Identifier
Mp00047: Ordered trees —to poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
Images
=>
Cc0021;cc-rep-0Cc0014;cc-rep-1Cc0014;cc-rep-2Cc0029;cc-rep-3
[]=>([],1)=>([],1)=>([],1) [[]]=>([(0,1)],2)=>([(0,1)],2)=>([(0,1)],2) [[],[]]=>([(0,2),(1,2)],3)=>([(0,1),(0,2)],3)=>([],1) [[[]]]=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3) [[],[],[]]=>([(0,3),(1,3),(2,3)],4)=>([(0,1),(0,2),(0,3)],4)=>([],1) [[],[[]]]=>([(0,3),(1,2),(2,3)],4)=>([(0,2),(0,3),(3,1)],4)=>([(0,1)],2) [[[]],[]]=>([(0,3),(1,2),(2,3)],4)=>([(0,2),(0,3),(3,1)],4)=>([(0,1)],2) [[[],[]]]=>([(0,3),(1,3),(3,2)],4)=>([(0,3),(3,1),(3,2)],4)=>([],1) [[[[]]]]=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4) [[],[],[],[]]=>([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(0,4)],5)=>([],1) [[],[],[[]]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,2),(0,3),(0,4),(4,1)],5)=>([(0,1)],2) [[],[[]],[]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,2),(0,3),(0,4),(4,1)],5)=>([(0,1)],2) [[],[[],[]]]=>([(0,4),(1,3),(2,3),(3,4)],5)=>([(0,3),(0,4),(4,1),(4,2)],5)=>([],1) [[],[[[]]]]=>([(0,4),(1,2),(2,3),(3,4)],5)=>([(0,2),(0,4),(3,1),(4,3)],5)=>([(0,2),(2,1)],3) [[[]],[],[]]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,2),(0,3),(0,4),(4,1)],5)=>([(0,1)],2) [[[]],[[]]]=>([(0,3),(1,2),(2,4),(3,4)],5)=>([(0,3),(0,4),(3,2),(4,1)],5)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[],[]],[]]=>([(0,4),(1,3),(2,3),(3,4)],5)=>([(0,3),(0,4),(4,1),(4,2)],5)=>([],1) [[[[]]],[]]=>([(0,4),(1,2),(2,3),(3,4)],5)=>([(0,2),(0,4),(3,1),(4,3)],5)=>([(0,2),(2,1)],3) [[[],[],[]]]=>([(0,4),(1,4),(2,4),(4,3)],5)=>([(0,4),(4,1),(4,2),(4,3)],5)=>([],1) [[[],[[]]]]=>([(0,4),(1,2),(2,4),(4,3)],5)=>([(0,4),(3,2),(4,1),(4,3)],5)=>([(0,1)],2) [[[[]],[]]]=>([(0,4),(1,2),(2,4),(4,3)],5)=>([(0,4),(3,2),(4,1),(4,3)],5)=>([(0,1)],2) [[[[],[]]]]=>([(0,4),(1,4),(2,3),(4,2)],5)=>([(0,3),(3,4),(4,1),(4,2)],5)=>([],1) [[[[[]]]]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,4),(2,3),(3,1),(4,2)],5) [[],[],[],[],[]]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(0,5)],6)=>([],1) [[],[],[],[[]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(0,3),(0,4),(0,5),(5,1)],6)=>([(0,1)],2) [[],[],[[]],[]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(0,3),(0,4),(0,5),(5,1)],6)=>([(0,1)],2) [[],[],[[],[]]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,3),(0,4),(0,5),(5,1),(5,2)],6)=>([],1) [[],[],[[[]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,2),(0,3),(0,5),(4,1),(5,4)],6)=>([(0,2),(2,1)],3) [[],[[]],[],[]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(0,3),(0,4),(0,5),(5,1)],6)=>([(0,1)],2) [[],[[]],[[]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,3),(0,4),(0,5),(4,2),(5,1)],6)=>([(0,1),(0,2),(1,3),(2,3)],4) [[],[[],[]],[]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,3),(0,4),(0,5),(5,1),(5,2)],6)=>([],1) [[],[[[]]],[]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,2),(0,3),(0,5),(4,1),(5,4)],6)=>([(0,2),(2,1)],3) [[],[[],[],[]]]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6)=>([(0,4),(0,5),(5,1),(5,2),(5,3)],6)=>([],1) [[],[[],[[]]]]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>([(0,3),(0,5),(4,2),(5,1),(5,4)],6)=>([(0,1)],2) [[],[[[]],[]]]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>([(0,3),(0,5),(4,2),(5,1),(5,4)],6)=>([(0,1)],2) [[],[[[],[]]]]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6)=>([(0,3),(0,4),(4,5),(5,1),(5,2)],6)=>([],1) [[],[[[[]]]]]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [[[]],[],[],[]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(0,3),(0,4),(0,5),(5,1)],6)=>([(0,1)],2) [[[]],[],[[]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,3),(0,4),(0,5),(4,2),(5,1)],6)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[]],[[]],[]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,3),(0,4),(0,5),(4,2),(5,1)],6)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[]],[[],[]]]=>([(0,4),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,4),(0,5),(4,3),(5,1),(5,2)],6)=>([(0,1)],2) [[[]],[[[]]]]=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[],[]],[],[]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,3),(0,4),(0,5),(5,1),(5,2)],6)=>([],1) [[[[]]],[],[]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,2),(0,3),(0,5),(4,1),(5,4)],6)=>([(0,2),(2,1)],3) [[[],[]],[[]]]=>([(0,4),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,4),(0,5),(4,3),(5,1),(5,2)],6)=>([(0,1)],2) [[[[]]],[[]]]=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[],[],[]],[]]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6)=>([(0,4),(0,5),(5,1),(5,2),(5,3)],6)=>([],1) [[[],[[]]],[]]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>([(0,3),(0,5),(4,2),(5,1),(5,4)],6)=>([(0,1)],2) [[[[]],[]],[]]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>([(0,3),(0,5),(4,2),(5,1),(5,4)],6)=>([(0,1)],2) [[[[],[]]],[]]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6)=>([(0,3),(0,4),(4,5),(5,1),(5,2)],6)=>([],1) [[[[[]]]],[]]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [[[],[],[],[]]]=>([(0,5),(1,5),(2,5),(3,5),(5,4)],6)=>([(0,5),(5,1),(5,2),(5,3),(5,4)],6)=>([],1) [[[],[],[[]]]]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