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Identifier
Mp00317: Integer partitions —odd parts⟶ Binary words
Images
[1] => 1
[2] => 0
[1,1] => 11
[3] => 1
[2,1] => 01
[1,1,1] => 111
[4] => 0
[3,1] => 11
[2,2] => 00
[2,1,1] => 011
[1,1,1,1] => 1111
[5] => 1
[4,1] => 01
[3,2] => 10
[3,1,1] => 111
[2,2,1] => 001
[2,1,1,1] => 0111
[1,1,1,1,1] => 11111
[6] => 0
[5,1] => 11
[4,2] => 00
[4,1,1] => 011
[3,3] => 11
[3,2,1] => 101
[3,1,1,1] => 1111
[2,2,2] => 000
[2,2,1,1] => 0011
[2,1,1,1,1] => 01111
[1,1,1,1,1,1] => 111111
[7] => 1
[6,1] => 01
[5,2] => 10
[5,1,1] => 111
[4,3] => 01
[4,2,1] => 001
[4,1,1,1] => 0111
[3,3,1] => 111
[3,2,2] => 100
[3,2,1,1] => 1011
[3,1,1,1,1] => 11111
[2,2,2,1] => 0001
[2,2,1,1,1] => 00111
[2,1,1,1,1,1] => 011111
[1,1,1,1,1,1,1] => 1111111
[8] => 0
[7,1] => 11
[6,2] => 00
[6,1,1] => 011
[5,3] => 11
[5,2,1] => 101
[5,1,1,1] => 1111
[4,4] => 00
[4,3,1] => 011
[4,2,2] => 000
[4,2,1,1] => 0011
[4,1,1,1,1] => 01111
[3,3,2] => 110
[3,3,1,1] => 1111
[3,2,2,1] => 1001
[3,2,1,1,1] => 10111
[3,1,1,1,1,1] => 111111
[2,2,2,2] => 0000
[2,2,2,1,1] => 00011
[2,2,1,1,1,1] => 001111
[2,1,1,1,1,1,1] => 0111111
[1,1,1,1,1,1,1,1] => 11111111
[9] => 1
[8,1] => 01
[7,2] => 10
[7,1,1] => 111
[6,3] => 01
[6,2,1] => 001
[6,1,1,1] => 0111
[5,4] => 10
[5,3,1] => 111
[5,2,2] => 100
[5,2,1,1] => 1011
[5,1,1,1,1] => 11111
[4,4,1] => 001
[4,3,2] => 010
[4,3,1,1] => 0111
[4,2,2,1] => 0001
[4,2,1,1,1] => 00111
[4,1,1,1,1,1] => 011111
[3,3,3] => 111
[3,3,2,1] => 1101
[3,3,1,1,1] => 11111
[3,2,2,2] => 1000
[3,2,2,1,1] => 10011
[3,2,1,1,1,1] => 101111
[3,1,1,1,1,1,1] => 1111111
[2,2,2,2,1] => 00001
[2,2,2,1,1,1] => 000111
[2,2,1,1,1,1,1] => 0011111
[2,1,1,1,1,1,1,1] => 01111111
[1,1,1,1,1,1,1,1,1] => 111111111
[10] => 0
[9,1] => 11
[8,2] => 00
[8,1,1] => 011
[7,3] => 11
>>> Load all 1211 entries. <<<
[7,2,1] => 101
[7,1,1,1] => 1111
[6,4] => 00
[6,3,1] => 011
[6,2,2] => 000
[6,2,1,1] => 0011
[6,1,1,1,1] => 01111
[5,5] => 11
[5,4,1] => 101
[5,3,2] => 110
[5,3,1,1] => 1111
[5,2,2,1] => 1001
[5,2,1,1,1] => 10111
[5,1,1,1,1,1] => 111111
[4,4,2] => 000
[4,4,1,1] => 0011
[4,3,3] => 011
[4,3,2,1] => 0101
[4,3,1,1,1] => 01111
[4,2,2,2] => 0000
[4,2,2,1,1] => 00011
[4,2,1,1,1,1] => 001111
[4,1,1,1,1,1,1] => 0111111
[3,3,3,1] => 1111
[3,3,2,2] => 1100
[3,3,2,1,1] => 11011
[3,3,1,1,1,1] => 111111
[3,2,2,2,1] => 10001
[3,2,2,1,1,1] => 100111
[3,2,1,1,1,1,1] => 1011111
