Identifier
Mp00093:
Dyck paths
—to binary word⟶
Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0
[1,0]=>10=>[1,1]=>[1,1]
[1,0,1,0]=>1010=>[1,1,1,1]=>[1,1,1,1]
[1,1,0,0]=>1100=>[2,2]=>[2,2]
[1,0,1,0,1,0]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,0,1,1,0,0]=>101100=>[1,1,2,2]=>[2,2,1,1]
[1,1,0,0,1,0]=>110010=>[2,2,1,1]=>[1,1,2,2]
[1,1,0,1,0,0]=>110100=>[2,1,1,2]=>[2,1,1,2]
[1,1,1,0,0,0]=>111000=>[3,3]=>[3,3]
[1,0,1,0,1,0,1,0]=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0]=>10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[1,0,1,1,0,0,1,0]=>10110010=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]
[1,0,1,1,0,1,0,0]=>10110100=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]
[1,0,1,1,1,0,0,0]=>10111000=>[1,1,3,3]=>[3,3,1,1]
[1,1,0,0,1,0,1,0]=>11001010=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]
[1,1,0,0,1,1,0,0]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[1,1,0,1,0,0,1,0]=>11010010=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]
[1,1,0,1,0,1,0,0]=>11010100=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
[1,1,0,1,1,0,0,0]=>11011000=>[2,1,2,3]=>[3,2,1,2]
[1,1,1,0,0,0,1,0]=>11100010=>[3,3,1,1]=>[1,1,3,3]
[1,1,1,0,0,1,0,0]=>11100100=>[3,2,1,2]=>[2,1,2,3]
[1,1,1,0,1,0,0,0]=>11101000=>[3,1,1,3]=>[3,1,1,3]
[1,1,1,1,0,0,0,0]=>11110000=>[4,4]=>[4,4]
[1,0,1,0,1,0,1,0,1,0]=>1010101010=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0]=>1010101100=>[1,1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0]=>1010110010=>[1,1,1,1,2,2,1,1]=>[1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0]=>1010110100=>[1,1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0]=>1010111000=>[1,1,1,1,3,3]=>[3,3,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0]=>1011001010=>[1,1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0]=>1011001100=>[1,1,2,2,2,2]=>[2,2,2,2,1,1]
[1,0,1,1,0,1,0,0,1,0]=>1011010010=>[1,1,2,1,1,2,1,1]=>[1,1,2,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,0]=>1011010100=>[1,1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1,1]
[1,0,1,1,0,1,1,0,0,0]=>1011011000=>[1,1,2,1,2,3]=>[3,2,1,2,1,1]
[1,0,1,1,1,0,0,0,1,0]=>1011100010=>[1,1,3,3,1,1]=>[1,1,3,3,1,1]
[1,0,1,1,1,0,0,1,0,0]=>1011100100=>[1,1,3,2,1,2]=>[2,1,2,3,1,1]
[1,0,1,1,1,0,1,0,0,0]=>1011101000=>[1,1,3,1,1,3]=>[3,1,1,3,1,1]
[1,0,1,1,1,1,0,0,0,0]=>1011110000=>[1,1,4,4]=>[4,4,1,1]
[1,1,0,0,1,0,1,0,1,0]=>1100101010=>[2,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,1,0,0]=>1100101100=>[2,2,1,1,2,2]=>[2,2,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0]=>1100110010=>[2,2,2,2,1,1]=>[1,1,2,2,2,2]
[1,1,0,0,1,1,0,1,0,0]=>1100110100=>[2,2,2,1,1,2]=>[2,1,1,2,2,2]
[1,1,0,0,1,1,1,0,0,0]=>1100111000=>[2,2,3,3]=>[3,3,2,2]
[1,1,0,1,0,0,1,0,1,0]=>1101001010=>[2,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,1,0,0]=>1101001100=>[2,1,1,2,2,2]=>[2,2,2,1,1,2]
[1,1,0,1,0,1,0,0,1,0]=>1101010010=>[2,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0]=>1101010100=>[2,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,1,0,0,0]=>1101011000=>[2,1,1,1,2,3]=>[3,2,1,1,1,2]
[1,1,0,1,1,0,0,0,1,0]=>1101100010=>[2,1,2,3,1,1]=>[1,1,3,2,1,2]
[1,1,0,1,1,0,0,1,0,0]=>1101100100=>[2,1,2,2,1,2]=>[2,1,2,2,1,2]
[1,1,0,1,1,0,1,0,0,0]=>1101101000=>[2,1,2,1,1,3]=>[3,1,1,2,1,2]
[1,1,0,1,1,1,0,0,0,0]=>1101110000=>[2,1,3,4]=>[4,3,1,2]
[1,1,1,0,0,0,1,0,1,0]=>1110001010=>[3,3,1,1,1,1]=>[1,1,1,1,3,3]
