Identifier
Mp00095:
Integer partitions
—to binary word⟶
Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Images
=>
Cc0002;cc-rep-0
[1]=>10=>[1,2]=>[1,2]
[2]=>100=>[1,3]=>[1,1,2]
[1,1]=>110=>[1,1,2]=>[1,3]
[3]=>1000=>[1,4]=>[1,1,1,2]
[2,1]=>1010=>[1,2,2]=>[1,2,2]
[1,1,1]=>1110=>[1,1,1,2]=>[1,4]
[4]=>10000=>[1,5]=>[1,1,1,1,2]
[3,1]=>10010=>[1,3,2]=>[1,2,1,2]
[2,2]=>1100=>[1,1,3]=>[1,1,3]
[2,1,1]=>10110=>[1,2,1,2]=>[1,3,2]
[1,1,1,1]=>11110=>[1,1,1,1,2]=>[1,5]
[5]=>100000=>[1,6]=>[1,1,1,1,1,2]
[4,1]=>100010=>[1,4,2]=>[1,2,1,1,2]
[3,2]=>10100=>[1,2,3]=>[1,1,2,2]
[3,1,1]=>100110=>[1,3,1,2]=>[1,3,1,2]
[2,2,1]=>11010=>[1,1,2,2]=>[1,2,3]
[2,1,1,1]=>101110=>[1,2,1,1,2]=>[1,4,2]
[1,1,1,1,1]=>111110=>[1,1,1,1,1,2]=>[1,6]
[6]=>1000000=>[1,7]=>[1,1,1,1,1,1,2]
[5,1]=>1000010=>[1,5,2]=>[1,2,1,1,1,2]
[4,2]=>100100=>[1,3,3]=>[1,1,2,1,2]
[4,1,1]=>1000110=>[1,4,1,2]=>[1,3,1,1,2]
[3,3]=>11000=>[1,1,4]=>[1,1,1,3]
[3,2,1]=>101010=>[1,2,2,2]=>[1,2,2,2]
[3,1,1,1]=>1001110=>[1,3,1,1,2]=>[1,4,1,2]
[2,2,2]=>11100=>[1,1,1,3]=>[1,1,4]
[2,2,1,1]=>110110=>[1,1,2,1,2]=>[1,3,3]
[2,1,1,1,1]=>1011110=>[1,2,1,1,1,2]=>[1,5,2]
[1,1,1,1,1,1]=>1111110=>[1,1,1,1,1,1,2]=>[1,7]
[7]=>10000000=>[1,8]=>[1,1,1,1,1,1,1,2]
[6,1]=>10000010=>[1,6,2]=>[1,2,1,1,1,1,2]
[5,2]=>1000100=>[1,4,3]=>[1,1,2,1,1,2]
[5,1,1]=>10000110=>[1,5,1,2]=>[1,3,1,1,1,2]
[4,3]=>101000=>[1,2,4]=>[1,1,1,2,2]
[4,2,1]=>1001010=>[1,3,2,2]=>[1,2,2,1,2]
[4,1,1,1]=>10001110=>[1,4,1,1,2]=>[1,4,1,1,2]
[3,3,1]=>110010=>[1,1,3,2]=>[1,2,1,3]
[3,2,2]=>101100=>[1,2,1,3]=>[1,1,3,2]
[3,2,1,1]=>1010110=>[1,2,2,1,2]=>[1,3,2,2]
[3,1,1,1,1]=>10011110=>[1,3,1,1,1,2]=>[1,5,1,2]
[2,2,2,1]=>111010=>[1,1,1,2,2]=>[1,2,4]
[2,2,1,1,1]=>1101110=>[1,1,2,1,1,2]=>[1,4,3]
[2,1,1,1,1,1]=>10111110=>[1,2,1,1,1,1,2]=>[1,6,2]
[1,1,1,1,1,1,1]=>11111110=>[1,1,1,1,1,1,1,2]=>[1,8]
[8]=>100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2]
[7,1]=>100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2]
[6,2]=>10000100=>[1,5,3]=>[1,1,2,1,1,1,2]
[6,1,1]=>100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2]
[5,3]=>1001000=>[1,3,4]=>[1,1,1,2,1,2]
[5,2,1]=>10001010=>[1,4,2,2]=>[1,2,2,1,1,2]
[5,1,1,1]=>100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2]
[4,4]=>110000=>[1,1,5]=>[1,1,1,1,3]
[4,3,1]=>1010010=>[1,2,3,2]=>[1,2,1,2,2]
[4,2,2]=>1001100=>[1,3,1,3]=>[1,1,3,1,2]
[4,2,1,1]=>10010110=>[1,3,2,1,2]=>[1,3,2,1,2]
[4,1,1,1,1]=>100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2]
[3,3,2]=>110100=>[1,1,2,3]=>[1,1,2,3]