[3,1,1,1,1,1,1,1] => 11111111
[2,2,2,2,2] => 00000
[2,2,2,2,1,1] => 000011
[2,2,2,1,1,1,1] => 0001111
[2,2,1,1,1,1,1,1] => 00111111
[2,1,1,1,1,1,1,1,1] => 011111111
[1,1,1,1,1,1,1,1,1,1] => 1111111111
[11] => 1
[10,1] => 01
[9,2] => 10
[9,1,1] => 111
[8,3] => 01
[8,2,1] => 001
[8,1,1,1] => 0111
[7,4] => 10
[7,3,1] => 111
[7,2,2] => 100
[7,2,1,1] => 1011
[7,1,1,1,1] => 11111
[6,5] => 01
[6,4,1] => 001
[6,3,2] => 010
[6,3,1,1] => 0111
[6,2,2,1] => 0001
[6,2,1,1,1] => 00111
[6,1,1,1,1,1] => 011111
[5,5,1] => 111
[5,4,2] => 100
[5,4,1,1] => 1011
[5,3,3] => 111
[5,3,2,1] => 1101
[5,3,1,1,1] => 11111
[5,2,2,2] => 1000
[5,2,2,1,1] => 10011
[5,2,1,1,1,1] => 101111
[5,1,1,1,1,1,1] => 1111111
[4,4,3] => 001
[4,4,2,1] => 0001
[4,4,1,1,1] => 00111
[4,3,3,1] => 0111
[4,3,2,2] => 0100
[4,3,2,1,1] => 01011
[4,3,1,1,1,1] => 011111
[4,2,2,2,1] => 00001
[4,2,2,1,1,1] => 000111
[4,2,1,1,1,1,1] => 0011111
[4,1,1,1,1,1,1,1] => 01111111
[3,3,3,2] => 1110
[3,3,3,1,1] => 11111
[3,3,2,2,1] => 11001
[3,3,2,1,1,1] => 110111
[3,3,1,1,1,1,1] => 1111111
[3,2,2,2,2] => 10000
[3,2,2,2,1,1] => 100011
[3,2,2,1,1,1,1] => 1001111
[3,2,1,1,1,1,1,1] => 10111111
[3,1,1,1,1,1,1,1,1] => 111111111
[2,2,2,2,2,1] => 000001
[2,2,2,2,1,1,1] => 0000111
[2,2,2,1,1,1,1,1] => 00011111
[2,2,1,1,1,1,1,1,1] => 001111111
[2,1,1,1,1,1,1,1,1,1] => 0111111111
[1,1,1,1,1,1,1,1,1,1,1] => 11111111111
[12] => 0
[11,1] => 11
[10,2] => 00
[10,1,1] => 011
[9,3] => 11
[9,2,1] => 101
[9,1,1,1] => 1111
[8,4] => 00
[8,3,1] => 011
[8,2,2] => 000
[8,2,1,1] => 0011
[8,1,1,1,1] => 01111
[7,5] => 11
[7,4,1] => 101
[7,3,2] => 110
[7,3,1,1] => 1111
[7,2,2,1] => 1001
[7,2,1,1,1] => 10111
[7,1,1,1,1,1] => 111111
[6,6] => 00
[6,5,1] => 011
[6,4,2] => 000
[6,4,1,1] => 0011
[6,3,3] => 011
[6,3,2,1] => 0101
[6,3,1,1,1] => 01111
[6,2,2,2] => 0000
[6,2,2,1,1] => 00011
[6,2,1,1,1,1] => 001111
[6,1,1,1,1,1,1] => 0111111
[5,5,2] => 110
[5,5,1,1] => 1111
[5,4,3] => 101
[5,4,2,1] => 1001
[5,4,1,1,1] => 10111
[5,3,3,1] => 1111
[5,3,2,2] => 1100
[5,3,2,1,1] => 11011
[5,3,1,1,1,1] => 111111
[5,2,2,2,1] => 10001
[5,2,2,1,1,1] => 100111
[5,2,1,1,1,1,1] => 1011111
[5,1,1,1,1,1,1,1] => 11111111
[4,4,4] => 000
[4,4,3,1] => 0011
[4,4,2,2] => 0000
[4,4,2,1,1] => 00011
[4,4,1,1,1,1] => 001111
[4,3,3,2] => 0110
[4,3,3,1,1] => 01111
[4,3,2,2,1] => 01001
[4,3,2,1,1,1] => 010111
[4,3,1,1,1,1,1] => 0111111
[4,2,2,2,2] => 00000
[4,2,2,2,1,1] => 000011