[1,1,1,0,0,0,1,1,0,0]=>1110001100=>[3,3,2,2]=>[2,2,3,3]
[1,1,1,0,0,1,0,0,1,0]=>1110010010=>[3,2,1,2,1,1]=>[1,1,2,1,2,3]
[1,1,1,0,0,1,0,1,0,0]=>1110010100=>[3,2,1,1,1,2]=>[2,1,1,1,2,3]
[1,1,1,0,0,1,1,0,0,0]=>1110011000=>[3,2,2,3]=>[3,2,2,3]
[1,1,1,0,1,0,0,0,1,0]=>1110100010=>[3,1,1,3,1,1]=>[1,1,3,1,1,3]
[1,1,1,0,1,0,0,1,0,0]=>1110100100=>[3,1,1,2,1,2]=>[2,1,2,1,1,3]
[1,1,1,0,1,0,1,0,0,0]=>1110101000=>[3,1,1,1,1,3]=>[3,1,1,1,1,3]
[1,1,1,0,1,1,0,0,0,0]=>1110110000=>[3,1,2,4]=>[4,2,1,3]
[1,1,1,1,0,0,0,0,1,0]=>1111000010=>[4,4,1,1]=>[1,1,4,4]
[1,1,1,1,0,0,0,1,0,0]=>1111000100=>[4,3,1,2]=>[2,1,3,4]
[1,1,1,1,0,0,1,0,0,0]=>1111001000=>[4,2,1,3]=>[3,1,2,4]
[1,1,1,1,0,1,0,0,0,0]=>1111010000=>[4,1,1,4]=>[4,1,1,4]
[1,1,1,1,1,0,0,0,0,0]=>1111100000=>[5,5]=>[5,5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>101010101010=>[1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>101010101100=>[1,1,1,1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>101010110010=>[1,1,1,1,1,1,2,2,1,1]=>[1,1,2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>101010110100=>[1,1,1,1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>101010111000=>[1,1,1,1,1,1,3,3]=>[3,3,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>101011001010=>[1,1,1,1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>101011001100=>[1,1,1,1,2,2,2,2]=>[2,2,2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>101011010010=>[1,1,1,1,2,1,1,2,1,1]=>[1,1,2,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>101011010100=>[1,1,1,1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>101011011000=>[1,1,1,1,2,1,2,3]=>[3,2,1,2,1,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>101011100010=>[1,1,1,1,3,3,1,1]=>[1,1,3,3,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>101011100100=>[1,1,1,1,3,2,1,2]=>[2,1,2,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>101011101000=>[1,1,1,1,3,1,1,3]=>[3,1,1,3,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>101011110000=>[1,1,1,1,4,4]=>[4,4,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>101100101010=>[1,1,2,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>101100101100=>[1,1,2,2,1,1,2,2]=>[2,2,1,1,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>101100110010=>[1,1,2,2,2,2,1,1]=>[1,1,2,2,2,2,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>101100110100=>[1,1,2,2,2,1,1,2]=>[2,1,1,2,2,2,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>101100111000=>[1,1,2,2,3,3]=>[3,3,2,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>101101001010=>[1,1,2,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>101101001100=>[1,1,2,1,1,2,2,2]=>[2,2,2,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>101101010010=>[1,1,2,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>101101010100=>[1,1,2,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>101101011000=>[1,1,2,1,1,1,2,3]=>[3,2,1,1,1,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>101101100010=>[1,1,2,1,2,3,1,1]=>[1,1,3,2,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>101101100100=>[1,1,2,1,2,2,1,2]=>[2,1,2,2,1,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>101101101000=>[1,1,2,1,2,1,1,3]=>[3,1,1,2,1,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>101101110000=>[1,1,2,1,3,4]=>[4,3,1,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>101110001010=>[1,1,3,3,1,1,1,1]=>[1,1,1,1,3,3,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