Identifier
Mp00095:
Integer partitions
—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
=>
Cc0002;cc-rep-0
[1]=>10=>[1,1]=>[1,1]
[2]=>100=>[1,2]=>[2,1]
[1,1]=>110=>[2,1]=>[1,2]
[3]=>1000=>[1,3]=>[3,1]
[2,1]=>1010=>[1,1,1,1]=>[1,1,1,1]
[1,1,1]=>1110=>[3,1]=>[1,3]
[4]=>10000=>[1,4]=>[4,1]
[3,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[2,2]=>1100=>[2,2]=>[2,2]
[2,1,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[1,1,1,1]=>11110=>[4,1]=>[1,4]
[5]=>100000=>[1,5]=>[5,1]
[4,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[3,1,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,2,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[2,1,1,1]=>101110=>[1,1,3,1]=>[1,3,1,1]
[1,1,1,1,1]=>111110=>[5,1]=>[1,5]
[6]=>1000000=>[1,6]=>[6,1]
[5,1]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[4,2]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,1,1]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[3,3]=>11000=>[2,3]=>[3,2]
[3,2,1]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,1,1]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[2,2,2]=>11100=>[3,2]=>[2,3]
[2,2,1,1]=>110110=>[2,1,2,1]=>[1,2,1,2]
[2,1,1,1,1]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[1,1,1,1,1,1]=>1111110=>[6,1]=>[1,6]
[7]=>10000000=>[1,7]=>[7,1]
[6,1]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[5,2]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[5,1,1]=>10000110=>[1,4,2,1]=>[1,2,4,1]
[4,3]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,2,1]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,1,1,1]=>10001110=>[1,3,3,1]=>[1,3,3,1]
[3,3,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[3,2,2]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,2,1,1]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,1,1,1,1]=>10011110=>[1,2,4,1]=>[1,4,2,1]
[2,2,2,1]=>111010=>[3,1,1,1]=>[1,1,1,3]
[2,2,1,1,1]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[2,1,1,1,1,1]=>10111110=>[1,1,5,1]=>[1,5,1,1]
[1,1,1,1,1,1,1]=>11111110=>[7,1]=>[1,7]
[8]=>100000000=>[1,8]=>[8,1]
[7,1]=>100000010=>[1,6,1,1]=>[1,1,6,1]
[6,2]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[6,1,1]=>100000110=>[1,5,2,1]=>[1,2,5,1]
[5,3]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,2,1]=>10001010=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]
[5,1,1,1]=>100001110=>[1,4,3,1]=>[1,3,4,1]
[4,4]=>110000=>[2,4]=>[4,2]
[4,3,1]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,2]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,2,1,1]=>10010110=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]
[4,1,1,1,1]=>100011110=>[1,3,4,1]=>[1,4,3,1]
[3,3,2]=>110100=>[2,1,1,2]=>[2,1,1,2]
[3,3,1,1]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,2,2,1]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,2,1,1,1]=>10101110=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]
[3,1,1,1,1,1]=>100111110=>[1,2,5,1]=>[1,5,2,1]
[2,2,2,2]=>111100=>[4,2]=>[2,4]
[2,2,2,1,1]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[2,2,1,1,1,1]=>11011110=>[2,1,4,1]=>[1,4,1,2]
[2,1,1,1,1,1,1]=>101111110=>[1,1,6,1]=>[1,6,1,1]
