Identifier
Mp00230: Integer partitions parallelogram polyominoDyck paths
Mp00025: Dyck paths to 132-avoiding permutationPermutations
Mp00175: Permutations inverse Foata bijectionPermutations
Images
=>
Cc0002;cc-rep-0Cc0005;cc-rep-1
[1]=>[1,0]=>[1]=>[1] [2]=>[1,0,1,0]=>[2,1]=>[2,1] [1,1]=>[1,1,0,0]=>[1,2]=>[1,2] [3]=>[1,0,1,0,1,0]=>[3,2,1]=>[3,2,1] [2,1]=>[1,0,1,1,0,0]=>[2,3,1]=>[2,3,1] [1,1,1]=>[1,1,0,1,0,0]=>[2,1,3]=>[2,1,3] [4]=>[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[4,3,2,1] [3,1]=>[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[3,4,2,1] [2,2]=>[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3] [2,1,1]=>[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[3,2,4,1] [1,1,1,1]=>[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[3,2,1,4] [5]=>[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[5,4,3,2,1] [4,1]=>[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[4,5,3,2,1] [3,2]=>[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[2,3,4,1] [3,1,1]=>[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[4,3,5,2,1] [2,2,1]=>[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[1,3,2,4] [2,1,1,1]=>[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[4,3,2,5,1] [1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[4,3,2,1,5] [6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1] [5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1] [4,2]=>[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[3,4,5,2,1] [4,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1] [3,3]=>[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4] [3,2,1]=>[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[2,4,3,5,1] [3,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1] [2,2,2]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4] [2,2,1,1]=>[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[1,4,3,2,5] [2,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1] [1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6] [7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1] [6,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[6,7,5,4,3,2,1] [5,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1] [5,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1] [4,3]=>[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[3,2,4,5,1] [4,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[3,5,4,6,2,1] [4,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1] [3,3,1]=>[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[2,1,4,3,5] [3,2,2]=>[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[2,3,4,5,1] [3,2,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[2,5,4,3,6,1] [3,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1] [2,2,2,1]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[1,2,4,3,5] [2,2,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[1,5,4,3,2,6] [2,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1] [1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7] [8]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1] [7,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[7,8,6,5,4,3,2,1] [6,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1] [6,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[7,6,8,5,4,3,2,1] [5,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1] [5,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[4,6,5,7,3,2,1] [5,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[7,6,5,8,4,3,2,1] [4,4]=>[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[3,2,1,4,5] [4,3,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[3,2,5,4,6,1] [4,2,2]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1] [4,2,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[3,6,5,4,7,2,1] [4,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[7,6,5,4,8,3,2,1] [3,3,2]=>[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[2,3,1,4,5] [3,3,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[2,1,5,4,3,6] [3,2,2,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[2,3,5,4,6,1] [3,2,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[2,6,5,4,3,7,1] [3,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>[7,6,5,4,3,8,2,1] [2,2,2,2]=>[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5] [2,2,2,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[1,2,5,4,3,6] [2,2,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[1,6,5,4,3,2,7] [2,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[7,6,5,4,3,2,8,1] [1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8] [9]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1] [8,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,2,1]=>[8,9,7,6,5,4,3,2,1] [7,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[6,7,8,5,4,3,2,1] [7,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,2,1]=>[8,7,9,6,5,4,3,2,1] [6,3]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1] [6,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[5,7,6,8,4,3,2,1] [6,