>101110001100=>[1,1,3,3,2,2]=>[2,2,3,3,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>101110010010=>[1,1,3,2,1,2,1,1]=>[1,1,2,1,2,3,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>101110010100=>[1,1,3,2,1,1,1,2]=>[2,1,1,1,2,3,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>101110011000=>[1,1,3,2,2,3]=>[3,2,2,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>101110100010=>[1,1,3,1,1,3,1,1]=>[1,1,3,1,1,3,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>101110100100=>[1,1,3,1,1,2,1,2]=>[2,1,2,1,1,3,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>101110101000=>[1,1,3,1,1,1,1,3]=>[3,1,1,1,1,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>101110110000=>[1,1,3,1,2,4]=>[4,2,1,3,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>101111000010=>[1,1,4,4,1,1]=>[1,1,4,4,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>101111000100=>[1,1,4,3,1,2]=>[2,1,3,4,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>101111001000=>[1,1,4,2,1,3]=>[3,1,2,4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>101111010000=>[1,1,4,1,1,4]=>[4,1,1,4,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>101111100000=>[1,1,5,5]=>[5,5,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>110010101010=>[2,2,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,2,2]
[1,1,0,0,1,0,1,0,1,1,0,0]=>110010101100=>[2,2,1,1,1,1,2,2]=>[2,2,1,1,1,1,2,2]
[1,1,0,0,1,0,1,1,0,0,1,0]=>110010110010=>[2,2,1,1,2,2,1,1]=>[1,1,2,2,1,1,2,2]
[1,1,0,0,1,0,1,1,0,1,0,0]=>110010110100=>[2,2,1,1,2,1,1,2]=>[2,1,1,2,1,1,2,2]
[1,1,0,0,1,0,1,1,1,0,0,0]=>110010111000=>[2,2,1,1,3,3]=>[3,3,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,0]=>110011001010=>[2,2,2,2,1,1,1,1]=>[1,1,1,1,2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0]=>110011001100=>[2,2,2,2,2,2]=>[2,2,2,2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0]=>110011010010=>[2,2,2,1,1,2,1,1]=>[1,1,2,1,1,2,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0]=>110011010100=>[2,2,2,1,1,1,1,2]=>[2,1,1,1,1,2,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0]=>110011011000=>[2,2,2,1,2,3]=>[3,2,1,2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0]=>110011100010=>[2,2,3,3,1,1]=>[1,1,3,3,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0]=>110011100100=>[2,2,3,2,1,2]=>[2,1,2,3,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0]=>110011101000=>[2,2,3,1,1,3]=>[3,1,1,3,2,2]
[1,1,0,0,1,1,1,1,0,0,0,0]=>110011110000=>[2,2,4,4]=>[4,4,2,2]
[1,1,0,1,0,0,1,0,1,0,1,0]=>110100101010=>[2,1,1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0]=>110100101100=>[2,1,1,2,1,1,2,2]=>[2,2,1,1,2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0]=>110100110010=>[2,1,1,2,2,2,1,1]=>[1,1,2,2,2,1,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0]=>110100110100=>[2,1,1,2,2,1,1,2]=>[2,1,1,2,2,1,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0]=>110100111000=>[2,1,1,2,3,3]=>[3,3,2,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0]=>110101001010=>[2,1,1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0]=>110101001100=>[2,1,1,1,1,2,2,2]=>[2,2,2,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0]=>110101010010=>[2,1,1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0]=>110101010100=>[2,1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0]=>110101011000=>[2,1,1,1,1,1,2,3]=>[3,2,1,1,1,1,1,2]