[1,1,1,1,1,1,1,1]=>111111110=>[8,1]=>[1,8]
[9]=>1000000000=>[1,9]=>[9,1]
[8,1]=>1000000010=>[1,7,1,1]=>[1,1,7,1]
[7,2]=>100000100=>[1,5,1,2]=>[2,1,5,1]
[7,1,1]=>1000000110=>[1,6,2,1]=>[1,2,6,1]
[6,3]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[6,2,1]=>100001010=>[1,4,1,1,1,1]=>[1,1,1,1,4,1]
[6,1,1,1]=>1000001110=>[1,5,3,1]=>[1,3,5,1]
[5,4]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,3,1]=>10010010=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
[5,2,2]=>10001100=>[1,3,2,2]=>[2,2,3,1]
[5,2,1,1]=>100010110=>[1,3,1,1,2,1]=>[1,2,1,1,3,1]
[5,1,1,1,1]=>1000011110=>[1,4,4,1]=>[1,4,4,1]
[4,4,1]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[4,3,2]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,1,1]=>10100110=>[1,1,1,2,2,1]=>[1,2,2,1,1,1]
[4,2,2,1]=>10011010=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]
[4,2,1,1,1]=>100101110=>[1,2,1,1,3,1]=>[1,3,1,1,2,1]
[4,1,1,1,1,1]=>1000111110=>[1,3,5,1]=>[1,5,3,1]
[3,3,3]=>111000=>[3,3]=>[3,3]
[3,3,2,1]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,3,1,1,1]=>11001110=>[2,2,3,1]=>[1,3,2,2]
[3,2,2,2]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[3,2,2,1,1]=>10110110=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]
[3,2,1,1,1,1]=>101011110=>[1,1,1,1,4,1]=>[1,4,1,1,1,1]
[3,1,1,1,1,1,1]=>1001111110=>[1,2,6,1]=>[1,6,2,1]
[2,2,2,2,1]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[2,2,2,1,1,1]=>11101110=>[3,1,3,1]=>[1,3,1,3]
[2,2,1,1,1,1,1]=>110111110=>[2,1,5,1]=>[1,5,1,2]
[2,1,1,1,1,1,1,1]=>1011111110=>[1,1,7,1]=>[1,7,1,1]
[1,1,1,1,1,1,1,1,1]=>1111111110=>[9,1]=>[1,9]
[10]=>10000000000=>[1,10]=>[10,1]
[9,1]=>10000000010=>[1,8,1,1]=>[1,1,8,1]
[8,2]=>1000000100=>[1,6,1,2]=>[2,1,6,1]
[8,1,1]=>10000000110=>[1,7,2,1]=>[1,2,7,1]
[7,3]=>100001000=>[1,4,1,3]=>[3,1,4,1]
[7,2,1]=>1000001010=>[1,5,1,1,1,1]=>[1,1,1,1,5,1]
[7,1,1,1]=>10000001110=>[1,6,3,1]=>[1,3,6,1]
[6,4]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[6,3,1]=>100010010=>[1,3,1,2,1,1]=>[1,1,2,1,3,1]
[6,2,2]=>100001100=>[1,4,2,2]=>[2,2,4,1]
[6,2,1,1]=>1000010110=>[1,4,1,1,2,1]=>[1,2,1,1,4,1]
[6,1,1,1,1]=>10000011110=>[1,5,4,1]=>[1,4,5,1]
[5,5]=>1100000=>[2,5]=>[5,2]
[5,4,1]=>10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
[5,3,2]=>10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
[5,3,1,1]=>100100110=>[1,2,1,2,2,1]=>[1,2,2,1,2,1]
[5,2,2,1]=>100011010=>[1,3,2,1,1,1]=>[1,1,1,2,3,1]
[5,2,1,1,1]=>1000101110=>[1,3,1,1,3,1]=>[1,3,1,1,3,1]
[5,1,1,1,1,1]=>10000111110=>[1,4,5,1]=>[1,5,4,1]
[4,4,2]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,4,1,1]=>11000110=>[2,3,2,1]=>[1,2,3,2]
[4,3,3]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,3,2,1]=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[4,3,1,1,1]=>101001110=>[1,1,1,2,3,1]=>[1,3,2,1,1,1]
[4,2,2,2]=>10011100=>[1,2,3,2]=>[2,3,2,1]
[4,2,2,1,1]=>100110110=>[1,2,2,1,2,1]=>[1,2,1,2,2,1]
[4,2,1,1,1,1]=>1001011110=>[1,2,1,1,4,1]=>[1,4,1,1,2,1]
[4,1,1,1,1,1,1]=>10001111110=>[1,3,6,1]=>[1,6,3,1]