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,9,5,4,3,2,1]=>[8,7,6,9,5,4,3,2,1] [5,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1] [5,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[4,3,6,5,7,2,1] [5,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1] [5,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>[4,7,6,5,8,3,2,1] [5,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,4,3,2,1]=>[8,7,6,5,9,4,3,2,1] [4,4,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[3,2,1,5,4,6] [4,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1] [4,3,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[3,2,6,5,4,7,1] [4,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[3,4,6,5,7,2,1] [4,2,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,2,1]=>[3,7,6,5,4,8,2,1] [4,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,3,2,1]=>[8,7,6,5,4,9,3,2,1] [3,3,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5] [3,3,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[2,3,1,5,4,6] [3,3,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[2,1,6,5,4,3,7] [3,2,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1] [3,2,2,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[2,3,6,5,4,7,1] [3,2,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,8,1]=>[2,7,6,5,4,3,8,1] [3,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,2,1]=>[8,7,6,5,4,3,9,2,1] [2,2,2,2,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[2,1,3,5,4,6] [2,2,2,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[1,2,6,5,4,3,7] [2,2,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,2,8]=>[1,7,6,5,4,3,2,8] [2,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[8,7,6,5,4,3,2,9,1] [1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9] [10]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1] [9,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[9,10,8,7,6,5,4,3,2,1] [8,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[7,8,9,6,5,4,3,2,1] [8,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[9,8,10,7,6,5,4,3,2,1] [7,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[6,5,7,8,4,3,2,1] [7,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[8,6,7,9,5,4,3,2,1]=>[6,8,7,9,5,4,3,2,1] [7,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[9,8,7,10,6,5,4,3,2,1] [6,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[5,4,3,6,7,2,1] [6,3,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>[5,4,7,6,8,3,2,1] [6,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[5,6,7,8,4,3,2,1] [6,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[8,7,5,6,9,4,3,2,1]=>[5,8,7,6,9,4,3,2,1] [6,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[9,8,7,6,10,5,4,3,2,1] [5,5]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6] [5,4,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[4,3,2,6,5,7,1] [5,3,2]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[4,5,3,6,7,2,1] [5,3,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,8,2,1]=>[4,3,7,6,5,8,2,1] [5,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[4,5,7,6,8,3,2,1] [5,2,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,5,9,3,2,1]=>[4,8,7,6,5,9,3,2,1] [5,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[9,8,7,6,5,10,4,3,2,1] [4,4,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6] [4,4,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[3,2,1,6,5,4,7] [4,3,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1] [4,3,2,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[3,4,2,6,5,7,1] [4,3,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,8,1]=>[3,2,7,6,5,4,8,1] [4,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[4,3,5,6,7,2,1] [4,2,2,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>[3,4,7,6,5,8,2,1] [4,2,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,3,4,9,2,1]=>[3,8,7,6,5,4,9,2,1] [4,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[9,8,7,6,5,4,10,3,2,1] [3,3,3,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[1,2,3,5,4,6] [3,3,2,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6] [3,3,2,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[2,3,1,6,5,4,7] [3,3,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,1,3,8]=>[2,1,7,6,5,4,3,8] [3,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[3,2,4,6,5,7,1] [3,2,2,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[2,3,7,6,5,4,8,1] [3,2,1,1,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,3,9,1]=>[2,8,7,6,5,4,3,9,1] [3,1,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[9,8,7,6,5,4,3,10,2,1] [2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6] [2,2,2,2,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[2,1,3,6,5,4,7] [2,2,2,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[1,2,7,6,5,4,3,8] [2,2,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,1,2,9]=>[1,8,7,6,5,4,3,2,9] [2,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[9,8,7,6,5,4,3,2,10,1] [1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