[1,1,0,1,0,1,1,0,0,0,1,0]=>110101100010=>[2,1,1,1,2,3,1,1]=>[1,1,3,2,1,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0]=>110101100100=>[2,1,1,1,2,2,1,2]=>[2,1,2,2,1,1,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0]=>110101101000=>[2,1,1,1,2,1,1,3]=>[3,1,1,2,1,1,1,2]
[1,1,0,1,0,1,1,1,0,0,0,0]=>110101110000=>[2,1,1,1,3,4]=>[4,3,1,1,1,2]
[1,1,0,1,1,0,0,0,1,0,1,0]=>110110001010=>[2,1,2,3,1,1,1,1]=>[1,1,1,1,3,2,1,2]
[1,1,0,1,1,0,0,0,1,1,0,0]=>110110001100=>[2,1,2,3,2,2]=>[2,2,3,2,1,2]
[1,1,0,1,1,0,0,1,0,0,1,0]=>110110010010=>[2,1,2,2,1,2,1,1]=>[1,1,2,1,2,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,0]=>110110010100=>[2,1,2,2,1,1,1,2]=>[2,1,1,1,2,2,1,2]
[1,1,0,1,1,0,0,1,1,0,0,0]=>110110011000=>[2,1,2,2,2,3]=>[3,2,2,2,1,2]
[1,1,0,1,1,0,1,0,0,0,1,0]=>110110100010=>[2,1,2,1,1,3,1,1]=>[1,1,3,1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,0,0]=>110110100100=>[2,1,2,1,1,2,1,2]=>[2,1,2,1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,0,0]=>110110101000=>[2,1,2,1,1,1,1,3]=>[3,1,1,1,1,2,1,2]
[1,1,0,1,1,0,1,1,0,0,0,0]=>110110110000=>[2,1,2,1,2,4]=>[4,2,1,2,1,2]
[1,1,0,1,1,1,0,0,0,0,1,0]=>110111000010=>[2,1,3,4,1,1]=>[1,1,4,3,1,2]
[1,1,0,1,1,1,0,0,0,1,0,0]=>110111000100=>[2,1,3,3,1,2]=>[2,1,3,3,1,2]
[1,1,0,1,1,1,0,0,1,0,0,0]=>110111001000=>[2,1,3,2,1,3]=>[3,1,2,3,1,2]
[1,1,0,1,1,1,0,1,0,0,0,0]=>110111010000=>[2,1,3,1,1,4]=>[4,1,1,3,1,2]
[1,1,0,1,1,1,1,0,0,0,0,0]=>110111100000=>[2,1,4,5]=>[5,4,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0]=>111000101010=>[3,3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3,3]
[1,1,1,0,0,0,1,0,1,1,0,0]=>111000101100=>[3,3,1,1,2,2]=>[2,2,1,1,3,3]
[1,1,1,0,0,0,1,1,0,0,1,0]=>111000110010=>[3,3,2,2,1,1]=>[1,1,2,2,3,3]
[1,1,1,0,0,0,1,1,0,1,0,0]=>111000110100=>[3,3,2,1,1,2]=>[2,1,1,2,3,3]
[1,1,1,0,0,0,1,1,1,0,0,0]=>111000111000=>[3,3,3,3]=>[3,3,3,3]
[1,1,1,0,0,1,0,0,1,0,1,0]=>111001001010=>[3,2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2,3]
[1,1,1,0,0,1,0,0,1,1,0,0]=>111001001100=>[3,2,1,2,2,2]=>[2,2,2,1,2,3]
[1,1,1,0,0,1,0,1,0,0,1,0]=>111001010010=>[3,2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2,3]
[1,1,1,0,0,1,0,1,0,1,0,0]=>111001010100=>[3,2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2,3]
[1,1,1,0,0,1,0,1,1,0,0,0]=>111001011000=>[3,2,1,1,2,3]=>[3,2,1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,0]=>111001100010=>[3,2,2,3,1,1]=>[1,1,3,2,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0]=>111001100100=>[3,2,2,2,1,2]=>[2,1,2,2,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0]=>111001101000=>[3,2,2,1,1,3]=>[3,1,1,2,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0]=>111001110000=>[3,2,3,4]=>[4,3,2,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>111010001010=>[3,1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0]=>111010001100=>[3,1,1,3,2,2]=>[2,2,3,1,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0]=>111010010010=>[3,1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1,3]
[1,1,1,0,1,0,0,1,0,1,0,0]=>111010010100=>[3,1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1,3]
[1,1,1,0,1,0,0,1,1,0,0,0]=>111010011000=>[3,1,1,2,2,3]=>[3,2,2,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,0]=>111010100010=>[3,1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0]=>111010100100=>[3,1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,0]=>111010101000=>[3,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0]=>111010110000=>[3,1,1,1,2,4]=>[4,2,1,1,1,3]