[3,3,3,1]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[3,3,2,2]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,3,2,1,1]=>11010110=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]
[3,3,1,1,1,1]=>110011110=>[2,2,4,1]=>[1,4,2,2]
[3,2,2,2,1]=>10111010=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]
[3,2,2,1,1,1]=>101101110=>[1,1,2,1,3,1]=>[1,3,1,2,1,1]
[3,2,1,1,1,1,1]=>1010111110=>[1,1,1,1,5,1]=>[1,5,1,1,1,1]
[3,1,1,1,1,1,1,1]=>10011111110=>[1,2,7,1]=>[1,7,2,1]
[2,2,2,2,2]=>1111100=>[5,2]=>[2,5]
[2,2,2,2,1,1]=>11110110=>[4,1,2,1]=>[1,2,1,4]
[2,2,2,1,1,1,1]=>111011110=>[3,1,4,1]=>[1,4,1,3]
[2,2,1,1,1,1,1,1]=>1101111110=>[2,1,6,1]=>[1,6,1,2]
[2,1,1,1,1,1,1,1,1]=>10111111110=>[1,1,8,1]=>[1,8,1,1]
[1,1,1,1,1,1,1,1,1,1]=>11111111110=>[10,1]=>[1,10]
[9,2]=>10000000100=>[1,7,1,2]=>[2,1,7,1]
[8,2,1]=>10000001010=>[1,6,1,1,1,1]=>[1,1,1,1,6,1]
[7,4]=>100010000=>[1,3,1,4]=>[4,1,3,1]
[7,2,1,1]=>10000010110=>[1,5,1,1,2,1]=>[1,2,1,1,5,1]
[6,5]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[6,4,1]=>100100010=>[1,2,1,3,1,1]=>[1,1,3,1,2,1]
[6,3,2]=>100010100=>[1,3,1,1,1,2]=>[2,1,1,1,3,1]
[6,2,1,1,1]=>10000101110=>[1,4,1,1,3,1]=>[1,3,1,1,4,1]
[6,1,1,1,1,1]=>100000111110=>[1,5,5,1]=>[1,5,5,1]
[5,5,1]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[5,4,2]=>10100100=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]
[5,4,1,1]=>101000110=>[1,1,1,3,2,1]=>[1,2,3,1,1,1]
[5,3,3]=>10011000=>[1,2,2,3]=>[3,2,2,1]
[5,3,2,1]=>100101010=>[1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1]
[5,3,1,1,1]=>1001001110=>[1,2,1,2,3,1]=>[1,3,2,1,2,1]
[5,2,2,2]=>100011100=>[1,3,3,2]=>[2,3,3,1]
[5,2,2,1,1]=>1000110110=>[1,3,2,1,2,1]=>[1,2,1,2,3,1]
[5,2,1,1,1,1]=>10001011110=>[1,3,1,1,4,1]=>[1,4,1,1,3,1]
[4,4,3]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[4,4,2,1]=>11001010=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]
[4,4,1,1,1]=>110001110=>[2,3,3,1]=>[1,3,3,2]
[4,3,3,1]=>10110010=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]
[4,3,2,2]=>10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[4,3,2,1,1]=>101010110=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]
[4,2,2,2,1]=>100111010=>[1,2,3,1,1,1]=>[1,1,1,3,2,1]
[4,2,1,1,1,1,1]=>10010111110=>[1,2,1,1,5,1]=>[1,5,1,1,2,1]
[3,3,3,2]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[3,3,3,1,1]=>11100110=>[3,2,2,1]=>[1,2,2,3]
[3,3,2,2,1]=>11011010=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]
[3,3,2,1,1,1]=>110101110=>[2,1,1,1,3,1]=>[1,3,1,1,1,2]
[3,2,2,2,2]=>10111100=>[1,1,4,2]=>[2,4,1,1]
[3,2,2,2,1,1]=>101110110=>[1,1,3,1,2,1]=>[1,2,1,3,1,1]
[3,2,1,1,1,1,1,1]=>10101111110=>[1,1,1,1,6,1]=>[1,6,1,1,1,1]
[2,2,2,2,2,1]=>11111010=>[5,1,1,1]=>[1,1,1,5]
[2,2,2,2,1,1,1]=>111101110=>[4,1,3,1]=>[1,3,1,4]
[2,2,2,1,1,1,1,1]=>1110111110=>[3,1,5,1]=>[1,5,1,3]
[2,2,1,1,1,1,1,1,1]=>11011111110=>[2,1,7,1]=>[1,7,1,2]
[7,5]=>100100000=>[1,2,1,5]=>[5,1,2,1]
[6,6]=>11000000=>[2,6]=>[6,2]
[6,5,1]=>101000010=>[1,1,1,4,1,1]=>[1,1,4,1,1,1]
[6,4,2]=>100100100=>[1,2,1,2,1,2]=>[2,1,2,1,2,1]
[6,3,3]=>100011000=>[1,3,2,3]=>[3,2,3,1]
[6,3,2,1]=>1000101010=>[1,3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3,1]