[4,2,2,1,1,1,1] => 0001111
[4,2,1,1,1,1,1,1] => 00111111
[4,1,1,1,1,1,1,1,1] => 011111111
[3,3,3,3] => 1111
[3,3,3,2,1] => 11101
[3,3,3,1,1,1] => 111111
[3,3,2,2,2] => 11000
[3,3,2,2,1,1] => 110011
[3,3,2,1,1,1,1] => 1101111
[3,3,1,1,1,1,1,1] => 11111111
[3,2,2,2,2,1] => 100001
[3,2,2,2,1,1,1] => 1000111
[3,2,2,1,1,1,1,1] => 10011111
[3,2,1,1,1,1,1,1,1] => 101111111
[3,1,1,1,1,1,1,1,1,1] => 1111111111
[2,2,2,2,2,2] => 000000
[2,2,2,2,2,1,1] => 0000011
[2,2,2,2,1,1,1,1] => 00001111
[2,2,2,1,1,1,1,1,1] => 000111111
[2,2,1,1,1,1,1,1,1,1] => 0011111111
[2,1,1,1,1,1,1,1,1,1,1] => 01111111111
[1,1,1,1,1,1,1,1,1,1,1,1] => 111111111111
[13] => 1
[12,1] => 01
[11,2] => 10
[11,1,1] => 111
[10,3] => 01
[10,2,1] => 001
[10,1,1,1] => 0111
[9,4] => 10
[9,3,1] => 111
[9,2,2] => 100
[9,2,1,1] => 1011
[9,1,1,1,1] => 11111
[8,5] => 01
[8,4,1] => 001
[8,3,2] => 010
[8,3,1,1] => 0111
[8,2,2,1] => 0001
[8,2,1,1,1] => 00111
[8,1,1,1,1,1] => 011111
[7,6] => 10
[7,5,1] => 111
[7,4,2] => 100
[7,4,1,1] => 1011
[7,3,3] => 111
[7,3,2,1] => 1101
[7,3,1,1,1] => 11111
[7,2,2,2] => 1000
[7,2,2,1,1] => 10011
[7,2,1,1,1,1] => 101111
[7,1,1,1,1,1,1] => 1111111
[6,6,1] => 001
[6,5,2] => 010
[6,5,1,1] => 0111
[6,4,3] => 001
[6,4,2,1] => 0001
[6,4,1,1,1] => 00111
[6,3,3,1] => 0111
[6,3,2,2] => 0100
[6,3,2,1,1] => 01011
[6,3,1,1,1,1] => 011111
[6,2,2,2,1] => 00001
[6,2,2,1,1,1] => 000111
[6,2,1,1,1,1,1] => 0011111
[6,1,1,1,1,1,1,1] => 01111111
[5,5,3] => 111
[5,5,2,1] => 1101
[5,5,1,1,1] => 11111
[5,4,4] => 100
[5,4,3,1] => 1011
[5,4,2,2] => 1000
[5,4,2,1,1] => 10011
[5,4,1,1,1,1] => 101111
[5,3,3,2] => 1110
[5,3,3,1,1] => 11111
[5,3,2,2,1] => 11001
[5,3,2,1,1,1] => 110111
[5,3,1,1,1,1,1] => 1111111
[5,2,2,2,2] => 10000
[5,2,2,2,1,1] => 100011
[5,2,2,1,1,1,1] => 1001111
[5,2,1,1,1,1,1,1] => 10111111
[5,1,1,1,1,1,1,1,1] => 111111111
[4,4,4,1] => 0001
[4,4,3,2] => 0010
[4,4,3,1,1] => 00111
[4,4,2,2,1] => 00001
[4,4,2,1,1,1] => 000111
[4,4,1,1,1,1,1] => 0011111
[4,3,3,3] => 0111
[4,3,3,2,1] => 01101
[4,3,3,1,1,1] => 011111
[4,3,2,2,2] => 01000
[4,3,2,2,1,1] => 010011
[4,3,2,1,1,1,1] => 0101111
[4,3,1,1,1,1,1,1] => 01111111
[4,2,2,2,2,1] => 000001
[4,2,2,2,1,1,1] => 0000111
[4,2,2,1,1,1,1,1] => 00011111
[4,2,1,1,1,1,1,1,1] => 001111111
[4,1,1,1,1,1,1,1,1,1] => 0111111111
[3,3,3,3,1] => 11111
[3,3,3,2,2] => 11100
[3,3,3,2,1,1] => 111011
[3,3,3,1,1,1,1] => 1111111
[3,3,2,2,2,1] => 110001