[3,3,1,1]=>1100110=>[1,1,3,1,2]=>[1,3,1,3]
[3,2,2,1]=>1011010=>[1,2,1,2,2]=>[1,2,3,2]
[3,2,1,1,1]=>10101110=>[1,2,2,1,1,2]=>[1,4,2,2]
[3,1,1,1,1,1]=>100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2]
[2,2,2,2]=>111100=>[1,1,1,1,3]=>[1,1,5]
[2,2,2,1,1]=>1110110=>[1,1,1,2,1,2]=>[1,3,4]
[2,2,1,1,1,1]=>11011110=>[1,1,2,1,1,1,2]=>[1,5,3]
[2,1,1,1,1,1,1]=>101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2]
[1,1,1,1,1,1,1,1]=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9]
[9]=>1000000000=>[1,10]=>[1,1,1,1,1,1,1,1,1,2]
[8,1]=>1000000010=>[1,8,2]=>[1,2,1,1,1,1,1,1,2]
[7,2]=>100000100=>[1,6,3]=>[1,1,2,1,1,1,1,2]
[7,1,1]=>1000000110=>[1,7,1,2]=>[1,3,1,1,1,1,1,2]
[6,3]=>10001000=>[1,4,4]=>[1,1,1,2,1,1,2]
[6,2,1]=>100001010=>[1,5,2,2]=>[1,2,2,1,1,1,2]
[6,1,1,1]=>1000001110=>[1,6,1,1,2]=>[1,4,1,1,1,1,2]
[5,4]=>1010000=>[1,2,5]=>[1,1,1,1,2,2]
[5,3,1]=>10010010=>[1,3,3,2]=>[1,2,1,2,1,2]
[5,2,2]=>10001100=>[1,4,1,3]=>[1,1,3,1,1,2]
[5,2,1,1]=>100010110=>[1,4,2,1,2]=>[1,3,2,1,1,2]
[5,1,1,1,1]=>1000011110=>[1,5,1,1,1,2]=>[1,5,1,1,1,2]
[4,4,1]=>1100010=>[1,1,4,2]=>[1,2,1,1,3]
[4,3,2]=>1010100=>[1,2,2,3]=>[1,1,2,2,2]
[4,3,1,1]=>10100110=>[1,2,3,1,2]=>[1,3,1,2,2]
[4,2,2,1]=>10011010=>[1,3,1,2,2]=>[1,2,3,1,2]
[4,2,1,1,1]=>100101110=>[1,3,2,1,1,2]=>[1,4,2,1,2]
[4,1,1,1,1,1]=>1000111110=>[1,4,1,1,1,1,2]=>[1,6,1,1,2]
[3,3,3]=>111000=>[1,1,1,4]=>[1,1,1,4]
[3,3,2,1]=>1101010=>[1,1,2,2,2]=>[1,2,2,3]
[3,3,1,1,1]=>11001110=>[1,1,3,1,1,2]=>[1,4,1,3]
[3,2,2,2]=>1011100=>[1,2,1,1,3]=>[1,1,4,2]
[3,2,2,1,1]=>10110110=>[1,2,1,2,1,2]=>[1,3,3,2]
[3,2,1,1,1,1]=>101011110=>[1,2,2,1,1,1,2]=>[1,5,2,2]
[3,1,1,1,1,1,1]=>1001111110=>[1,3,1,1,1,1,1,2]=>[1,7,1,2]
[2,2,2,2,1]=>1111010=>[1,1,1,1,2,2]=>[1,2,5]
[2,2,2,1,1,1]=>11101110=>[1,1,1,2,1,1,2]=>[1,4,4]
[2,2,1,1,1,1,1]=>110111110=>[1,1,2,1,1,1,1,2]=>[1,6,3]
[2,1,1,1,1,1,1,1]=>1011111110=>[1,2,1,1,1,1,1,1,2]=>[1,8,2]
[1,1,1,1,1,1,1,1,1]=>1111111110=>[1,1,1,1,1,1,1,1,1,2]=>[1,10]
[10]=>10000000000=>[1,11]=>[1,1,1,1,1,1,1,1,1,1,2]
[9,1]=>10000000010=>[1,9,2]=>[1,2,1,1,1,1,1,1,1,2]
[8,2]=>1000000100=>[1,7,3]=>[1,1,2,1,1,1,1,1,2]
[8,1,1]=>10000000110=>[1,8,1,2]=>[1,3,1,1,1,1,1,1,2]
[7,3]=>100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2]
[7,2,1]=>1000001010=>[1,6,2,2]=>[1,2,2,1,1,1,1,2]
[7,1,1,1]=>10000001110=>[1,7,1,1,2]=>[1,4,1,1,1,1,1,2]
[6,4]=>10010000=>[1,3,5]=>[1,1,1,1,2,1,2]
[6,3,1]=>100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2]