[5,5,2]=>11000100=>[2,3,1,2]=>[2,1,3,2]
[5,5,1,1]=>110000110=>[2,4,2,1]=>[1,2,4,2]
[5,4,3]=>10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[5,4,2,1]=>101001010=>[1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1]
[5,4,1,1,1]=>1010001110=>[1,1,1,3,3,1]=>[1,3,3,1,1,1]
[5,3,3,1]=>100110010=>[1,2,2,2,1,1]=>[1,1,2,2,2,1]
[5,3,2,2]=>100101100=>[1,2,1,1,2,2]=>[2,2,1,1,2,1]
[5,3,2,1,1]=>1001010110=>[1,2,1,1,1,1,2,1]=>[1,2,1,1,1,1,2,1]
[5,2,2,2,1]=>1000111010=>[1,3,3,1,1,1]=>[1,1,1,3,3,1]
[4,4,4]=>1110000=>[3,4]=>[4,3]
[4,4,3,1]=>11010010=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]
[4,4,2,2]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[4,4,2,1,1]=>110010110=>[2,2,1,1,2,1]=>[1,2,1,1,2,2]
[4,4,1,1,1,1]=>1100011110=>[2,3,4,1]=>[1,4,3,2]
[4,3,3,2]=>10110100=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]
[4,3,3,1,1]=>101100110=>[1,1,2,2,2,1]=>[1,2,2,2,1,1]
[4,3,2,2,1]=>101011010=>[1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1]
[4,2,2,2,2]=>100111100=>[1,2,4,2]=>[2,4,2,1]
[3,3,3,3]=>1111000=>[4,3]=>[3,4]
[3,3,3,2,1]=>11101010=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]
[3,3,3,1,1,1]=>111001110=>[3,2,3,1]=>[1,3,2,3]
[3,3,2,2,2]=>11011100=>[2,1,3,2]=>[2,3,1,2]
[3,3,2,2,1,1]=>110110110=>[2,1,2,1,2,1]=>[1,2,1,2,1,2]
[3,2,2,2,2,1]=>101111010=>[1,1,4,1,1,1]=>[1,1,1,4,1,1]
[2,2,2,2,2,2]=>11111100=>[6,2]=>[2,6]
[2,2,2,2,2,1,1]=>111110110=>[5,1,2,1]=>[1,2,1,5]
[2,2,2,2,1,1,1,1]=>1111011110=>[4,1,4,1]=>[1,4,1,4]
[9,4]=>10000010000=>[1,5,1,4]=>[4,1,5,1]
[8,4,1]=>10000100010=>[1,4,1,3,1,1]=>[1,1,3,1,4,1]
[7,6]=>101000000=>[1,1,1,6]=>[6,1,1,1]
[6,6,1]=>110000010=>[2,5,1,1]=>[1,1,5,2]
[6,5,2]=>101000100=>[1,1,1,3,1,2]=>[2,1,3,1,1,1]
[6,4,3]=>100101000=>[1,2,1,1,1,3]=>[3,1,1,1,2,1]
[6,4,2,1]=>1001001010=>[1,2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2,1]
[6,3,3,1]=>1000110010=>[1,3,2,2,1,1]=>[1,1,2,2,3,1]
[6,3,2,2]=>1000101100=>[1,3,1,1,2,2]=>[2,2,1,1,3,1]
[5,5,3]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[5,5,2,1]=>110001010=>[2,3,1,1,1,1]=>[1,1,1,1,3,2]
[5,4,4]=>10110000=>[1,1,2,4]=>[4,2,1,1]
[5,4,3,1]=>101010010=>[1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1]
[5,4,2,2]=>101001100=>[1,1,1,2,2,2]=>[2,2,2,1,1,1]
[5,4,2,1,1]=>1010010110=>[1,1,1,2,1,1,2,1]=>[1,2,1,1,2,1,1,1]
[5,3,3,2]=>100110100=>[1,2,2,1,1,2]=>[2,1,1,2,2,1]
[5,3,3,1,1]=>1001100110=>[1,2,2,2,2,1]=>[1,2,2,2,2,1]
[5,3,2,2,1]=>1001011010=>[1,2,1,1,2,1,1,1]=>[1,1,1,2,1,1,2,1]
[5,2,2,2,2]=>1000111100=>[1,3,4,2]=>[2,4,3,1]
[4,4,4,1]=>11100010=>[3,3,1,1]=>[1,1,3,3]
[4,4,3,2]=>11010100=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
[4,4,3,1,1]=>110100110=>[2,1,1,2,2,1]=>[1,2,2,1,1,2]
[4,4,2,2,1]=>110011010=>[2,2,2,1,1,1]=>[1,1,1,2,2,2]
[4,4,2,1,1,1]=>1100101110=>[2,2,1,1,3,1]=>[1,3,1,1,2,2]
[4,3,3,3]=>10111000=>[1,1,3,3]=>[3,3,1,1]
[4,3,3,2,1]=>101101010=>[1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1]
[4,3,2,2,2]=>101011100=>[1,1,1,1,3,2]=>[2,3,1,1,1,1]
[3,3,3,3,1]=>11110010=>[4,2,1,1]=>[1,1,2,4]
[3,3,3,2,2]=>11101100=>[3,1,2,2]=>[2,2,1,3]
[3,3,3,2,1,1]=>111010110=>[3,1,1,1,2,1]=>[1,2,1,1,1,3]