10] [11]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1] [10,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[10,11,9,8,7,6,5,4,3,2,1] [9,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[8,9,10,7,6,5,4,3,2,1] [9,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,9,11,8,7,6,5,4,3,2,1]=>[10,9,11,8,7,6,5,4,3,2,1] [8,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[7,6,8,9,5,4,3,2,1]=>[7,6,8,9,5,4,3,2,1] [7,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[6,5,4,7,8,3,2,1] [7,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[6,7,8,9,5,4,3,2,1] [6,5]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1] [6,4,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,2,1]=>[5,4,3,7,6,8,2,1] [6,3,2]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[5,6,4,7,8,3,2,1] [5,5,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[4,3,2,1,6,5,7] [5,4,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,7,1] [5,4,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,8,1]=>[4,3,2,7,6,5,8,1] [5,3,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[3,4,5,6,7,2,1] [5,3,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,8,2,1]=>[4,5,3,7,6,8,2,1] [5,3,1,1,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,3,5,9,2,1]=>[4,3,8,7,6,5,9,2,1] [5,2,2,2]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[5,4,6,7,8,3,2,1] [5,2,2,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[8,7,4,5,6,9,3,2,1]=>[4,5,8,7,6,9,3,2,1] [4,4,3]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6] [4,4,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[3,4,2,1,6,5,7] [4,4,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,1,4,8]=>[3,2,1,7,6,5,4,8] [4,3,3,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[2,3,4,6,5,7,1] [4,3,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,7,1] [4,3,2,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,2,5,8,1]=>[3,4,2,7,6,5,8,1] [4,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,6,8,2,1]=>[4,3,5,7,6,8,2,1] [3,3,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[1,3,2,4,5,6] [3,3,3,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[1,2,3,6,5,4,7] [3,3,2,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[3,2,4,1,6,5,7] [3,3,2,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,1,4,8]=>[2,3,1,7,6,5,4,8] [3,3,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,1,3,9]=>[2,1,8,7,6,5,4,3,9] [3,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1] [3,2,2,2,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,8,1]=>[3,2,4,7,6,5,8,1] [2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[3,2,1,4,6,5,7] [2,2,2,2,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,1,3,4,8]=>[2,1,3,7,6,5,4,8] [2,2,2,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,1,2,3,9]=>[1,2,8,7,6,5,4,3,9] [2,2,1,1,1,1,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,1,2,10]=>[1,9,8,7,6,5,4,3,2,10] [2,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[10,9,8,7,6,5,4,3,2,11,1] [1,1,1,1,1,1,1,1,1,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11] [10,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[11,10,12,9,8,7,6,5,4,3,2,1]=>[11,10,12,9,8,7,6,5,4,3,2,1] [9,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[8,7,9,10,6,5,4,3,2,1]=>[8,7,9,10,6,5,4,3,2,1] [8,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[7,8,9,10,6,5,4,3,2,1] [7,5]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[6,5,4,3,7,8,2,1] [6,6]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7] [6,5,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,8,1]=>[5,4,3,2,7,6,8,1] [6,4,2]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,2,1]=>[5,6,4,3,7,8,2,1] [6,4,1,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[8,7,5,4,3,6,9,2,1]=>[5,4,3,8,7,6,9,2,1] [6,3,3]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,8,3,2,1] [6,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,9,4,3,2,1]=>[6,5,7,8,9,4,3,2,1] [5,5,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6,7] [5,5,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>[4,3,2,1,7,6,5,8] [5,4,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,7,1] [5,4,2,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,8,1]=>[4,5,3,2,7,6,8,1] [5,4,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,3,2,5,9,1]=>[4,3,2,8,7,6,5,9,1] [5,3,3,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,2,1]=>[3,4,5,7,6,8,2,1] [5,3,2,2]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,2,1]=>[5,4,6,3,7,8,2,1] [5,3,2,1,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8,7,4,5,3,6,9,2,1]=>[4,5,3,8,7,6,9,2,1] [5,2,2,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[8,5,4,6,7,9,3,2,1]=>[5,4,6,8,7,9,3,2,1] [4,4,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6] [4,4,3,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[2,3,4,1,6,5,7] [4,4,2,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7] [4,4,2,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,2,1,5,8]=>[3,4,2,1,7,6,5,8] [4,4