>([(0,5),(4,3),(5,1),(5,2),(5,4)],6)=>([(0,1)],2) [[[],[[]],[]]]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>([(0,5),(4,3),(5,1),(5,2),(5,4)],6)=>([(0,1)],2) [[[],[[],[]]]]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>([(0,5),(4,2),(4,3),(5,1),(5,4)],6)=>([],1) [[[],[[[]]]]]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>([(0,5),(3,4),(4,2),(5,1),(5,3)],6)=>([(0,2),(2,1)],3) [[[[]],[],[]]]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>([(0,5),(4,3),(5,1),(5,2),(5,4)],6)=>([(0,1)],2) [[[[]],[[]]]]=>([(0,4),(1,3),(3,5),(4,5),(5,2)],6)=>([(0,5),(3,2),(4,1),(5,3),(5,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[[],[]],[]]]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>([(0,5),(4,2),(4,3),(5,1),(5,4)],6)=>([],1) [[[[[]]],[]]]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>([(0,5),(3,4),(4,2),(5,1),(5,3)],6)=>([(0,2),(2,1)],3) [[[[],[],[]]]]=>([(0,5),(1,5),(2,5),(3,4),(5,3)],6)=>([(0,4),(4,5),(5,1),(5,2),(5,3)],6)=>([],1) [[[[],[[]]]]]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>([(0,1)],2) [[[[[]],[]]]]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>([(0,1)],2) [[[[[],[]]]]]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>([(0,4),(3,5),(4,3),(5,1),(5,2)],6)=>([],1) [[[[[[]]]]]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[],[],[],[],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)=>([],1) [[],[],[],[],[[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)=>([(0,1)],2) [[],[],[],[[]],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)=>([(0,1)],2) [[],[],[],[[],[]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)=>([],1) [[],[],[],[[[]]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7)=>([(0,2),(2,1)],3) [[],[],[[]],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)=>([(0,1)],2) [[],[],[[]],[[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[],[],[[],[]],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)=>([],1) [[],[],[[[]]],[]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7)=>([(0,2),(2,1)],3) [[],[],[[],[],[]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)=>([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)=>([],1) [[],[],[[],[[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)=>([(0,1)],2) [[],[],[[[]],[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)=>([(0,1)],2) [[],[],[[[],[]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7)=>([],1) [[],[],[[[[]]]]]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [[],[[]],[],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)=>([(0,1)],2) [[],[[]],[],[[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[],[[]],[[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[],[[]],[[],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)=>([(0,1)],2) [[],[[]],[[[]]]]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[],[[],[]],[],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)=>([],1) [[],[[[]]],[],[]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7)=>([(0,2),(2,1)],3) [[],[[],[]],[[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)=>([(0,1)],2) [[],[[[]]],[[]]]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[],[[],[],[]],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)=>([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)=>([],1) [[],[[],[[]]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)=>([(0,1)],2) [[],[[[]],[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)=>([(0,1)],2) [[],[[[],[]]],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7)=>([],1) [[],[[[[]]]],[]]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [[],[[],[],[],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)=>([],1) [[],[[],[],[[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)=>([(0,1)],2) [[],[[],[[]],[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)=>([(0,1)],2) [[],[[],[[],[]]]]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)=>([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)=>([],1) [[],[[],[[[]]]]]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)=>([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)=>([(0,2),(2,1)],3) [[],[[[]],[],[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)=>([(0,1)],2) [[],[[[]],[[]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[],[[[],[]],[]]]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)=>([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)=>([],1) [[],[[[[]]],[]]]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)=>([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)=>([(0,2),(2,1)],3) [[],[[[],[],[]]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)=>([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)=>([],1) [[],[[[],[[]]]]]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)=>([(0,1)],2) [[],[[[[]],[]]]]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)=>([(0,1)],2) [[],[[[[],[]]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)=>([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)=>([],1) [[],[[[[[]]]]]]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [[[]],[],[],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)=>([(0,1)],2) [[[]],[],[],[[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