[3,3,3,1,1,1,1]=>1110011110=>[3,2,4,1]=>[1,4,2,3]
[3,3,2,2,2,1]=>110111010=>[2,1,3,1,1,1]=>[1,1,1,3,1,2]
[3,2,2,2,2,2]=>101111100=>[1,1,5,2]=>[2,5,1,1]
[2,2,2,2,2,2,1]=>111111010=>[6,1,1,1]=>[1,1,1,6]
[8,6]=>1001000000=>[1,2,1,6]=>[6,1,2,1]
[8,5,1]=>10001000010=>[1,3,1,4,1,1]=>[1,1,4,1,3,1]
[8,4,2]=>10000100100=>[1,4,1,2,1,2]=>[2,1,2,1,4,1]
[7,7]=>110000000=>[2,7]=>[7,2]
[7,6,1]=>1010000010=>[1,1,1,5,1,1]=>[1,1,5,1,1,1]
[7,4,2,1]=>10001001010=>[1,3,1,2,1,1,1,1]=>[1,1,1,1,2,1,3,1]
[6,6,2]=>110000100=>[2,4,1,2]=>[2,1,4,2]
[6,6,1,1]=>1100000110=>[2,5,2,1]=>[1,2,5,2]
[6,5,3]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[6,5,2,1]=>1010001010=>[1,1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1,1]
[6,4,4]=>100110000=>[1,2,2,4]=>[4,2,2,1]
[6,4,3,1]=>1001010010=>[1,2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2,1]
[6,4,2,2]=>1001001100=>[1,2,1,2,2,2]=>[2,2,2,1,2,1]
[6,3,3,2]=>1000110100=>[1,3,2,1,1,2]=>[2,1,1,2,3,1]
[5,5,4]=>11010000=>[2,1,1,4]=>[4,1,1,2]
[5,5,3,1]=>110010010=>[2,2,1,2,1,1]=>[1,1,2,1,2,2]
[5,5,2,2]=>110001100=>[2,3,2,2]=>[2,2,3,2]
[5,4,4,1]=>101100010=>[1,1,2,3,1,1]=>[1,1,3,2,1,1]
[5,4,3,2]=>101010100=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[5,4,3,1,1]=>1010100110=>[1,1,1,1,1,2,2,1]=>[1,2,2,1,1,1,1,1]
[5,4,2,2,1]=>1010011010=>[1,1,1,2,2,1,1,1]=>[1,1,1,2,2,1,1,1]
[5,3,3,3]=>100111000=>[1,2,3,3]=>[3,3,2,1]
[5,3,3,2,1]=>1001101010=>[1,2,2,1,1,1,1,1]=>[1,1,1,1,1,2,2,1]
[4,4,4,2]=>11100100=>[3,2,1,2]=>[2,1,2,3]
[4,4,4,1,1]=>111000110=>[3,3,2,1]=>[1,2,3,3]
[4,4,3,3]=>11011000=>[2,1,2,3]=>[3,2,1,2]
[4,4,3,2,1]=>110101010=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]
[4,4,3,1,1,1]=>1101001110=>[2,1,1,2,3,1]=>[1,3,2,1,1,2]
[4,4,2,2,2]=>110011100=>[2,2,3,2]=>[2,3,2,2]
[4,4,2,2,1,1]=>1100110110=>[2,2,2,1,2,1]=>[1,2,1,2,2,2]
[4,3,3,3,1]=>101110010=>[1,1,3,2,1,1]=>[1,1,2,3,1,1]
[4,3,3,2,2]=>101101100=>[1,1,2,1,2,2]=>[2,2,1,2,1,1]
[3,3,3,3,2]=>11110100=>[4,1,1,2]=>[2,1,1,4]
[3,3,3,3,1,1]=>111100110=>[4,2,2,1]=>[1,2,2,4]
[3,3,3,2,2,1]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[3,3,2,2,2,2]=>110111100=>[2,1,4,2]=>[2,4,1,2]
[3,2,2,2,2,2,1]=>1011111010=>[1,1,5,1,1,1]=>[1,1,1,5,1,1]
[2,2,2,2,2,2,2]=>111111100=>[7,2]=>[2,7]
[2,2,2,2,2,2,1,1]=>1111110110=>[6,1,2,1]=>[1,2,1,6]
[8,7]=>1010000000=>[1,1,1,7]=>[7,1,1,1]
[8,5,2]=>10001000100=>[1,3,1,3,1,2]=>[2,1,3,1,3,1]
[8,4,3]=>10000101000=>[1,4,1,1,1,3]=>[3,1,1,1,4,1]
[7,7,1]=>1100000010=>[2,6,1,1]=>[1,1,6,2]
[7,5,2,1]=>10010001010=>[1,2,1,3,1,1,1,1]=>[1,1,1,1,3,1,2,1]
[7,4,3,1]=>10001010010=>[1,3,1,1,1,2,1,1]=>[1,1,2,1,1,1,3,1]
[6,6,3]=>110001000=>[2,3,1,3]=>[3,1,3,2]
[6,6,2,1]=>1100001010=>[2,4,1,1,1,1]=>[1,1,1,1,4,2]
[6,5,4]=>101010000=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]
[6,5,3,1]=>1010010010=>[1,1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1,1]
[6,5,2,2]=>1010001100=>[1,1,1,3,2,2]=>[2,2,3,1,1,1]
[6,4,4,1]=>1001100010=>[1,2,2,3,1,1]=>[1,1,3,2,2,1]
[6,4,3,2]=>1001010100=>[1,2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2,1]
[6,3,3,3]=>1000111000=>[1,3,3,3]=>[3,3,3,1]