,1,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,3,2,1,4,9]=>[3,2,1,8,7,6,5,4,9] [4,3,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[2,4,3,5,6,7,1] [4,3,3,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,8,1]=>[2,3,4,7,6,5,8,1] [4,3,2,2,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,8,1]=>[4,3,5,2,7,6,8,1] [4,2,2,2,2]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,2,1]=>[5,4,3,6,7,8,2,1] [3,3,3,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6] [3,3,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[1,3,2,4,6,5,7] [3,3,3,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[1,2,3,7,6,5,4,8] [3,3,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7] [3,3,2,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,1,5,8]=>[3,2,4,1,7,6,5,8] [3,3,2,1,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,2,3,1,4,9]=>[2,3,1,8,7,6,5,4,9] [3,3,1,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,2,1,3,10]=>[2,1,9,8,7,6,5,4,3,10] [3,2,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,5,6,8,1]=>[4,3,2,5,7,6,8,1] [2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7] [2,2,2,2,2,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>[3,2,1,4,7,6,5,8] [2,2,2,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,1,2,3,10]=>[1,2,9,8,7,6,5,4,3,10] [2,1,1,1,1,1,1,1,1,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,10,9,8,7,6,5,4,3,2,12,1]=>[11,10,9,8,7,6,5,4,3,2,12,1] [7,6]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[6,5,4,3,2,7,8,1] [7,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[5,6,7,8,9,4,3,2,1] [6,6,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1,6,8]=>[5,4,3,2,1,7,6,8] [6,4,3]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,2,1]=>[4,5,6,3,7,8,2,1] [5,5,3]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7] [5,5,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,1,6,8]=>[4,5,3,2,1,7,6,8] [5,5,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,3,2,1,5,9]=>[4,3,2,1,8,7,6,5,9] [5,4,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1] [5,4,3,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,6,8,1]=>[3,4,5,2,7,6,8,1] [5,4,2,2]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,8,1]=>[5,4,6,3,2,7,8,1] [5,4,2,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[8,7,4,5,3,2,6,9,1]=>[4,5,3,2,8,7,6,9,1] [5,3,3,2]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,2,1]=>[3,5,4,6,7,8,2,1] [5,3,3,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[8,7,3,4,5,6,9,2,1]=>[3,4,5,8,7,6,9,2,1] [5,3,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[8,5,4,6,3,7,9,2,1]=>[5,4,6,3,8,7,9,2,1] [4,4,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[2,1,3,4,6,5,7] [4,4,3,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[2,4,3,5,1,6,7] [4,4,3,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,1,5,8]=>[2,3,4,1,7,6,5,8] [4,4,2,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,1,6,8]=>[4,3,5,2,1,7,6,8] [4,4,2,1,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[8,7,6,3,4,2,1,5,9]=>[3,4,2,1,8,7,6,5,9] [4,4,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,3,2,1,4,10]=>[3,2,1,9,8,7,6,5,4,10] [4,3,3,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1] [4,3,3,2,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,8,1]=>[2,4,3,5,7,6,8,1] [4,3,2,2,2]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>[5,4,3,6,2,7,8,1] [3,3,3,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[1,2,3,4,6,5,7] [3,3,3,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[1,4,3,2,5,6,7] [3,3,3,2,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,1,2,4,5,8]=>[1,3,2,4,7,6,5,8] [3,3,3,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,1,2,3,4,9]=>[1,2,3,8,7,6,5,4,9] [3,3,2,2,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,5,1,6,8]=>[4,3,2,5,1,7,6,8] [3,3,1,1,1,1,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,2,1,3,11]=>[2,1,10,9,8,7,6,5,4,3,11] [3,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,8,1] [2,2,2,2,2,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[4,3,2,1,5,7,6,8] [8,3,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[6,7,8,9,10,5,4,3,2,1] [7,7]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8] [7,6,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,7,9,1]=>[6,5,4,3,2,8,7,9,1] [6,6,2]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>[5,6,4,3,2,1,7,8] [6,6,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[8,7,5,4,3,2,1,6,9]=>[5,4,3,2,1,8,7,6,9] [6,5,3]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,7,8,1]=>[4,5,6,3,2,7,8,1] [6,4,4]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,2,1]=>[4,3,5,6,7,8,2,1] [5,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7] [5,5,3,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,1,6,8]=>[3,4,5,2,1,7,6,8] [5,5,2,2]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>[5,4,6,3,2,1,7,8] [5,5,2,1,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[8,7,4,5,3,2,1,6,9]=>[4,5,3,2,1,8,7,6,9] [5,5,