[]],[],[[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[]],[],[[],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)=>([(0,1)],2) [[[]],[],[[[]]]]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[]],[[]],[],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[]],[[]],[[]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)=>([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) [[[]],[[],[]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)=>([(0,1)],2) [[[]],[[[]]],[]]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[]],[[],[],[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7)=>([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7)=>([(0,1)],2) [[[]],[[],[[]]]]=>([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)=>([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[]],[[[]],[]]]=>([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)=>([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[]],[[[],[]]]]=>([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)=>([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7)=>([(0,1)],2) [[[]],[[[[]]]]]=>([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) [[[],[]],[],[],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)=>([],1) [[[[]]],[],[],[]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7)=>([(0,2),(2,1)],3) [[[],[]],[],[[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)=>([(0,1)],2) [[[[]]],[],[[]]]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[],[]],[[]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)=>([(0,1)],2) [[[[]]],[[]],[]]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[],[]],[[],[]]]=>([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7)=>([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7)=>([],1) [[[],[]],[[[]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)=>([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7)=>([(0,2),(2,1)],3) [[[[]]],[[],[]]]=>([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)=>([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7)=>([(0,2),(2,1)],3) [[[[]]],[[[]]]]=>([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)=>([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)=>([(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) [[[],[],[]],[],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)=>([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)=>([],1) [[[],[[]]],[],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)=>([(0,1)],2) [[[[]],[]],[],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)=>([(0,1)],2) [[[[],[]]],[],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7)=>([],1) [[[[[]]]],[],[]]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [[[],[],[]],[[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7)=>([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7)=>([(0,1)],2) [[[],[[]]],[[]]]=>([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)=>([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[[]],[]],[[]]]=>([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)=>([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[[],[]]],[[]]]=>([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)=>([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7)=>([(0,1)],2) [[[[[]]]],[[]]]=>([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) [[[],[],[],[]],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)=>([],1) [[[],[],[[]]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)=>([(0,1)],2) [[[],[[]],[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)=>([(0,1)],2) [[[],[[],[]]],[]]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)=>([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)=>([],1) [[[],[[[]]]],[]]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)=>([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)=>([(0,2),(2,1)],3) [[[[]],[],[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)=>([(0,1)],2) [[[[]],[[]]],[]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[[],[]],[]],[]]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)=>([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)=>([],1) [[[[[]]],[]],[]]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)=>([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)=>([(0,2),(2,1)],3) [[[[],[],[]]],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)=>([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)=>([],1) [[[[],[[]]]],[]]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)=>([(0,1)],2) [[[[[]],[]]],[]]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)=>([(0,1)],2) [[[[[],[]]]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)=>([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)=>([],1) [[[[[[]]]]],[]]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [[[],[],[],[],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)=>([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)=>([],1) [[[],[],[],[[]]]]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)=>([(0,1)],2) [[[],[],[[]],[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)=>([(0,1)],2) [[[],[],[[],[]]]]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)=>([],1) [[[],[],[[[]]]]]