[6,2,2]=>100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2]
[6,2,1,1]=>1000010110=>[1,5,2,1,2]=>[1,3,2,1,1,1,2]
[6,1,1,1,1]=>10000011110=>[1,6,1,1,1,2]=>[1,5,1,1,1,1,2]
[5,5]=>1100000=>[1,1,6]=>[1,1,1,1,1,3]
[5,4,1]=>10100010=>[1,2,4,2]=>[1,2,1,1,2,2]
[5,3,2]=>10010100=>[1,3,2,3]=>[1,1,2,2,1,2]
[5,3,1,1]=>100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2]
[5,2,2,1]=>100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2]
[5,2,1,1,1]=>1000101110=>[1,4,2,1,1,2]=>[1,4,2,1,1,2]
[5,1,1,1,1,1]=>10000111110=>[1,5,1,1,1,1,2]=>[1,6,1,1,1,2]
[4,4,2]=>1100100=>[1,1,3,3]=>[1,1,2,1,3]
[4,4,1,1]=>11000110=>[1,1,4,1,2]=>[1,3,1,1,3]
[4,3,3]=>1011000=>[1,2,1,4]=>[1,1,1,3,2]
[4,3,2,1]=>10101010=>[1,2,2,2,2]=>[1,2,2,2,2]
[4,3,1,1,1]=>101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2]
[4,2,2,2]=>10011100=>[1,3,1,1,3]=>[1,1,4,1,2]
[4,2,2,1,1]=>100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2]
[4,2,1,1,1,1]=>1001011110=>[1,3,2,1,1,1,2]=>[1,5,2,1,2]
[4,1,1,1,1,1,1]=>10001111110=>[1,4,1,1,1,1,1,2]=>[1,7,1,1,2]
[3,3,3,1]=>1110010=>[1,1,1,3,2]=>[1,2,1,4]
[3,3,2,2]=>1101100=>[1,1,2,1,3]=>[1,1,3,3]
[3,3,2,1,1]=>11010110=>[1,1,2,2,1,2]=>[1,3,2,3]
[3,3,1,1,1,1]=>110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3]
[3,2,2,2,1]=>10111010=>[1,2,1,1,2,2]=>[1,2,4,2]
[3,2,2,1,1,1]=>101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2]
[3,2,1,1,1,1,1]=>1010111110=>[1,2,2,1,1,1,1,2]=>[1,6,2,2]
[3,1,1,1,1,1,1,1]=>10011111110=>[1,3,1,1,1,1,1,1,2]=>[1,8,1,2]
[2,2,2,2,2]=>1111100=>[1,1,1,1,1,3]=>[1,1,6]
[2,2,2,2,1,1]=>11110110=>[1,1,1,1,2,1,2]=>[1,3,5]
[2,2,2,1,1,1,1]=>111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4]
[2,2,1,1,1,1,1,1]=>1101111110=>[1,1,2,1,1,1,1,1,2]=>[1,7,3]
[2,1,1,1,1,1,1,1,1]=>10111111110=>[1,2,1,1,1,1,1,1,1,2]=>[1,9,2]
[1,1,1,1,1,1,1,1,1,1]=>11111111110=>[1,1,1,1,1,1,1,1,1,1,2]=>[1,11]
[7,4]=>100010000=>[1,4,5]=>[1,1,1,1,2,1,1,2]
[6,5]=>10100000=>[1,2,6]=>[1,1,1,1,1,2,2]
[6,4,1]=>100100010=>[1,3,4,2]=>[1,2,1,1,2,1,2]
[6,3,2]=>100010100=>[1,4,2,3]=>[1,1,2,2,1,1,2]
[5,5,1]=>11000010=>[1,1,5,2]=>[1,2,1,1,1,3]
[5,4,2]=>10100100=>[1,2,3,3]=>[1,1,2,1,2,2]
[5,4,1,1]=>101000110=>[1,2,4,1,2]=>[1,3,1,1,2,2]
[5,3,3]=>10011000=>[1,3,1,4]=>[1,1,1,3,1,2]
[5,3,2,1]=>100101010=>[1,3,2,2,2]=>[1,2,2,2,1,2]
[5,2,2,2]=>100011100=>[1,4,1,1,3]=>[1,1,4,1,1,2]
[4,4,3]=>1101000=>[1,1,2,4]=>[1,1,1,2,3]
[4,4,2,1]=>11001010=>[1,1,3,2,2]=>[1,2,2,1,3]
[4,4,1,1,1]=>110001110=>[1,1,4,1,1,2]=>[1,4,1,1,3]