[6,3,3,1,1,1]=>100011001110=>[1,3,2,2,3,1]=>[1,3,2,2,3,1]
[5,5,5]=>11100000=>[3,5]=>[5,3]
[5,5,4,1]=>110100010=>[2,1,1,3,1,1]=>[1,1,3,1,1,2]
[5,5,3,2]=>110010100=>[2,2,1,1,1,2]=>[2,1,1,1,2,2]
[5,5,3,1,1]=>1100100110=>[2,2,1,2,2,1]=>[1,2,2,1,2,2]
[5,4,4,2]=>101100100=>[1,1,2,2,1,2]=>[2,1,2,2,1,1]
[5,4,3,3]=>101011000=>[1,1,1,1,2,3]=>[3,2,1,1,1,1]
[5,4,3,2,1]=>1010101010=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1]
[5,3,3,2,2]=>1001101100=>[1,2,2,1,2,2]=>[2,2,1,2,2,1]
[4,4,4,3]=>11101000=>[3,1,1,3]=>[3,1,1,3]
[4,4,4,2,1]=>111001010=>[3,2,1,1,1,1]=>[1,1,1,1,2,3]
[4,4,3,3,1]=>110110010=>[2,1,2,2,1,1]=>[1,1,2,2,1,2]
[4,4,3,2,2]=>110101100=>[2,1,1,1,2,2]=>[2,2,1,1,1,2]
[4,3,3,3,2]=>101110100=>[1,1,3,1,1,2]=>[2,1,1,3,1,1]
[3,3,3,3,3]=>11111000=>[5,3]=>[3,5]
[3,3,3,3,2,1]=>111101010=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]
[3,3,3,2,2,2]=>111011100=>[3,1,3,2]=>[2,3,1,3]
[3,2,2,2,2,2,2]=>1011111100=>[1,1,6,2]=>[2,6,1,1]
[2,2,2,2,2,2,2,1]=>1111111010=>[7,1,1,1]=>[1,1,1,7]
[8,8]=>1100000000=>[2,8]=>[8,2]
[8,6,2]=>10010000100=>[1,2,1,4,1,2]=>[2,1,4,1,2,1]
[8,5,3]=>10001001000=>[1,3,1,2,1,3]=>[3,1,2,1,3,1]
[7,5,3,1]=>10010010010=>[1,2,1,2,1,2,1,1]=>[1,1,2,1,2,1,2,1]
[7,4,3,2]=>10001010100=>[1,3,1,1,1,1,1,2]=>[2,1,1,1,1,1,3,1]
[6,6,4]=>110010000=>[2,2,1,4]=>[4,1,2,2]
[6,6,3,1]=>1100010010=>[2,3,1,2,1,1]=>[1,1,2,1,3,2]
[6,6,2,2]=>1100001100=>[2,4,2,2]=>[2,2,4,2]
[6,6,1,1,1,1]=>110000011110=>[2,5,4,1]=>[1,4,5,2]
[6,5,5]=>101100000=>[1,1,2,5]=>[5,2,1,1]
[6,5,4,1]=>1010100010=>[1,1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1,1]
[6,5,3,2]=>1010010100=>[1,1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1,1]
[6,4,4,2]=>1001100100=>[1,2,2,2,1,2]=>[2,1,2,2,2,1]
[6,4,3,3]=>1001011000=>[1,2,1,1,2,3]=>[3,2,1,1,2,1]
[6,4,3,2,1]=>10010101010=>[1,2,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,2,1]
[6,4,2,2,1,1]=>100100110110=>[1,2,1,2,2,1,2,1]=>[1,2,1,2,2,1,2,1]
[6,2,2,2,2,2]=>100001111100=>[1,4,5,2]=>[2,5,4,1]
[5,5,5,1]=>111000010=>[3,4,1,1]=>[1,1,4,3]
[5,5,4,2]=>110100100=>[2,1,1,2,1,2]=>[2,1,2,1,1,2]
[5,5,3,3]=>110011000=>[2,2,2,3]=>[3,2,2,2]
[5,5,3,2,1]=>1100101010=>[2,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,2]
[5,5,2,2,2]=>1100011100=>[2,3,3,2]=>[2,3,3,2]
[5,4,4,3]=>101101000=>[1,1,2,1,1,3]=>[3,1,1,2,1,1]
[5,4,4,2,1]=>1011001010=>[1,1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1,1]
[5,4,3,3,1]=>1010110010=>[1,1,1,1,2,2,1,1]=>[1,1,2,2,1,1,1,1]
[5,4,3,2,2]=>1010101100=>[1,1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1,1]
[5,3,3,3,2]=>1001110100=>[1,2,3,1,1,2]=>[2,1,1,3,2,1]
[4,4,4,4]=>11110000=>[4,4]=>[4,4]
[4,4,4,3,1]=>111010010=>[3,1,1,2,1,1]=>[1,1,2,1,1,3]
[4,4,4,2,2]=>111001100=>[3,2,2,2]=>[2,2,2,3]
[4,4,3,3,2]=>110110100=>[2,1,2,1,1,2]=>[2,1,1,2,1,2]
[4,4,3,3,1,1]=>1101100110=>[2,1,2,2,2,1]=>[1,2,2,2,1,2]
[4,4,3,2,2,1]=>1101011010=>[2,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,2]
[4,4,2,2,2,2]=>1100111100=>[2,2,4,2]=>[2,4,2,2]
[4,3,3,3,3]=>101111000=>[1,1,4,3]=>[3,4,1,1]
[3,3,3,3,3,1]=>111110010=>[5,2,1,1]=>[1,1,2,5]
