]=>[2,3,1]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],1)
[3,2,1]=>[3,1,2]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],1)
[1,2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4)
[1,2,4,3]=>[1,2,4,3]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)
[1,3,2,4]=>[1,3,2,4]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([],1)
[1,3,4,2]=>[1,4,3,2]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)
[1,4,2,3]=>[1,3,4,2]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([],1)
[1,4,3,2]=>[1,4,2,3]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([],1)
[2,1,3,4]=>[2,1,3,4]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)
[2,1,4,3]=>[2,1,4,3]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,1)],2)
[2,3,1,4]=>[3,2,1,4]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)
[2,3,4,1]=>[4,2,3,1]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([],1)
[2,4,1,3]=>[3,2,4,1]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([],1)
[2,4,3,1]=>[4,2,1,3]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([],1)
[3,1,2,4]=>[2,3,1,4]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([],1)
[3,1,4,2]=>[3,4,1,2]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,1)],2)
[3,2,1,4]=>[3,1,2,4]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([],1)
[3,2,4,1]=>[4,3,2,1]=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4)
[3,4,1,2]=>[2,4,3,1]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([],1)
[3,4,2,1]=>[4,1,3,2]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([],1)
[4,1,2,3]=>[2,3,4,1]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)
[4,1,3,2]=>[3,4,2,1]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)
[4,2,3,1]=>[4,3,1,2]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)
[4,3,2,1]=>[4,1,2,3]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)
[1,2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,4),(2,3),(3,1),(4,2)],5)
[1,2,3,5,4]=>[1,2,3,5,4]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[1,2,4,5,3]=>[1,2,5,4,3]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([],1)
[1,4,3,5,2]=>[1,5,4,3,2]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[2,1,3,4,5]=>[2,1,3,4,5]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[2,1,4,5,3]=>[2,1,5,4,3]=>([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)=>([],1)
[2,3,1,4,5]=>[3,2,1,4,5]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([],1)
[2,3,1,5,4]=>[3,2,1,5,4]=>([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)=>([],1)
[3,2,4,1,5]=>[4,3,2,1,5]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[3,4,2,5,1]=>[5,4,3,2,1]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,4),(2,3),(3,1),(4,2)],5)
[3,5,1,4,2]=>[4,5,3,2,1]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[3,5,2,4,1]=>[5,4,3,1,2]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[4,2,5,1,3]=>[3,4,5,2,1]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([],1)
[4,2,5,3,1]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>([],1)
[5,1,2,3,4]=>[2,3,4,5,1]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[5,2,4,1,3]=>[3,4,5,1,2]=>([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)=>([],1)
[5,3,1,4,2]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)=>([],1)
[5,4,3,2,1]=>[5,1,2,3,4]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)=>([(0,1)],2)
[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)=>([(0,1)],2)
[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[4,3,6,1,5,2]=>[5,6,4,3,2,1]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[4,3,6,2,5,1]=>[6,5,4,3,1,2]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[5,1,3,6,2,4]=>[3,4,5,6,1,2]=>([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[5,2,6,1,4,3]=>[4,5,6,3,2,1]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[5,2,6,3,4,1]=>[6,5,4,1,2,3]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[5,3,1,6,4,2]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[6,1,3,5,2,4]=>[3,4,5,6,2,1]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[6,4,2,5,3,1]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)=>([(0,3),(2,1),(3,2)],4)
[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)=>([],1)
[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>([(0,5),(0,6),(1,11),(2,3),(2,13),(3,4),(3,10),(4,9),(4,14),(5,1),(5,12),(6,2),(6,12),(7,14),(9,8),(10,9),(10,14),(11,7),(12,11),(12,13),(13,7),(13,10),(14,8)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>([(0,5),(0,6),(1,14),(2,4),(2,13),(3,1),(3,11),(4,9),(4,14),(5,2),(5,12),(6,3),(6,12),(8,10),(8,15),(9,10),(9,15),(10,7),(11,8),(11,14),(12,11),(12,13),(13,8),(13,9),(14,15),(15,7)],16)=>([],1)
[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)=>([],1)
[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>([(0,5),(0,6),(1,14),(2,4),(2,13),(3,1),(3,11),(4,9),(4,14),(5,2),(5,12),(6,3),(6,12),(8,10),(8,15),(9,10),(9,15),(10,7),(11,8),(11,14),(12,11),(12,13),(13,8),(13,9),(14,15),(15,7)],16)=>([],1)
[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>([(0,5),(0,6),(1,11),(2,3),(2,13),(3,4),(3,10),(4,9),(4,14),(5,1),(5,12),(6,2),(6,12),(7,14),(9,8),(10,9),(10,14),(11,7),(12,11),(12,13),(13,7),(13,10),(14,8)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[4,5,3,7,1,6,2]=>[6,7,5,4,3,2,1]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
[4,5,3,7,2,6,1]=>[7,6,5,4,3,1,2]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
[4,6,2,7,1,5,3]=>[5,6,7,4,3,2,1]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[4,6,2,7,3,5,1]=>[7,6,5,4,1,2,3]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[6,2,4,7,1,3,5]=>[3,4,5,6,7,2,1]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[6,2,5,3,7,1,4]=>[4,5,6,7,3,2,1]=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)=>([],1)
[6,3,5,2,7,4,1]=>[7,6,5,1,2,3,4]=>([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)=>([],1)
[6,4,2,7,5,3,1]=>[7,6,1,2,3,4,5]=>([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
[7,2,4,6,1,3,5]=>[3,4,5,6,7,1,2]=>([(0,5),(0,6),(1,11),(2,3),(2,13),(3,4),(3,10),(4,9),(4,14),(5,1),(5,12),(6,2),(6,12),(7,14),(9,8),(10,9),(10,14),(11,7),(12,11),(12,13),(13,7),(13,10),(14,8)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[7,3,6,2,5,1,4]=>[4,5,6,7,1,2,3]=>([(0,5),(0,6),(1,14),(2,4),(2,13),(3,1),(3,11),(4,9),(4,14),(5,2),(5,12),(6,3),(6,12),(8,10),(8,15),(9,10),(9,15),(10,7),(11,8),(11,14),(12,11),(12,13),(13,8),(13,9),(14,15),(15,7)],16)=>([],1)
[7,4,1,5,2,6,3]=>[5,6,7,1,2,3,4]=>([(0,5),(0,6),(1,14),(2,4),(2,13),(3,1),(3,11),(4,9),(4,14),(5,2),(5,12),(6,3),(6,12),(8,10),(8,15),(9,10),(9,15),(10,7),(11,8),(11,14),(12,11),(12,13),(13,8),(13,9),(14,15),(15,7)],16)=>([],1)
[7,5,3,1,6,4,2]=>[6,7,1,2,3,4,5]=>([(0,5),(0,6),(1,11),(2,3),(2,13),(3,4),(3,10),(4,9),(4,14),(5,1),(5,12),(6,2),(6,12),(7,14),(9,8),(10,9),(10,14),(11,7),(12,11),(12,13),(13,7),(13,10),(14,8)],15)=>([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
[7,6,5,4,3,2,1]=>[7,1,2,3,4,5,6]=>([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)=>([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
Map
antichains of maximal size
Description
The lattice of antichains of maximal size in a poset.
The set of antichains of maximal size can be ordered by setting $A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$, where $\mathop{\downarrow} A$ is the order ideal generated by $A$.
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.
The set of antichains of maximal size can be ordered by setting $A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$, where $\mathop{\downarrow} A$ is the order ideal generated by $A$.
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.
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