[4,3,3,1]=>10110010=>[1,2,1,3,2]=>[1,2,1,3,2]
[4,3,2,2]=>10101100=>[1,2,2,1,3]=>[1,1,3,2,2]
[4,3,2,1,1]=>101010110=>[1,2,2,2,1,2]=>[1,3,2,2,2]
[4,2,2,2,1]=>100111010=>[1,3,1,1,2,2]=>[1,2,4,1,2]
[3,3,3,2]=>1110100=>[1,1,1,2,3]=>[1,1,2,4]
[3,3,3,1,1]=>11100110=>[1,1,1,3,1,2]=>[1,3,1,4]
[3,3,2,2,1]=>11011010=>[1,1,2,1,2,2]=>[1,2,3,3]
[3,3,2,1,1,1]=>110101110=>[1,1,2,2,1,1,2]=>[1,4,2,3]
[3,2,2,2,2]=>10111100=>[1,2,1,1,1,3]=>[1,1,5,2]
[3,2,2,2,1,1]=>101110110=>[1,2,1,1,2,1,2]=>[1,3,4,2]
[2,2,2,2,2,1]=>11111010=>[1,1,1,1,1,2,2]=>[1,2,6]
[2,2,2,2,1,1,1]=>111101110=>[1,1,1,1,2,1,1,2]=>[1,4,5]
[7,5]=>100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2]
[6,6]=>11000000=>[1,1,7]=>[1,1,1,1,1,1,3]
[6,5,1]=>101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2]
[6,4,2]=>100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2]
[6,3,3]=>100011000=>[1,4,1,4]=>[1,1,1,3,1,1,2]
[5,5,2]=>11000100=>[1,1,4,3]=>[1,1,2,1,1,3]
[5,5,1,1]=>110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3]
[5,4,3]=>10101000=>[1,2,2,4]=>[1,1,1,2,2,2]
[5,4,2,1]=>101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2]
[5,3,3,1]=>100110010=>[1,3,1,3,2]=>[1,2,1,3,1,2]
[5,3,2,2]=>100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2]
[4,4,4]=>1110000=>[1,1,1,5]=>[1,1,1,1,4]
[4,4,3,1]=>11010010=>[1,1,2,3,2]=>[1,2,1,2,3]
[4,4,2,2]=>11001100=>[1,1,3,1,3]=>[1,1,3,1,3]
[4,4,2,1,1]=>110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3]
[4,3,3,2]=>10110100=>[1,2,1,2,3]=>[1,1,2,3,2]
[4,3,3,1,1]=>101100110=>[1,2,1,3,1,2]=>[1,3,1,3,2]
[4,3,2,2,1]=>101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2]
[4,2,2,2,2]=>100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2]
[3,3,3,3]=>1111000=>[1,1,1,1,4]=>[1,1,1,5]
[3,3,3,2,1]=>11101010=>[1,1,1,2,2,2]=>[1,2,2,4]
[3,3,3,1,1,1]=>111001110=>[1,1,1,3,1,1,2]=>[1,4,1,4]
[3,3,2,2,2]=>11011100=>[1,1,2,1,1,3]=>[1,1,4,3]
[3,3,2,2,1,1]=>110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3]
[3,2,2,2,2,1]=>101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2]
[2,2,2,2,2,2]=>11111100=>[1,1,1,1,1,1,3]=>[1,1,7]
[2,2,2,2,2,1,1]=>111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6]
[7,6]=>101000000=>[1,2,7]=>[1,1,1,1,1,1,2,2]
[6,6,1]=>110000010=>[1,1,6,2]=>[1,2,1,1,1,1,3]
[6,5,2]=>101000100=>[1,2,4,3]=>[1,1,2,1,1,2,2]
[6,4,3]=>100101000=>[1,3,2,4]=>[1,1,1,2,2,1,2]
[5,5,3]=>11001000=>[1,1,3,4]=>[1,1,1,2,1,3]
[5,5,2,1]=>110001010=>[1,1,4,2,2]=>[1,2,2,1,1,3]
[5,4,4]=>10110000=>[1,2,1,5]=>[1,1,1,1,3,2]