[3,3,3,3,2,2]=>111101100=>[4,1,2,2]=>[2,2,1,4]
[2,2,2,2,2,2,2,2]=>1111111100=>[8,2]=>[2,8]
[8,6,3]=>10010001000=>[1,2,1,3,1,3]=>[3,1,3,1,2,1]
[7,7,3]=>1100001000=>[2,4,1,3]=>[3,1,4,2]
[7,6,3,1]=>10100010010=>[1,1,1,3,1,2,1,1]=>[1,1,2,1,3,1,1,1]
[7,5,4,1]=>10010100010=>[1,2,1,1,1,3,1,1]=>[1,1,3,1,1,1,2,1]
[7,5,3,2]=>10010010100=>[1,2,1,2,1,1,1,2]=>[2,1,1,1,2,1,2,1]
[6,6,5]=>110100000=>[2,1,1,5]=>[5,1,1,2]
[6,5,5,1]=>1011000010=>[1,1,2,4,1,1]=>[1,1,4,2,1,1]
[6,5,4,2]=>1010100100=>[1,1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1,1]
[6,5,3,3]=>1010011000=>[1,1,1,2,2,3]=>[3,2,2,1,1,1]
[6,5,3,2,1]=>10100101010=>[1,1,1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1,1,1]
[6,4,4,3]=>1001101000=>[1,2,2,1,1,3]=>[3,1,1,2,2,1]
[6,4,4,1,1,1]=>100110001110=>[1,2,2,3,3,1]=>[1,3,3,2,2,1]
[6,4,3,2,1,1]=>100101010110=>[1,2,1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1,2,1]
[6,3,3,3,1,1]=>100011100110=>[1,3,3,2,2,1]=>[1,2,2,3,3,1]
[5,5,5,2]=>111000100=>[3,3,1,2]=>[2,1,3,3]
[5,5,4,3]=>110101000=>[2,1,1,1,1,3]=>[3,1,1,1,1,2]
[5,5,4,2,1]=>1101001010=>[2,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,2]
[5,5,3,3,1]=>1100110010=>[2,2,2,2,1,1]=>[1,1,2,2,2,2]
[5,5,3,2,2]=>1100101100=>[2,2,1,1,2,2]=>[2,2,1,1,2,2]
[5,4,4,4]=>101110000=>[1,1,3,4]=>[4,3,1,1]
[5,4,4,3,1]=>1011010010=>[1,1,2,1,1,2,1,1]=>[1,1,2,1,1,2,1,1]
[5,4,4,2,2]=>1011001100=>[1,1,2,2,2,2]=>[2,2,2,2,1,1]
[5,4,3,3,2]=>1010110100=>[1,1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1,1]
[5,3,3,3,3]=>1001111000=>[1,2,4,3]=>[3,4,2,1]
[4,4,4,4,1]=>111100010=>[4,3,1,1]=>[1,1,3,4]
[4,4,4,3,2]=>111010100=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]
[4,4,3,3,3]=>110111000=>[2,1,3,3]=>[3,3,1,2]
[3,3,3,3,3,2]=>111110100=>[5,1,1,2]=>[2,1,1,5]
[]=>=>[]=>[]
[6,5,4,3,2,1]=>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]
[6,4,4,3,2,1]=>100110101010=>[1,2,2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2,2,1]
[4,4,4,3,2,1]=>1110101010=>[3,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,3]
[6,5,3,3,2,1]=>101001101010=>[1,1,1,2,2,1,1,1,1,1]=>[1,1,1,1,1,2,2,1,1,1]
[6,4,3,3,2,1]=>100101101010=>[1,2,1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1,2,1]
[6,5,4,2,2,1]=>101010011010=>[1,1,1,1,1,2,2,1,1,1]=>[1,1,1,2,2,1,1,1,1,1]
[6,4,4,2,2,1]=>100110011010=>[1,2,2,2,2,1,1,1]=>[1,1,1,2,2,2,2,1]
[6,5,3,2,2,1]=>101001011010=>[1,1,1,2,1,1,2,1,1,1]=>[1,1,1,2,1,1,2,1,1,1]
[6,4,3,2,2,1]=>100101011010=>[1,2,1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1,2,1]
[6,5,4,3,1,1]=>101010100110=>[1,1,1,1,1,1,1,2,2,1]=>[1,2,2,1,1,1,1,1,1,1]
[6,4,4,3,1,1]=>100110100110=>[1,2,2,1,1,2,2,1]=>[1,2,2,1,1,2,2,1]
[6,5,3,3,1,1]=>101001100110=>[1,1,1,2,2,2,2,1]=>[1,2,2,2,2,1,1,1]
[6,4,3,3,1,1]=>100101100110=>[1,2,1,1,2,2,2,1]=>[1,2,2,2,1,1,2,1]
[6,5,4,2,1,1]=>101010010110=>[1,1,1,1,1,2,1,1,2,1]=>[1,2,1,1,2,1,1,1,1,1]
[6,4,4,2,1,1]=>100110010110=>[1,2,2,2,1,1,2,1]=>[1,2,1,1,2,2,2,1]
[6,5,3,2,1,1]=>101001010110=>[1,1,1,2,1,1,1,1,2,1]=>[1,2,1,1,1,1,2,1,1,1]
[5,5,4,3,2]=>1101010100=>[2,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,2]