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,4,3,2,1,5,10]=>[4,3,2,1,9,8,7,6,5,10] [5,4,4,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,6,8,1]=>[3,2,4,5,7,6,8,1] [5,4,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,7,8,1]=>[3,5,4,6,2,7,8,1] [5,4,3,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[8,7,3,4,5,2,6,9,1]=>[3,4,5,2,8,7,6,9,1] [5,4,2,2,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[8,5,4,6,3,2,7,9,1]=>[5,4,6,3,2,8,7,9,1] [5,3,3,3]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1]=>[3,4,5,6,7,8,2,1] [5,3,3,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[8,5,3,4,6,7,9,2,1]=>[3,5,4,6,8,7,9,2,1] [4,4,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[2,1,4,3,5,6,7] [4,4,3,3]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7] [4,4,3,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,1,6,8]=>[2,4,3,5,1,7,6,8] [4,4,2,2,2]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,1,7,8]=>[5,4,3,6,2,1,7,8] [4,4,1,1,1,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,3,2,1,4,11]=>[3,2,1,10,9,8,7,6,5,4,11] [4,3,3,3,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,8,1]=>[2,3,4,5,7,6,8,1] [4,3,3,2,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,8,1]=>[2,5,4,3,6,7,8,1] [3,3,3,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[1,2,4,3,5,6,7] [3,3,3,3,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,2,3,4,5,8]=>[1,2,3,4,7,6,5,8] [3,3,3,2,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,1,2,5,6,8]=>[1,4,3,2,5,7,6,8] [3,3,3,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,1,2,3,4,10]=>[1,2,3,9,8,7,6,5,4,10] [3,3,2,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[5,4,3,2,6,1,7,8] [2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8] [8,7]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,9,1]=>[7,6,5,4,3,2,8,9,1] [7,7,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,1,7,9]=>[6,5,4,3,2,1,8,7,9] [7,4,4]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,9,3,2,1]=>[5,4,6,7,8,9,3,2,1] [6,6,3]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[4,5,6,3,2,1,7,8] [6,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,6,4,3,2,1,7,9]=>[5,6,4,3,2,1,8,7,9] [6,6,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,8,7,5,4,3,2,1,6,10]=>[5,4,3,2,1,9,8,7,6,10] [6,5,4]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,8,1]=>[4,3,5,6,2,7,8,1] [6,3,3,3]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[4,5,6,7,8,9,3,2,1] [5,5,5]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7] [5,5,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,1,6,8]=>[3,2,4,5,1,7,6,8] [5,5,3,2]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,1,7,8]=>[3,5,4,6,2,1,7,8] [5,4,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,7,8,1]=>[3,2,5,4,6,7,8,1] [5,4,3,3]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[3,4,5,6,2,7,8,1] [5,4,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[8,5,3,4,6,2,7,9,1]=>[3,5,4,6,2,8,7,9,1] [4,4,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7] [4,4,4,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,1,3,5,6,8]=>[2,1,4,3,5,7,6,8] [4,4,3,3,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[2,3,4,5,1,7,6,8] [4,4,3,2,2]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,1,7,8]=>[2,5,4,3,6,1,7,8] [4,3,3,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>[2,3,5,4,6,7,8,1] [3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7] [3,3,3,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[7,4,1,2,3,5,6,8]=>[1,2,4,3,5,7,6,8] [3,3,3,3,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[8,7,6,1,2,3,4,5,9]=>[1,2,3,4,8,7,6,5,9] [3,3,3,2,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[1,5,4,3,2,6,7,8] [3,2,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,7,8,9,1]=>[6,5,4,3,2,7,8,9,1] [8,8]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9] [8,4,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,10,4,3,2,1]=>[6,5,7,8,9,10,4,3,2,1] [7,7,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,5,4,3,2,1,8,9]=>[6,7,5,4,3,2,1,8,9] [7,7,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,8,6,5,4,3,2,1,7,10]=>[6,5,4,3,2,1,9,8,7,10] [7,3,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[5,6,7,8,9,10,4,3,2,1] [6,6,4]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,1,7,8]=>[4,3,5,6,2,1,7,8] [6,6,1,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,5,4,3,2,1,6,11]=>[5,4,3,2,1,10,9,8,7,6,11] [6,5,5]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[4,3,2,5,6,7,8,1] [5,5,5,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,1,4,5,6,8]=>[3,2,1,4,5,7,6,8] [5,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,1,7,8]=>[3,2,5,4,6,1,7,8] [5,5,3,3]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[3,4,5,6,2,1,7,8] [5,4,4,3]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>[3,4,2,5,6,7,8,1] [4,4,4,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7] [4,4,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,1,4,5,6,8]=>[2,3,1,4,5,7,6,8] [4,4,4,2,2