[5,4,3,1]=>101010010=>[1,2,2,3,2]=>[1,2,1,2,2,2]
[5,4,2,2]=>101001100=>[1,2,3,1,3]=>[1,1,3,1,2,2]
[5,3,3,2]=>100110100=>[1,3,1,2,3]=>[1,1,2,3,1,2]
[4,4,4,1]=>11100010=>[1,1,1,4,2]=>[1,2,1,1,4]
[4,4,3,2]=>11010100=>[1,1,2,2,3]=>[1,1,2,2,3]
[4,4,3,1,1]=>110100110=>[1,1,2,3,1,2]=>[1,3,1,2,3]
[4,4,2,2,1]=>110011010=>[1,1,3,1,2,2]=>[1,2,3,1,3]
[4,3,3,3]=>10111000=>[1,2,1,1,4]=>[1,1,1,4,2]
[4,3,3,2,1]=>101101010=>[1,2,1,2,2,2]=>[1,2,2,3,2]
[4,3,2,2,2]=>101011100=>[1,2,2,1,1,3]=>[1,1,4,2,2]
[3,3,3,3,1]=>11110010=>[1,1,1,1,3,2]=>[1,2,1,5]
[3,3,3,2,2]=>11101100=>[1,1,1,2,1,3]=>[1,1,3,4]
[3,3,3,2,1,1]=>111010110=>[1,1,1,2,2,1,2]=>[1,3,2,4]
[3,3,2,2,2,1]=>110111010=>[1,1,2,1,1,2,2]=>[1,2,4,3]
[3,2,2,2,2,2]=>101111100=>[1,2,1,1,1,1,3]=>[1,1,6,2]
[2,2,2,2,2,2,1]=>111111010=>[1,1,1,1,1,1,2,2]=>[1,2,7]
[7,7]=>110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3]
[6,6,2]=>110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3]
[6,5,3]=>101001000=>[1,2,3,4]=>[1,1,1,2,1,2,2]
[6,4,4]=>100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2]
[5,5,4]=>11010000=>[1,1,2,5]=>[1,1,1,1,2,3]
[5,5,3,1]=>110010010=>[1,1,3,3,2]=>[1,2,1,2,1,3]
[5,5,2,2]=>110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3]
[5,4,4,1]=>101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2]
[5,4,3,2]=>101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2]
[5,3,3,3]=>100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2]
[4,4,4,2]=>11100100=>[1,1,1,3,3]=>[1,1,2,1,4]
[4,4,4,1,1]=>111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4]
[4,4,3,3]=>11011000=>[1,1,2,1,4]=>[1,1,1,3,3]
[4,4,3,2,1]=>110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3]
[4,4,2,2,2]=>110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3]
[4,3,3,3,1]=>101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2]
[4,3,3,2,2]=>101101100=>[1,2,1,2,1,3]=>[1,1,3,3,2]
[3,3,3,3,2]=>11110100=>[1,1,1,1,2,3]=>[1,1,2,5]
[3,3,3,3,1,1]=>111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5]
[3,3,3,2,2,1]=>111011010=>[1,1,1,2,1,2,2]=>[1,2,3,4]
[3,3,2,2,2,2]=>110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3]
[2,2,2,2,2,2,2]=>111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8]
[6,6,3]=>110001000=>[1,1,4,4]=>[1,1,1,2,1,1,3]
[6,5,4]=>101010000=>[1,2,2,5]=>[1,1,1,1,2,2,2]
[5,5,5]=>11100000=>[1,1,1,6]=>[1,1,1,1,1,4]
[5,5,4,1]=>110100010=>[1,1,2,4,2]=>[1,2,1,1,2,3]
[5,5,3,2]=>110010100=>[1,1,3,2,3]=>[1,1,2,2,1,3]
[5,4,4,2]=>101100100=>[1,2,1,3,3]=>[1,1,2,1,3,2]
