Identifier
Values
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>1 [1,0,1,0]=>[1,2]=>[2,1]=>1 [1,1,0,0]=>[2,1]=>[1,2]=>1 [1,0,1,0,1,0]=>[1,2,3]=>[3,2,1]=>2 [1,0,1,1,0,0]=>[1,3,2]=>[2,3,1]=>1 [1,1,0,0,1,0]=>[2,1,3]=>[3,1,2]=>1 [1,1,0,1,0,0]=>[2,3,1]=>[1,3,2]=>1 [1,1,1,0,0,0]=>[3,2,1]=>[1,2,3]=>1 [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[4,3,2,1]=>16 [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[3,4,2,1]=>5 [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[4,2,3,1]=>6 [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,3,1]=>3 [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[2,3,4,1]=>1 [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[4,3,1,2]=>5 [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,4,1,2]=>2 [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[4,1,3,2]=>3 [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[1,4,3,2]=>2 [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[1,3,4,2]=>1 [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[4,1,2,3]=>1 [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[1,4,2,3]=>1 [1,1,1,0,1,0,0,0]=>[4,2,3,1]=>[1,3,2,4]=>1 [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[1,2,3,4]=>1 [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>768 [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[4,5,3,2,1]=>168 [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[5,3,4,2,1]=>216 [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[3,5,4,2,1]=>70 [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,4,5,2,1]=>14 [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[5,4,2,3,1]=>216 [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[4,5,2,3,1]=>56 [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[5,2,4,3,1]=>90 [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,5,4,3,1]=>35 [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[2,4,5,3,1]=>9 [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[5,2,3,4,1]=>20 [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[2,5,3,4,1]=>10 [1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>[2,4,3,5,1]=>4 [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[2,3,4,5,1]=>1 [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[5,4,3,1,2]=>168 [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[4,5,3,1,2]=>42 [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[5,3,4,1,2]=>56 [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,5,4,1,2]=>21 [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[3,4,5,1,2]=>5 [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[5,4,1,3,2]=>70 [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,5,1,3,2]=>21 [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[5,1,4,3,2]=>35 [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[1,5,4,3,2]=>16 [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[1,4,5,3,2]=>5 [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[5,1,3,4,2]=>10 [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[1,5,3,4,2]=>6 [1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>[1,4,3,5,2]=>3 [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[1,3,4,5,2]=>1 [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[5,4,1,2,3]=>14 [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,5,1,2,3]=>5 [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[5,1,4,2,3]=>9 [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[1,5,4,2,3]=>5 [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[1,4,5,2,3]=>2 [1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>[5,1,3,2,4]=>4 [1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>[1,5,3,2,4]=>3 [1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>[1,4,3,2,5]=>2 [1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>[1,3,4,2,5]=>1 [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[5,1,2,3,4]=>1 [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[1,5,2,3,4]=>1 [1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>[1,4,2,3,5]=>1 [1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>[1,2,4,3,5]=>1 [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1 [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>292864 [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>48048 [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>64064 [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>15015 [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>2112 [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>68640 [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>12870 [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>21450 [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>5775 [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>990 [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>3520 [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>1155 [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>288 [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>42 [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>64064 [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>11583 [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>16016 [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>4158 [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>660 [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>21450 [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>4455 [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>7700 [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>2310 [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>450 [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[6,2,4,5,3,1]=>1540 [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>567 [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>162 [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>28 [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>3520 [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>825 [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[6,2,5,3,4,1]=>1540 [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>525 [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>120 [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>448 [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>189 [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>64 [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>[2,4,5,3,6,1]=>14 [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>70 [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>35 [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>[2,5,3,4,6,1]=>15 [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>[2,3,5,4,6,1]=>5 [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>1 [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>48048 [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>8580 [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>11583 [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>2970 [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>462 [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>12870 [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>2640 [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>4455 [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>1320 [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>252 [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>825 [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>300 [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>[3,5,4,6,1,2]=>84 [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>14 [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>15015 [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>2970 [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>4158 [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>1188 [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>210 [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>5775 [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>1320 [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>2310 [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>768 [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>168 [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>525 [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>216 [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>[1,5,4,6,3,2]=>70 [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>14 [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>1155 [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>300 [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>567 [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>216 [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>56 [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>[6,1,4,3,5,2]=>189 [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>[1,6,4,3,5,2]=>90 [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>35 [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>[1,4,5,3,6,2]=>9 [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>35 [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>20 [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>[1,5,3,4,6,2]=>10 [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>[1,3,5,4,6,2]=>4 [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>1 [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>2112 [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>462 [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>660 [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>210 [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>42 [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>990 [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>252 [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>450 [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>168 [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>42 [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>120 [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>56 [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>21 [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>5 [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>288 [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>[5,6,1,3,2,4]=>84 [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>162 [1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>70 [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>21 [1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>64 [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>35 [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>16 [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>[1,4,5,3,2,6]=>5 [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>[6,1,3,4,2,5]=>15 [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>[1,6,3,4,2,5]=>10 [1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>6 [1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>[1,3,5,4,2,6]=>3 [1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>[1,3,4,5,2,6]=>1 [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>42 [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>14 [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>28 [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>14 [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>5 [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>14 [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>9 [1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>5 [1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>2 [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>5 [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>4 [1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>3 [1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>2 [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>[1,2,4,5,3,6]=>1 [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>1 [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>1 [1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>1 [1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>1 [1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>1 [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>1 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>6534528 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>42 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>292864 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[1,6,7,5,4,3,2]=>48048 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>[1,6,5,7,4,3,2]=>15015 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2]=>2112 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2]=>68640 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>[1,7,5,4,6,3,2]=>21450 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>[1,6,5,4,7,3,2]=>5775 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>[1,5,6,4,7,3,2]=>990 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[1,7,4,5,6,3,2]=>3520 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>[1,7,5,4,3,6,2]=>7700 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>[1,6,5,4,3,7,2]=>2310 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>[1,7,4,5,3,6,2]=>1540 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>972400 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>171600 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>50050 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>30030 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>9009 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>462 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4]=>42 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>132 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>42 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5]=>14 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>1 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>1 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[1,7,8,6,5,4,3,2]=>141892608 [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,8,6,7,1]=>[1,7,6,8,5,4,3,2]=>34918884 [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>[1,6,7,8,5,4,3,2]=>3734016 [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,8,5,6,7,1]=>[1,7,6,5,8,4,3,2]=>10720710 [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>[1,7,8,6,5,3,4,2]=>26604864 [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,5,3,4,8,6,7,1]=>[1,7,6,8,4,3,5,2]=>2362932 [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>[1,6,7,8,3,4,5,2]=>50050 [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,8,6,7,1]=>[1,7,6,8,5,4,2,3]=>5105100 [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,8,4,5,6,7,1]=>[1,7,6,5,4,8,2,3]=>640640 [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8,3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3,8]=>2640 [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8,3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3,8]=>14 [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[1,6,7,8,2,3,4,5]=>462 [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>[1,7,8,2,3,4,5,6]=>42 [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8,5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5,8]=>14 [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[8,5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5,8]=>28 [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[8,6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6,8]=>14 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8,7,4,3,6,5,2,1]=>[1,2,5,6,3,4,7,8]=>2 [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>1 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>1 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>1 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>1 []=>[]=>[]=>1 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>1 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>1
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Description
The number of reduced words for a permutation.
This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..