[3,3,2,2,1,1,1] => 1100111
[3,3,2,1,1,1,1,1] => 11011111
[3,3,1,1,1,1,1,1,1] => 111111111
[3,2,2,2,2,2] => 100000
[3,2,2,2,2,1,1] => 1000011
[3,2,2,2,1,1,1,1] => 10001111
[3,2,2,1,1,1,1,1,1] => 100111111
[3,2,1,1,1,1,1,1,1,1] => 1011111111
[3,1,1,1,1,1,1,1,1,1,1] => 11111111111
[2,2,2,2,2,2,1] => 0000001
[2,2,2,2,2,1,1,1] => 00000111
[2,2,2,2,1,1,1,1,1] => 000011111
[2,2,2,1,1,1,1,1,1,1] => 0001111111
[2,2,1,1,1,1,1,1,1,1,1] => 00111111111
[2,1,1,1,1,1,1,1,1,1,1,1] => 011111111111
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 1111111111111
[14] => 0
[13,1] => 11
[12,2] => 00
[12,1,1] => 011
[11,3] => 11
[11,2,1] => 101
[11,1,1,1] => 1111
[10,4] => 00
[10,3,1] => 011
[10,2,2] => 000
[10,2,1,1] => 0011
[10,1,1,1,1] => 01111
[9,5] => 11
[9,4,1] => 101
[9,3,2] => 110
[9,3,1,1] => 1111
[9,2,2,1] => 1001
[9,2,1,1,1] => 10111
[9,1,1,1,1,1] => 111111
[8,6] => 00
[8,5,1] => 011
[8,4,2] => 000
[8,4,1,1] => 0011
[8,3,3] => 011
[8,3,2,1] => 0101
[8,3,1,1,1] => 01111
[8,2,2,2] => 0000
[8,2,2,1,1] => 00011
[8,2,1,1,1,1] => 001111
[8,1,1,1,1,1,1] => 0111111
[7,7] => 11
[7,6,1] => 101
[7,5,2] => 110
[7,5,1,1] => 1111
[7,4,3] => 101
[7,4,2,1] => 1001
[7,4,1,1,1] => 10111
[7,3,3,1] => 1111
[7,3,2,2] => 1100
[7,3,2,1,1] => 11011
[7,3,1,1,1,1] => 111111
[7,2,2,2,1] => 10001
[7,2,2,1,1,1] => 100111
[7,2,1,1,1,1,1] => 1011111
[7,1,1,1,1,1,1,1] => 11111111
[6,6,2] => 000
[6,6,1,1] => 0011
[6,5,3] => 011
[6,5,2,1] => 0101
[6,5,1,1,1] => 01111
[6,4,4] => 000
[6,4,3,1] => 0011
[6,4,2,2] => 0000
[6,4,2,1,1] => 00011
[6,4,1,1,1,1] => 001111
[6,3,3,2] => 0110
[6,3,3,1,1] => 01111
[6,3,2,2,1] => 01001
[6,3,2,1,1,1] => 010111
[6,3,1,1,1,1,1] => 0111111
[6,2,2,2,2] => 00000
[6,2,2,2,1,1] => 000011
[6,2,2,1,1,1,1] => 0001111
[6,2,1,1,1,1,1,1] => 00111111
[6,1,1,1,1,1,1,1,1] => 011111111
[5,5,4] => 110
[5,5,3,1] => 1111
[5,5,2,2] => 1100
[5,5,2,1,1] => 11011
[5,5,1,1,1,1] => 111111
[5,4,4,1] => 1001
[5,4,3,2] => 1010
[5,4,3,1,1] => 10111
[5,4,2,2,1] => 10001
[5,4,2,1,1,1] => 100111
[5,4,1,1,1,1,1] => 1011111
[5,3,3,3] => 1111
[5,3,3,2,1] => 11101
[5,3,3,1,1,1] => 111111
[5,3,2,2,2] => 11000
[5,3,2,2,1,1] => 110011
[5,3,2,1,1,1,1] => 1101111
[5,3,1,1,1,1,1,1] => 11111111
[5,2,2,2,2,1] => 100001
[5,2,2,2,1,1,1] => 1000111
[5,2,2,1,1,1,1,1] => 10011111
[5,2,1,1,1,1,1,1,1] => 101111111
[5,1,1,1,1,1,1,1,1,1] => 1111111111
[4,4,4,2] => 0000
[4,4,4,1,1] => 00011
[4,4,3,3] => 0011