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)=>([(0,2),(2,1)],3) [[[],[[]],[],[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)=>([(0,1)],2) [[[],[[]],[[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,6),(4,3),(5,2),(6,1),(6,4),(6,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[],[[],[]],[]]]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)=>([],1) [[[],[[[]]],[]]]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)=>([(0,2),(2,1)],3) [[[],[[],[],[]]]]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)=>([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)=>([],1) [[[],[[],[[]]]]]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)=>([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7)=>([(0,1)],2) [[[],[[[]],[]]]]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)=>([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7)=>([(0,1)],2) [[[],[[[],[]]]]]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)=>([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)=>([],1) [[[],[[[[]]]]]]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)=>([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [[[[]],[],[],[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)=>([(0,1)],2) [[[[]],[],[[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,6),(4,3),(5,2),(6,1),(6,4),(6,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[[]],[[]],[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,6),(4,3),(5,2),(6,1),(6,4),(6,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[[]],[[],[]]]]=>([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)=>([(0,6),(4,3),(5,1),(5,2),(6,4),(6,5)],7)=>([(0,1)],2) [[[[]],[[[]]]]]=>([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)=>([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[[],[]],[],[]]]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)=>([],1) [[[[[]]],[],[]]]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)=>([(0,2),(2,1)],3) [[[[],[]],[[]]]]=>([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)=>([(0,6),(4,3),(5,1),(5,2),(6,4),(6,5)],7)=>([(0,1)],2) [[[[[]]],[[]]]]=>([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)=>([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[[],[],[]],[]]]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)=>([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)=>([],1) [[[[],[[]]],[]]]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)=>([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7)=>([(0,1)],2) [[[[[]],[]],[]]]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)=>([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7)=>([(0,1)],2) [[[[[],[]]],[]]]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)=>([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)=>([],1) [[[[[[]]]],[]]]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)=>([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [[[[],[],[],[]]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)=>([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)=>([],1) [[[[],[],[[]]]]]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7)=>([(0,1)],2) [[[[],[[]],[]]]]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7)=>([(0,1)],2) [[[[],[[],[]]]]]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)=>([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7)=>([],1) [[[[],[[[]]]]]]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)=>([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)=>([(0,2),(2,1)],3) [[[[[]],[],[]]]]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7)=>([(0,1)],2) [[[[[]],[[]]]]]=>([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)=>([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)=>([(0,1),(0,2),(1,3),(2,3)],4) [[[[[],[]],[]]]]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)=>([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7)=>([],1) [[[[[[]]],[]]]]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)=>([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)=>([(0,2),(2,1)],3) [[[[[],[],[]]]]]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)=>([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)=>([],1) [[[[[],[[]]]]]]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)=>([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)=>([(0,1)],2) [[[[[[]],[]]]]]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)=>([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)=>([(0,1)],2) [[[[[[],[]]]]]]=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)=>([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)=>([],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)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[],[],[],[],[[[]]]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)=>([(0,2),(2,1)],3) [[],[],[],[[[]]],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)=>([(0,2),(2,1)],3) [[],[],[],[[[[]]]]]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8)=>([(0,3),(2,1),(3,2)],4) [[],[],[[]],[[[]]]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[],[],[[[]]],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)=>([(0,2),(2,1)],3) [[],[],[[[]]],[[]]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[],[],