]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[2,1,5,4,3,6,7,8] [4,4,3,3,2]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,1,7,8]=>[2,3,5,4,6,1,7,8] [4,3,3,3,3]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[3,2,4,5,6,7,8,1] [4,3,3,2,2,2]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,2,3,7,8,9,1]=>[2,6,5,4,3,7,8,9,1] [3,3,3,3,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,3,4,5,6,8]=>[2,1,3,4,5,7,6,8] [3,3,3,3,2,2]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[1,2,5,4,3,6,7,8] [3,3,3,3,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,1,2,3,4,5,10]=>[1,2,3,4,9,8,7,6,5,10] [3,3,2,2,2,2,2]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,7,1,8,9]=>[6,5,4,3,2,7,1,8,9] [2,2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9] [9,8]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,9,10,1]=>[8,7,6,5,4,3,2,9,10,1] [8,8,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,7,6,5,4,3,2,1,8,10]=>[7,6,5,4,3,2,1,9,8,10] [7,7,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[10,9,8,6,5,4,3,2,1,7,11]=>[6,5,4,3,2,1,10,9,8,7,11] [7,5,5]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,6,7,8,9,2,1]=>[5,4,3,6,7,8,9,2,1] [6,6,5]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,1,7,8]=>[4,3,2,5,6,1,7,8] [6,4,4,3]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[4,5,3,6,7,8,9,2,1]=>[4,5,3,6,7,8,9,2,1] [5,5,5,2]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[3,2,1,5,4,6,7,8] [5,5,4,3]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,1,7,8]=>[3,4,2,5,6,1,7,8] [5,4,4,4]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,1] [5,3,3,3,3]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,6,7,8,9,2,1]=>[4,3,5,6,7,8,9,2,1] [4,4,4,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,7,6,8] [4,4,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[2,3,1,5,4,6,7,8] [4,4,3,3,3]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,1,7,8]=>[3,2,4,5,6,1,7,8] [3,3,3,3,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[2,1,3,5,4,6,7,8] [3,3,3,2,2,2,2]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,1,2,7,8,9]=>[1,6,5,4,3,2,7,8,9] [3,2,2,2,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,8,9,10,1]=>[7,6,5,4,3,2,8,9,10,1] []=>[]=>[]=>[] [6,5,4,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[9,6,4,3,5,7,2,8,10,1]=>[4,3,6,5,7,2,9,8,10,1] [6,5,4,3,3,2,1]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[11,8,5,4,6,3,7,9,2,10,12,1]=>[5,4,6,3,8,7,9,2,11,10,12,1] [4,4,4,4,3,1]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[8,3,1,2,4,5,6,7,9]=>[1,3,2,4,5,6,8,7,9] [5,4,4,4,3]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,9,1]=>[2,4,3,5,6,7,8,9,1] [7,3,3,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,5,7,8,9,10,11,4,3,2,1]=>[6,5,7,8,9,10,11,4,3,2,1] [4,4,4,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[1,2,3,5,4,6,7,8] [6,5,5,4]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,9,1]=>[3,4,5,2,6,7,8,9,1] [2,2,2,2,2,2,2,2,2]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10] [3,3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8] [3,3,3,3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10] [3,3,3,3,3,3,1]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[8,3,2,1,4,5,6,7,9]=>[3,2,1,4,5,6,8,7,9] [3,3,3,3,3,3,3]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9] [4,3,3,3,3,3]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,5,6,7,8,9,1]=>[4,3,2,5,6,7,8,9,1] [4,4,4,4,4]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8] [4,4,4,3,3,3]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,5,1,6,7,8,9]=>[4,3,2,5,1,6,7,8,9] [4,4,4,4,4,4]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9] [5,5,5,5]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8] [6,6,6,6]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9] [6,6,6]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8] [7,6,6]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,6,7,8,9,1]=>[5,4,3,2,6,7,8,9,1] [10,10]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,4,3,2,1,10,11]=>[9,8,7,6,5,4,3,2,1,10,11] [6,6,6,6,6]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10] [5,5,5,5,5,5]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10] [7,7,7,7]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10] [7,7,7]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9] [5,5,5,5,5]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9] [9,9]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10] [8,8,8]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10] [4,4,4,4,4,4,4]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10] [6,5,5,5]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,1]=>[3,2,4,5,6,7,8,9,1] [5,4,4,4,4]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,9,1] [4,4,4,4,4,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,8,7,9] [5,5,5,5,1]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1,3,4,5,6,7,9]=>[2,1,3,4,5,6,8,7,9]
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.