[4,4,3,2,1] => 00101
[4,4,3,1,1,1] => 001111
[4,4,2,2,2] => 00000
[4,4,2,2,1,1] => 000011
[4,4,2,1,1,1,1] => 0001111
[4,4,1,1,1,1,1,1] => 00111111
[4,3,3,3,1] => 01111
[4,3,3,2,2] => 01100
[4,3,3,2,1,1] => 011011
[4,3,3,1,1,1,1] => 0111111
[4,3,2,2,2,1] => 010001
[4,3,2,2,1,1,1] => 0100111
[4,3,2,1,1,1,1,1] => 01011111
[4,3,1,1,1,1,1,1,1] => 011111111
[4,2,2,2,2,2] => 000000
[4,2,2,2,2,1,1] => 0000011
[4,2,2,2,1,1,1,1] => 00001111
[4,2,2,1,1,1,1,1,1] => 000111111
[4,2,1,1,1,1,1,1,1,1] => 0011111111
[4,1,1,1,1,1,1,1,1,1,1] => 01111111111
[3,3,3,3,2] => 11110
[3,3,3,3,1,1] => 111111
[3,3,3,2,2,1] => 111001
[3,3,3,2,1,1,1] => 1110111
[3,3,3,1,1,1,1,1] => 11111111
[3,3,2,2,2,2] => 110000
[3,3,2,2,2,1,1] => 1100011
[3,3,2,2,1,1,1,1] => 11001111
[3,3,2,1,1,1,1,1,1] => 110111111
[3,3,1,1,1,1,1,1,1,1] => 1111111111
[3,2,2,2,2,2,1] => 1000001
[3,2,2,2,2,1,1,1] => 10000111
[3,2,2,2,1,1,1,1,1] => 100011111
[3,2,2,1,1,1,1,1,1,1] => 1001111111
[3,2,1,1,1,1,1,1,1,1,1] => 10111111111
[3,1,1,1,1,1,1,1,1,1,1,1] => 111111111111
[2,2,2,2,2,2,2] => 0000000
[2,2,2,2,2,2,1,1] => 00000011
[2,2,2,2,2,1,1,1,1] => 000001111
[2,2,2,2,1,1,1,1,1,1] => 0000111111
[2,2,2,1,1,1,1,1,1,1,1] => 00011111111
[2,2,1,1,1,1,1,1,1,1,1,1] => 001111111111
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 0111111111111
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 11111111111111
[15] => 1
[14,1] => 01
[13,2] => 10
[13,1,1] => 111
[12,3] => 01
[12,2,1] => 001
[12,1,1,1] => 0111
[11,4] => 10
[11,3,1] => 111
[11,2,2] => 100
[11,2,1,1] => 1011
[11,1,1,1,1] => 11111
[10,5] => 01
[10,4,1] => 001
[10,3,2] => 010
[10,3,1,1] => 0111
[10,2,2,1] => 0001
[10,2,1,1,1] => 00111
[10,1,1,1,1,1] => 011111
[9,6] => 10
[9,5,1] => 111
[9,4,2] => 100
[9,4,1,1] => 1011
[9,3,3] => 111
[9,3,2,1] => 1101
[9,3,1,1,1] => 11111
[9,2,2,2] => 1000
[9,2,2,1,1] => 10011
[9,2,1,1,1,1] => 101111
[9,1,1,1,1,1,1] => 1111111
[8,7] => 01
[8,6,1] => 001
[8,5,2] => 010
[8,5,1,1] => 0111
[8,4,3] => 001
[8,4,2,1] => 0001
[8,4,1,1,1] => 00111
[8,3,3,1] => 0111
[8,3,2,2] => 0100
[8,3,2,1,1] => 01011
[8,3,1,1,1,1] => 011111
[8,2,2,2,1] => 00001
[8,2,2,1,1,1] => 000111
[8,2,1,1,1,1,1] => 0011111
[8,1,1,1,1,1,1,1] => 01111111
[7,7,1] => 111
[7,6,2] => 100
[7,6,1,1] => 1011
[7,5,3] => 111
[7,5,2,1] => 1101
[7,5,1,1,1] => 11111
[7,4,4] => 100
[7,4,3,1] => 1011
[7,4,2,2] => 1000
[7,4,2,1,1] => 10011
[7,4,1,1,1,1] => 101111