[5,4,3,3]=>101011000=>[1,2,2,1,4]=>[1,1,1,3,2,2]
[5,4,3,2,1]=>1010101010=>[1,2,2,2,2,2]=>[1,2,2,2,2,2]
[4,4,4,3]=>11101000=>[1,1,1,2,4]=>[1,1,1,2,4]
[4,4,4,2,1]=>111001010=>[1,1,1,3,2,2]=>[1,2,2,1,4]
[4,4,3,3,1]=>110110010=>[1,1,2,1,3,2]=>[1,2,1,3,3]
[4,4,3,2,2]=>110101100=>[1,1,2,2,1,3]=>[1,1,3,2,3]
[4,3,3,3,2]=>101110100=>[1,2,1,1,2,3]=>[1,1,2,4,2]
[3,3,3,3,3]=>11111000=>[1,1,1,1,1,4]=>[1,1,1,6]
[3,3,3,3,2,1]=>111101010=>[1,1,1,1,2,2,2]=>[1,2,2,5]
[3,3,3,2,2,2]=>111011100=>[1,1,1,2,1,1,3]=>[1,1,4,4]
[6,6,4]=>110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3]
[6,5,5]=>101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2]
[5,5,5,1]=>111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4]
[5,5,4,2]=>110100100=>[1,1,2,3,3]=>[1,1,2,1,2,3]
[5,5,3,3]=>110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3]
[5,5,3,2,1]=>1100101010=>[1,1,3,2,2,2]=>[1,2,2,2,1,3]
[5,4,4,3]=>101101000=>[1,2,1,2,4]=>[1,1,1,2,3,2]
[5,4,4,2,1]=>1011001010=>[1,2,1,3,2,2]=>[1,2,2,1,3,2]
[5,4,3,3,1]=>1010110010=>[1,2,2,1,3,2]=>[1,2,1,3,2,2]
[5,4,3,2,2]=>1010101100=>[1,2,2,2,1,3]=>[1,1,3,2,2,2]
[4,4,4,4]=>11110000=>[1,1,1,1,5]=>[1,1,1,1,5]
[4,4,4,3,1]=>111010010=>[1,1,1,2,3,2]=>[1,2,1,2,4]
[4,4,4,2,2]=>111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4]
[4,4,3,3,2]=>110110100=>[1,1,2,1,2,3]=>[1,1,2,3,3]
[4,3,3,3,3]=>101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2]
[3,3,3,3,3,1]=>111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6]
[3,3,3,3,2,2]=>111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5]
[6,6,5]=>110100000=>[1,1,2,6]=>[1,1,1,1,1,2,3]
[5,5,5,2]=>111000100=>[1,1,1,4,3]=>[1,1,2,1,1,4]
[5,5,4,3]=>110101000=>[1,1,2,2,4]=>[1,1,1,2,2,3]
[5,5,4,2,1]=>1101001010=>[1,1,2,3,2,2]=>[1,2,2,1,2,3]
[5,5,3,3,1]=>1100110010=>[1,1,3,1,3,2]=>[1,2,1,3,1,3]
[5,5,3,2,2]=>1100101100=>[1,1,3,2,1,3]=>[1,1,3,2,1,3]
[5,4,4,4]=>101110000=>[1,2,1,1,5]=>[1,1,1,1,4,2]
[5,4,4,3,1]=>1011010010=>[1,2,1,2,3,2]=>[1,2,1,2,3,2]
[5,4,4,2,2]=>1011001100=>[1,2,1,3,1,3]=>[1,1,3,1,3,2]
[5,4,3,3,2]=>1010110100=>[1,2,2,1,2,3]=>[1,1,2,3,2,2]
[4,4,4,4,1]=>111100010=>[1,1,1,1,4,2]=>[1,2,1,1,5]
[4,4,4,3,2]=>111010100=>[1,1,1,2,2,3]=>[1,1,2,2,4]
[4,4,3,3,3]=>110111000=>[1,1,2,1,1,4]=>[1,1,1,4,3]
[3,3,3,3,3,2]=>111110100=>[1,1,1,1,1,2,3]=>[1,1,2,6]
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
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Map
conjugate
searching the database
Sorry, this map was not found in the database.