Identifier
Values
=>
Cc0020;cc-rep-2 Cc0029;cc-rep
[1]=>[1]=>([],1)=>([],1)=>1 [1,2]=>[1,2]=>([],2)=>([],1)=>1 [2,1]=>[2,1]=>([(0,1)],2)=>([(0,1)],2)=>1 [1,2,3]=>[1,2,3]=>([],3)=>([],1)=>1 [1,3,2]=>[1,3,2]=>([(1,2)],3)=>([(0,1)],2)=>1 [2,1,3]=>[2,1,3]=>([(1,2)],3)=>([(0,1)],2)=>1 [2,3,1]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,3,4]=>[1,2,3,4]=>([],4)=>([],1)=>1 [1,2,4,3]=>[1,2,4,3]=>([(2,3)],4)=>([(0,1)],2)=>1 [1,3,2,4]=>[1,3,2,4]=>([(2,3)],4)=>([(0,1)],2)=>1 [1,3,4,2]=>[1,4,3,2]=>([(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [1,4,2,3]=>[1,4,2,3]=>([(1,3),(2,3)],4)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,4,3,2]=>[1,3,4,2]=>([(1,3),(2,3)],4)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)=>([(0,1)],2)=>1 [2,1,4,3]=>[2,1,4,3]=>([(0,3),(1,2)],4)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [2,3,1,4]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>([(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)=>1 [4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>([(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)=>1 [4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)=>([(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)=>1 [4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)=>([(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)=>1 [1,2,3,4,5]=>[1,2,3,4,5]=>([],5)=>([],1)=>1 [1,2,3,5,4]=>[1,2,3,5,4]=>([(3,4)],5)=>([(0,1)],2)=>1 [1,2,4,3,5]=>[1,2,4,3,5]=>([(3,4)],5)=>([(0,1)],2)=>1 [1,2,4,5,3]=>[1,2,5,4,3]=>([(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [1,2,5,3,4]=>[1,2,5,3,4]=>([(2,4),(3,4)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,5,4,3]=>[1,2,4,5,3]=>([(2,4),(3,4)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,3,2,4,5]=>[1,3,2,4,5]=>([(3,4)],5)=>([(0,1)],2)=>1 [1,3,2,5,4]=>[1,3,2,5,4]=>([(1,4),(2,3)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,3,4,2,5]=>[1,4,3,2,5]=>([(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [1,4,2,3,5]=>[1,4,2,3,5]=>([(2,4),(3,4)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,4,3,2,5]=>[1,3,4,2,5]=>([(2,4),(3,4)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,5,2,3,4]=>[1,5,2,3,4]=>([(1,4),(2,4),(3,4)],5)=>([(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)=>1 [1,5,3,2,4]=>[1,3,5,2,4]=>([(1,4),(2,3),(3,4)],5)=>([(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)=>1 [1,5,4,2,3]=>[1,4,2,5,3]=>([(1,4),(2,3),(3,4)],5)=>([(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)=>1 [1,5,4,3,2]=>[1,3,4,5,2]=>([(1,4),(2,4),(3,4)],5)=>([(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)=>1 [2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)=>([(0,1)],2)=>1 [2,1,3,5,4]=>[2,1,3,5,4]=>([(1,4),(2,3)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [2,1,4,3,5]=>[2,1,4,3,5]=>([(1,4),(2,3)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [2,1,5,3,4]=>[2,1,5,3,4]=>([(0,1),(2,4),(3,4)],5)=>([(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)=>1 [2,1,5,4,3]=>[2,1,4,5,3]=>([(0,1),(2,4),(3,4)],5)=>([(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)=>1 [2,3,1,4,5]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [3,1,2,5,4]=>[3,1,2,5,4]=>([(0,1),(2,4),(3,4)],5)=>([(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)=>1 [3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [3,2,1,5,4]=>[2,3,1,5,4]=>([(0,1),(2,4),(3,4)],5)=>([(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)=>1 [4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>([(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)=>1 [4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>([(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)=>1 [4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)=>([(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)=>1 [4,3,2,1,5]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)=>([(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)=>1 [1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)=>([],1)=>1 [1,2,3,4,6,5]=>[1,2,3,4,6,5]=>([(4,5)],6)=>([(0,1)],2)=>1 [1,2,3,5,4,6]=>[1,2,3,5,4,6]=>([(4,5)],6)=>([(0,1)],2)=>1 [1,2,3,5,6,4]=>[1,2,3,6,5,4]=>([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [1,2,3,6,4,5]=>[1,2,3,6,4,5]=>([(3,5),(4,5)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,3,6,5,4]=>[1,2,3,5,6,4]=>([(3,5),(4,5)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,4,3,5,6]=>[1,2,4,3,5,6]=>([(4,5)],6)=>([(0,1)],2)=>1 [1,2,4,3,6,5]=>[1,2,4,3,6,5]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,4,5,3,6]=>[1,2,5,4,3,6]=>([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [1,2,5,3,4,6]=>[1,2,5,3,4,6]=>([(3,5),(4,5)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,5,4,3,6]=>[1,2,4,5,3,6]=>([(3,5),(4,5)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,6,3,4,5]=>[1,2,6,3,4,5]=>([(2,5),(3,5),(4,5)],6)=>([(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)=>1 [1,2,6,4,3,5]=>[1,2,4,6,3,5]=>([(2,5),(3,4),(4,5)],6)=>([(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)=>1 [1,2,6,5,3,4]=>[1,2,5,3,6,4]=>([(2,5),(3,4),(4,5)],6)=>([(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)=>1 [1,2,6,5,4,3]=>[1,2,4,5,6,3]=>([(2,5),(3,5),(4,5)],6)=>([(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)=>1 [1,3,2,4,5,6]=>[1,3,2,4,5,6]=>([(4,5)],6)=>([(0,1)],2)=>1 [1,3,2,4,6,5]=>[1,3,2,4,6,5]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,3,2,5,4,6]=>[1,3,2,5,4,6]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,3,2,6,4,5]=>[1,3,2,6,4,5]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [1,3,2,6,5,4]=>[1,3,2,5,6,4]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [1,3,4,2,5,6]=>[1,4,3,2,5,6]=>([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [1,4,2,3,5,6]=>[1,4,2,3,5,6]=>([(3,5),(4,5)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,4,2,3,6,5]=>[1,4,2,3,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [1,4,3,2,5,6]=>[1,3,4,2,5,6]=>([(3,5),(4,5)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,4,3,2,6,5]=>[1,3,4,2,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [1,5,2,3,4,6]=>[1,5,2,3,4,6]=>([(2,5),(3,5),(4,5)],6)=>([(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)=>1 [1,5,3,2,4,6]=>[1,3,5,2,4,6]=>([(2,5),(3,4),(4,5)],6)=>([(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)=>1 [1,5,4,2,3,6]=>[1,4,2,5,3,6]=>([(2,5),(3,4),(4,5)],6)=>([(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)=>1 [1,5,4,3,2,6]=>[1,3,4,5,2,6]=>([(2,5),(3,5),(4,5)],6)=>([(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)=>1 [2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)=>([(0,1)],2)=>1 [2,1,3,4,6,5]=>[2,1,3,4,6,5]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [2,1,3,5,4,6]=>[2,1,3,5,4,6]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [2,1,3,6,4,5]=>[2,1,3,6,4,5]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [2,1,3,6,5,4]=>[2,1,3,5,6,4]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [2,1,4,3,5,6]=>[2,1,4,3,5,6]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [2,1,4,3,6,5]=>[2,1,4,3,6,5]=>([(0,5),(1,4),(2,3)],6)=>([(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)=>1 [2,1,5,3,4,6]=>[2,1,5,3,4,6]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [2,1,5,4,3,6]=>[2,1,4,5,3,6]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [2,3,1,4,5,6]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [3,1,2,4,6,5]=>[3,1,2,4,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [3,1,2,5,4,6]=>[3,1,2,5,4,6]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [3,2,1,4,6,5]=>[2,3,1,4,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [3,2,1,5,4,6]=>[2,3,1,5,4,6]=>([(1,2),(3,5),(4,5)],6)=>([(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)=>1 [4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>([(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)=>1 [4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)=>([(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)=>1 [4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6)=>([(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)=>1 [4,3,2,1,5,6]=>[2,3,4,1,5,6]=>([(2,5),(3,5),(4,5)],6)=>([(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)=>1 [1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)=>([],1)=>1 [1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>([(5,6)],7)=>([(0,1)],2)=>1 [1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>([(5,6)],7)=>([(0,1)],2)=>1 [1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>([(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>([(4,6),(5,6)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>([(4,6),(5,6)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>([(5,6)],7)=>([(0,1)],2)=>1 [1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>([(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>([(4,6),(5,6)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>([(4,6),(5,6)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>([(3,6),(4,6),(5,6)],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)=>1 [1,2,3,7,5,4,6]=>[1,2,3,5,7,4,6]=>([(3,6),(4,5),(5,6)],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)=>1 [1,2,3,7,6,4,5]=>[1,2,3,6,4,7,5]=>([(3,6),(4,5),(5,6)],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)=>1 [1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]=>([(3,6),(4,6),(5,6)],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)=>1 [1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>([(5,6)],7)=>([(0,1)],2)=>1 [1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>([(2,3),(4,6),(5,6)],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)=>1 [1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>([(2,3),(4,6),(5,6)],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)=>1 [1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>([(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>([(4,6),(5,6)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>([(2,3),(4,6),(5,6)],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)=>1 [1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>([(4,6),(5,6)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>([(2,3),(4,6),(5,6)],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)=>1 [1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>([(3,6),(4,6),(5,6)],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)=>1 [1,2,6,4,3,5,7]=>[1,2,4,6,3,5,7]=>([(3,6),(4,5),(5,6)],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)=>1 [1,2,6,5,3,4,7]=>[1,2,5,3,6,4,7]=>([(3,6),(4,5),(5,6)],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)=>1 [1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]=>([(3,6),(4,6),(5,6)],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)=>1 [1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>([(5,6)],7)=>([(0,1)],2)=>1 [1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>([(2,3),(4,6),(5,6)],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)=>1 [1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>([(2,3),(4,6),(5,6)],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)=>1 [1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>([(1,6),(2,5),(3,4)],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)=>1 [1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>([(2,3),(4,6),(5,6)],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)=>1 [1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>([(2,3),(4,6),(5,6)],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)=>1 [1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>([(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>([(4,6),(5,6)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>([(2,3),(4,6),(5,6)],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)=>1 [1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>([(2,3),(4,6),(5,6)],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)=>1 [1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>([(4,6),(5,6)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>([(2,3),(4,6),(5,6)],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)=>1 [1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>([(2,3),(4,6),(5,6)],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)=>1 [1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>([(3,6),(4,6),(5,6)],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)=>1 [1,5,3,2,4,6,7]=>[1,3,5,2,4,6,7]=>([(3,6),(4,5),(5,6)],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)=>1 [1,5,4,2,3,6,7]=>[1,4,2,5,3,6,7]=>([(3,6),(4,5),(5,6)],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)=>1 [1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]=>([(3,6),(4,6),(5,6)],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)=>1 [2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(5,6)],7)=>([(0,1)],2)=>1 [2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>([(2,3),(4,6),(5,6)],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)=>1 [2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>([(2,3),(4,6),(5,6)],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)=>1 [2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>([(1,6),(2,5),(3,4)],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)=>1 [2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>([(2,3),(4,6),(5,6)],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)=>1 [2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>([(2,3),(4,6),(5,6)],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)=>1 [2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>([(1,6),(2,5),(3,4)],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)=>1 [2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>([(1,6),(2,5),(3,4)],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)=>1 [2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>([(2,3),(4,6),(5,6)],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)=>1 [2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>([(2,3),(4,6),(5,6)],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)=>1 [2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>([(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1 [3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>([(2,3),(4,6),(5,6)],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)=>1 [3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>([(2,3),(4,6),(5,6)],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)=>1 [3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>([(2,3),(4,6),(5,6)],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)=>1 [3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>([(4,6),(5,6)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>1 [3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>([(2,3),(4,6),(5,6)],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)=>1 [3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>([(2,3),(4,6),(5,6)],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)=>1 [3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>([(2,3),(4,6),(5,6)],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)=>1 [4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],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)=>1 [4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>([(3,6),(4,5),(5,6)],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)=>1 [4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>([(3,6),(4,5),(5,6)],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)=>1 [4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>([(3,6),(4,6),(5,6)],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)=>1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of shortest chains of small intervals from the bottom to the top in a lattice.
An interval $[a, b]$ in a lattice is small if $b$ is a join of elements covering $a$.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
connected vertex partitions
Description
Sends a graph to the lattice of its connected vertex partitions.
A connected vertex partition of a graph $G = (V,E)$ is a set partition of $V$ such that each part induced a connected subgraph of $G$. The connected vertex partitions of $G$ form a lattice under refinement. If $G = K_n$ is a complete graph, the resulting lattice is the lattice of set partitions on $n$ elements.
In the language of matroid theory, this map sends a graph to the lattice of flats of its graphic matroid. The resulting lattice is a geometric lattice, i.e. it is atomistic and semimodular.