[7,3,3,2] => 1110
[7,3,3,1,1] => 11111
[7,3,2,2,1] => 11001
[7,3,2,1,1,1] => 110111
[7,3,1,1,1,1,1] => 1111111
[7,2,2,2,2] => 10000
[7,2,2,2,1,1] => 100011
[7,2,2,1,1,1,1] => 1001111
[7,2,1,1,1,1,1,1] => 10111111
[7,1,1,1,1,1,1,1,1] => 111111111
[6,6,3] => 001
[6,6,2,1] => 0001
[6,6,1,1,1] => 00111
[6,5,4] => 010
[6,5,3,1] => 0111
[6,5,2,2] => 0100
[6,5,2,1,1] => 01011
[6,5,1,1,1,1] => 011111
[6,4,4,1] => 0001
[6,4,3,2] => 0010
[6,4,3,1,1] => 00111
[6,4,2,2,1] => 00001
[6,4,2,1,1,1] => 000111
[6,4,1,1,1,1,1] => 0011111
[6,3,3,3] => 0111
[6,3,3,2,1] => 01101
[6,3,3,1,1,1] => 011111
[6,3,2,2,2] => 01000
[6,3,2,2,1,1] => 010011
[6,3,2,1,1,1,1] => 0101111
[6,3,1,1,1,1,1,1] => 01111111
[6,2,2,2,2,1] => 000001
[6,2,2,2,1,1,1] => 0000111
[6,2,2,1,1,1,1,1] => 00011111
[6,2,1,1,1,1,1,1,1] => 001111111
[6,1,1,1,1,1,1,1,1,1] => 0111111111
[5,5,5] => 111
[5,5,4,1] => 1101
[5,5,3,2] => 1110
[5,5,3,1,1] => 11111
[5,5,2,2,1] => 11001
[5,5,2,1,1,1] => 110111
[5,5,1,1,1,1,1] => 1111111
[5,4,4,2] => 1000
[5,4,4,1,1] => 10011
[5,4,3,3] => 1011
[5,4,3,2,1] => 10101
[5,4,3,1,1,1] => 101111
[5,4,2,2,2] => 10000
[5,4,2,2,1,1] => 100011
[5,4,2,1,1,1,1] => 1001111
[5,4,1,1,1,1,1,1] => 10111111
[5,3,3,3,1] => 11111
[5,3,3,2,2] => 11100
[5,3,3,2,1,1] => 111011
[5,3,3,1,1,1,1] => 1111111
[5,3,2,2,2,1] => 110001
[5,3,2,2,1,1,1] => 1100111
[5,3,2,1,1,1,1,1] => 11011111
[5,3,1,1,1,1,1,1,1] => 111111111
[5,2,2,2,2,2] => 100000
[5,2,2,2,2,1,1] => 1000011
[5,2,2,2,1,1,1,1] => 10001111
[5,2,2,1,1,1,1,1,1] => 100111111
[5,2,1,1,1,1,1,1,1,1] => 1011111111
[5,1,1,1,1,1,1,1,1,1,1] => 11111111111
[4,4,4,3] => 0001
[4,4,4,2,1] => 00001
[4,4,4,1,1,1] => 000111
[4,4,3,3,1] => 00111
[4,4,3,2,2] => 00100
[4,4,3,2,1,1] => 001011
[4,4,3,1,1,1,1] => 0011111
[4,4,2,2,2,1] => 000001
[4,4,2,2,1,1,1] => 0000111
[4,4,2,1,1,1,1,1] => 00011111
[4,4,1,1,1,1,1,1,1] => 001111111
[4,3,3,3,2] => 01110
[4,3,3,3,1,1] => 011111
[4,3,3,2,2,1] => 011001
[4,3,3,2,1,1,1] => 0110111
[4,3,3,1,1,1,1,1] => 01111111
[4,3,2,2,2,2] => 010000
[4,3,2,2,2,1,1] => 0100011
[4,3,2,2,1,1,1,1] => 01001111
[4,3,2,1,1,1,1,1,1] => 010111111
[4,3,1,1,1,1,1,1,1,1] => 0111111111
[4,2,2,2,2,2,1] => 0000001
[4,2,2,2,2,1,1,1] => 00000111
[4,2,2,2,1,1,1,1,1] => 000011111
[4,2,2,1,1,1,1,1,1,1] => 0001111111
[4,2,1,1,1,1,1,1,1,1,1] => 00111111111
[4,1,1,1,1,1,1,1,1,1,1,1] => 011111111111
[3,3,3,3,3] => 11111
[3,3,3,3,2,1] => 111101