[[[[]]]],[]]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8)=>([(0,3),(2,1),(3,2)],4) [[],[[]],[],[[[]]]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[],[[]],[[[]]],[]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[],[[]],[[[[]]]]]=>([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)=>([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) [[],[[[]]],[],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)=>([(0,2),(2,1)],3) [[],[[[]]],[],[[]]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[],[[[]]],[[]],[]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[],[[],[]],[[[]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8)=>([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8)=>([(0,2),(2,1)],3) [[],[[[]]],[[],[]]]=>([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8)=>([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8)=>([(0,2),(2,1)],3) [[],[[[]]],[[[]]]]=>([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8)=>([(0,3),(0,6),(0,7),(4,2),(5,1),(6,4),(7,5)],8)=>([(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) [[],[[[[]]]],[],[]]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8)=>([(0,3),(2,1),(3,2)],4) [[],[[[[]]]],[[]]]=>([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)=>([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) [[],[[],[[[[]]]]]]=>([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)=>([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8)=>([(0,3),(2,1),(3,2)],4) [[],[[[[[]]]],[]]]=>([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)=>([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8)=>([(0,3),(2,1),(3,2)],4) [[[]],[],[],[[[]]]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[]],[],[[[]]],[]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[]],[],[[[[]]]]]=>([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)=>([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) [[[]],[[[]]],[],[]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[]],[[[[]]]],[]]=>([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)=>([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) [[[[]]],[],[],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)=>([(0,2),(2,1)],3) [[[[]]],[],[],[[]]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[[]]],[],[[]],[]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[],[]],[],[[[]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8)=>([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8)=>([(0,2),(2,1)],3) [[[[]]],[],[[],[]]]=>([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8)=>([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8)=>([(0,2),(2,1)],3) [[[[]]],[],[[[]]]]=>([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8)=>([(0,3),(0,6),(0,7),(4,2),(5,1),(6,4),(7,5)],8)=>([(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) [[[[]]],[[]],[],[]]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[[],[]],[[[]]],[]]=>([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8)=>([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8)=>([(0,2),(2,1)],3) [[[[]]],[[],[]],[]]=>([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8)=>([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8)=>([(0,2),(2,1)],3) [[[[]]],[[[]]],[]]=>([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8)=>([(0,3),(0,6),(0,7),(4,2),(5,1),(6,4),(7,5)],8)=>([(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) [[[],[]],[[[[]]]]]=>([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)=>([(0,6),(0,7),(4,5),(5,3),(6,4),(7,1),(7,2)],8)=>([(0,3),(2,1),(3,2)],4) [[[[]]],[[[[]]]]]=>([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)=>([(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) [[[[[]]]],[],[],[]]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8)=>([(0,3),(2,1),(3,2)],4) [[[[[]]]],[],[[]]]=>([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)=>([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) [[[[[]]]],[[]],[]]=>([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)=>([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) [[[[[]]]],[[],[]]]=>([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)=>([(0,6),(0,7),(4,5),(5,3),(6,4),(7,1),(7,2)],8)=>([(0,3),(2,1),(3,2)],4) [[[[[]]]],[[[]]]]=>([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)=>([(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) [[[],[[[[]]]]],[]]=>([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)=>([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8)=>([(0,3),(2,1),(3,2)],4) [[[[[[]]]],[]],[]]=>([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)=>([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8)=>([(0,3),(2,1),(3,2)],4) [[[[],[[[[]]]]]]]=>([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)=>([(0,6),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],8)=>([(0,3),(2,1),(3,2)],4) [[[[[[[]]]],[]]]]=>([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)=>([(0,6),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],8)=>([(0,3),(2,1),(3,2)],4)
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.
Map
dual poset
Description
The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.
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.