[1,1,1,0,1,1,0,0,0,0,1,0]=>111011000010=>[3,1,2,4,1,1]=>[1,1,4,2,1,3]
[1,1,1,0,1,1,0,0,0,1,0,0]=>111011000100=>[3,1,2,3,1,2]=>[2,1,3,2,1,3]
[1,1,1,0,1,1,0,0,1,0,0,0]=>111011001000=>[3,1,2,2,1,3]=>[3,1,2,2,1,3]
[1,1,1,0,1,1,0,1,0,0,0,0]=>111011010000=>[3,1,2,1,1,4]=>[4,1,1,2,1,3]
[1,1,1,0,1,1,1,0,0,0,0,0]=>111011100000=>[3,1,3,5]=>[5,3,1,3]
[1,1,1,1,0,0,0,0,1,0,1,0]=>111100001010=>[4,4,1,1,1,1]=>[1,1,1,1,4,4]
[1,1,1,1,0,0,0,0,1,1,0,0]=>111100001100=>[4,4,2,2]=>[2,2,4,4]
[1,1,1,1,0,0,0,1,0,0,1,0]=>111100010010=>[4,3,1,2,1,1]=>[1,1,2,1,3,4]
[1,1,1,1,0,0,0,1,0,1,0,0]=>111100010100=>[4,3,1,1,1,2]=>[2,1,1,1,3,4]
[1,1,1,1,0,0,0,1,1,0,0,0]=>111100011000=>[4,3,2,3]=>[3,2,3,4]
[1,1,1,1,0,0,1,0,0,0,1,0]=>111100100010=>[4,2,1,3,1,1]=>[1,1,3,1,2,4]
[1,1,1,1,0,0,1,0,0,1,0,0]=>111100100100=>[4,2,1,2,1,2]=>[2,1,2,1,2,4]
[1,1,1,1,0,0,1,0,1,0,0,0]=>111100101000=>[4,2,1,1,1,3]=>[3,1,1,1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,0]=>111100110000=>[4,2,2,4]=>[4,2,2,4]
[1,1,1,1,0,1,0,0,0,0,1,0]=>111101000010=>[4,1,1,4,1,1]=>[1,1,4,1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0]=>111101000100=>[4,1,1,3,1,2]=>[2,1,3,1,1,4]
[1,1,1,1,0,1,0,0,1,0,0,0]=>111101001000=>[4,1,1,2,1,3]=>[3,1,2,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>111101010000=>[4,1,1,1,1,4]=>[4,1,1,1,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0]=>111101100000=>[4,1,2,5]=>[5,2,1,4]
[1,1,1,1,1,0,0,0,0,0,1,0]=>111110000010=>[5,5,1,1]=>[1,1,5,5]
[1,1,1,1,1,0,0,0,0,1,0,0]=>111110000100=>[5,4,1,2]=>[2,1,4,5]
[1,1,1,1,1,0,0,0,1,0,0,0]=>111110001000=>[5,3,1,3]=>[3,1,3,5]
[1,1,1,1,1,0,0,1,0,0,0,0]=>111110010000=>[5,2,1,4]=>[4,1,2,5]
[1,1,1,1,1,0,1,0,0,0,0,0]=>111110100000=>[5,1,1,5]=>[5,1,1,5]
[1,1,1,1,1,1,0,0,0,0,0,0]=>111111000000=>[6,6]=>[6,6]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>10101011001100=>[1,1,1,1,1,1,2,2,2,2]=>[2,2,2,2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>10101100101100=>[1,1,1,1,2,2,1,1,2,2]=>[2,2,1,1,2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>10101101001100=>[1,1,1,1,2,1,1,2,2,2]=>[2,2,2,1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>10101101100100=>[1,1,1,1,2,1,2,2,1,2]=>[2,1,2,2,1,2,1,1,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>10110011001100=>[1,1,2,2,2,2,2,2]=>[2,2,2,2,2,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>10110100101100=>[1,1,2,1,1,2,1,1,2,2]=>[2,2,1,1,2,1,1,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>10110101001100=>[1,1,2,1,1,1,1,2,2,2]=>[2,2,2,1,1,1,1,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>11001011001100=>[2,2,1,1,2,2,2,2]=>[2,2,2,2,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>11001100101100=>[2,2,2,2,1,1,2,2]=>[2,2,1,1,2,2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>11001101001100=>[2,2,2,1,1,2,2,2]=>[2,2,2,1,1,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>1010101010101010=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[]=>=>[]=>[]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>10101010101010101010=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
Map
to binary word
Description
Return the Dyck word as binary word.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
Map
reverse
Description
Return the reversal of a composition.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
searching the database
Sorry, this map was not found in the database.