[3,3,3,3,1,1,1] => 1111111
[3,3,3,2,2,2] => 111000
[3,3,3,2,2,1,1] => 1110011
[3,3,3,2,1,1,1,1] => 11101111
[3,3,3,1,1,1,1,1,1] => 111111111
[3,3,2,2,2,2,1] => 1100001
[3,3,2,2,2,1,1,1] => 11000111
[3,3,2,2,1,1,1,1,1] => 110011111
[3,3,2,1,1,1,1,1,1,1] => 1101111111
[3,3,1,1,1,1,1,1,1,1,1] => 11111111111
[3,2,2,2,2,2,2] => 1000000
[3,2,2,2,2,2,1,1] => 10000011
[3,2,2,2,2,1,1,1,1] => 100001111
[3,2,2,2,1,1,1,1,1,1] => 1000111111
[3,2,2,1,1,1,1,1,1,1,1] => 10011111111
[3,2,1,1,1,1,1,1,1,1,1,1] => 101111111111
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 1111111111111
[2,2,2,2,2,2,2,1] => 00000001
[2,2,2,2,2,2,1,1,1] => 000000111
[2,2,2,2,2,1,1,1,1,1] => 0000011111
[2,2,2,2,1,1,1,1,1,1,1] => 00001111111
[2,2,2,1,1,1,1,1,1,1,1,1] => 000111111111
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 0011111111111
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 01111111111111
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 111111111111111
[16] => 0
[15,1] => 11
[14,2] => 00
[14,1,1] => 011
[13,3] => 11
[13,2,1] => 101
[13,1,1,1] => 1111
[12,4] => 00
[12,3,1] => 011
[12,2,2] => 000
[12,2,1,1] => 0011
[12,1,1,1,1] => 01111
[11,5] => 11
[11,4,1] => 101
[11,3,2] => 110
[11,3,1,1] => 1111
[11,2,2,1] => 1001
[11,2,1,1,1] => 10111
[11,1,1,1,1,1] => 111111
[10,6] => 00
[10,5,1] => 011
[10,4,2] => 000
[10,4,1,1] => 0011
[10,3,3] => 011
[10,3,2,1] => 0101
[10,3,1,1,1] => 01111
[10,2,2,2] => 0000
[10,2,2,1,1] => 00011
[10,2,1,1,1,1] => 001111
[10,1,1,1,1,1,1] => 0111111
[9,7] => 11
[9,6,1] => 101
[9,5,2] => 110
[9,5,1,1] => 1111
[9,4,3] => 101
[9,4,2,1] => 1001
[9,4,1,1,1] => 10111
[9,3,3,1] => 1111
[9,3,2,2] => 1100
[9,3,2,1,1] => 11011
[9,3,1,1,1,1] => 111111
[9,2,2,2,1] => 10001
[9,2,2,1,1,1] => 100111
[9,2,1,1,1,1,1] => 1011111
[9,1,1,1,1,1,1,1] => 11111111
[8,8] => 00
[8,7,1] => 011
[8,6,2] => 000
[8,6,1,1] => 0011
[8,5,3] => 011
[8,5,2,1] => 0101
[8,5,1,1,1] => 01111
[8,4,4] => 000
[8,4,3,1] => 0011
[8,4,2,2] => 0000
[8,4,2,1,1] => 00011
[8,4,1,1,1,1] => 001111
[8,3,3,2] => 0110
[8,3,3,1,1] => 01111
[8,3,2,2,1] => 01001
[8,3,2,1,1,1] => 010111
[8,3,1,1,1,1,1] => 0111111
[8,2,2,2,2] => 00000
[8,2,2,2,1,1] => 000011
[8,2,2,1,1,1,1] => 0001111
[8,2,1,1,1,1,1,1] => 00111111
[8,1,1,1,1,1,1,1,1] => 011111111
[7,7,2] => 110
[7,7,1,1] => 1111
[7,6,3] => 101
[7,6,2,1] => 1001
[7,6,1,1,1] => 10111
[7,5,4] => 110
[7,5,3,1] => 1111
[7,5,2,2] => 1100
[7,5,2,1,1] => 11011