[5,4,4,3,2]=>1011010100=>[1,1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1,1]
[5,5,3,3,2]=>1100110100=>[2,2,2,1,1,2]=>[2,1,1,2,2,2]
[5,5,4,2,2]=>1101001100=>[2,1,1,2,2,2]=>[2,2,2,1,1,2]
[6,5,4,3,1]=>10101010010=>[1,1,1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1,1,1]
[5,5,4,3,1]=>1101010010=>[2,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,2]
[6,5,4,2,1]=>10101001010=>[1,1,1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1,1,1]
[6,5,4,3]=>1010101000=>[1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1]
[3,3,3,3,3,2,1]=>1111101010=>[5,1,1,1,1,1]=>[1,1,1,1,1,5]
[6,6,5,4,3,2]=>110101010100=>[2,1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1,2]
[6,5,5,4,3,2]=>101101010100=>[1,1,2,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,2,1,1]
[6,5,4,4,3,2]=>101011010100=>[1,1,1,1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1,1,1,1]
[6,5,4,3,3,2]=>101010110100=>[1,1,1,1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1,1,1,1]
[4,3,3,3,3,2]=>1011110100=>[1,1,4,1,1,2]=>[2,1,1,4,1,1]
[6,5,4,3,2,2]=>101010101100=>[1,1,1,1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1,1,1,1]
[4,4,4,3,2,2]=>1110101100=>[3,1,1,1,2,2]=>[2,2,1,1,1,3]
[6,6,2,2,2,2]=>110000111100=>[2,4,4,2]=>[2,4,4,2]
[6,6,5,4,3,1]=>110101010010=>[2,1,1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1,1,2]
[6,5,5,4,3,1]=>101101010010=>[1,1,2,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,2,1,1]
[4,4,4,4,3,1]=>1111010010=>[4,1,1,2,1,1]=>[1,1,2,1,1,4]
[4,4,4,4,2,1]=>1111001010=>[4,2,1,1,1,1]=>[1,1,1,1,2,4]
[6,6,5,3,2,1]=>110100101010=>[2,1,1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1,1,2]
[6,6,4,3,2,1]=>110010101010=>[2,2,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,2,2]
[5,4,4,4,3]=>1011101000=>[1,1,3,1,1,3]=>[3,1,1,3,1,1]
[5,4,3,3,3]=>1010111000=>[1,1,1,1,3,3]=>[3,3,1,1,1,1]
[4,4,4,4,2]=>111100100=>[4,2,1,2]=>[2,1,2,4]
[6,5,5,4]=>1011010000=>[1,1,2,1,1,4]=>[4,1,1,2,1,1]
[7,6,5,2]=>10101000100=>[1,1,1,1,1,3,1,2]=>[2,1,3,1,1,1,1,1]
[7,6,5]=>1010100000=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]
[3,3,3,3,3,3]=>111111000=>[6,3]=>[3,6]
[2,2,2,2,2,2,2,2,2,2]=>111111111100=>[10,2]=>[2,10]
[3,3,3,3,3,3,1]=>1111110010=>[6,2,1,1]=>[1,1,2,6]
[4,3,3,3,3,3]=>1011111000=>[1,1,5,3]=>[3,5,1,1]
[4,4,4,4,4]=>111110000=>[5,4]=>[4,5]
[4,4,4,3,3,3]=>1110111000=>[3,1,3,3]=>[3,3,1,3]
[4,4,4,4,4,4]=>1111110000=>[6,4]=>[4,6]
[5,5,5,5]=>111100000=>[4,5]=>[5,4]
[6,6,6,6]=>1111000000=>[4,6]=>[6,4]
[6,6,6]=>111000000=>[3,6]=>[6,3]
[7,6,6]=>1011000000=>[1,1,2,6]=>[6,2,1,1]
[10,10]=>110000000000=>[2,10]=>[10,2]
[8,7,6,5,4,3,2,1]=>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]
[5,5,5,5,5]=>1111100000=>[5,5]=>[5,5]
[9,9]=>11000000000=>[2,9]=>[9,2]
[6,5,5,5]=>1011100000=>[1,1,3,5]=>[5,3,1,1]
[5,4,4,4,4]=>1011110000=>[1,1,4,4]=>[4,4,1,1]
[4,4,4,4,4,1]=>1111100010=>[5,3,1,1]=>[1,1,3,5]
[5,5,5,5,1]=>1111000010=>[4,4,1,1]=>[1,1,4,4]
[6,6,6,1]=>1110000010=>[3,5,1,1]=>[1,1,5,3]
Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
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.