[7,5,1,1,1,1] => 111111
[7,4,4,1] => 1001
[7,4,3,2] => 1010
[7,4,3,1,1] => 10111
[7,4,2,2,1] => 10001
[7,4,2,1,1,1] => 100111
[7,4,1,1,1,1,1] => 1011111
[7,3,3,3] => 1111
[7,3,3,2,1] => 11101
[7,3,3,1,1,1] => 111111
[7,3,2,2,2] => 11000
[7,3,2,2,1,1] => 110011
[7,3,2,1,1,1,1] => 1101111
[7,3,1,1,1,1,1,1] => 11111111
[7,2,2,2,2,1] => 100001
[7,2,2,2,1,1,1] => 1000111
[7,2,2,1,1,1,1,1] => 10011111
[7,2,1,1,1,1,1,1,1] => 101111111
[7,1,1,1,1,1,1,1,1,1] => 1111111111
[6,6,4] => 000
[6,6,3,1] => 0011
[6,6,2,2] => 0000
[6,6,2,1,1] => 00011
[6,6,1,1,1,1] => 001111
[6,5,5] => 011
[6,5,4,1] => 0101
[6,5,3,2] => 0110
[6,5,3,1,1] => 01111
[6,5,2,2,1] => 01001
[6,5,2,1,1,1] => 010111
[6,5,1,1,1,1,1] => 0111111
[6,4,4,2] => 0000
[6,4,4,1,1] => 00011
[6,4,3,3] => 0011
[6,4,3,2,1] => 00101
[6,4,3,1,1,1] => 001111
[6,4,2,2,2] => 00000
[6,4,2,2,1,1] => 000011
[6,4,2,1,1,1,1] => 0001111
[6,4,1,1,1,1,1,1] => 00111111
[6,3,3,3,1] => 01111
[6,3,3,2,2] => 01100
[6,3,3,2,1,1] => 011011
[6,3,3,1,1,1,1] => 0111111
[6,3,2,2,2,1] => 010001
[6,3,2,2,1,1,1] => 0100111
[6,3,2,1,1,1,1,1] => 01011111
[6,3,1,1,1,1,1,1,1] => 011111111
[6,2,2,2,2,2] => 000000
[6,2,2,2,2,1,1] => 0000011
[6,2,2,2,1,1,1,1] => 00001111
[6,2,2,1,1,1,1,1,1] => 000111111
[6,2,1,1,1,1,1,1,1,1] => 0011111111
[6,1,1,1,1,1,1,1,1,1,1] => 01111111111
[5,5,5,1] => 1111
[5,5,4,2] => 1100
[5,5,4,1,1] => 11011
[5,5,3,3] => 1111
[5,5,3,2,1] => 11101
[5,5,3,1,1,1] => 111111
[5,5,2,2,2] => 11000
[5,5,2,2,1,1] => 110011
[5,5,2,1,1,1,1] => 1101111
[5,5,1,1,1,1,1,1] => 11111111
[5,4,4,3] => 1001
[5,4,4,2,1] => 10001
[5,4,4,1,1,1] => 100111
[5,4,3,3,1] => 10111
[5,4,3,2,2] => 10100
[5,4,3,2,1,1] => 101011
[5,4,3,1,1,1,1] => 1011111
[5,4,2,2,2,1] => 100001
[5,4,2,2,1,1,1] => 1000111
[5,4,2,1,1,1,1,1] => 10011111
[5,4,1,1,1,1,1,1,1] => 101111111
[5,3,3,3,2] => 11110
[5,3,3,3,1,1] => 111111
[5,3,3,2,2,1] => 111001
[5,3,3,2,1,1,1] => 1110111
[5,3,3,1,1,1,1,1] => 11111111
[5,3,2,2,2,2] => 110000
[5,3,2,2,2,1,1] => 1100011
[5,3,2,2,1,1,1,1] => 11001111
[5,3,2,1,1,1,1,1,1] => 110111111
[5,3,1,1,1,1,1,1,1,1] => 1111111111
[5,2,2,2,2,2,1] => 1000001
[5,2,2,2,2,1,1,1] => 10000111
[5,2,2,2,1,1,1,1,1] => 100011111
[5,2,2,1,1,1,1,1,1,1] => 1001111111
[5,2,1,1,1,1,1,1,1,1,1] => 10111111111
[5,1,1,1,1,1,1,1,1,1,1,1] => 111111111111
[4,4,4,4] => 0000
[4,4,4,3,1] => 00011
[4,4,4,2,2] => 00000
[4,4,4,2,1,1] => 000011
[4,4,4,1,1,1,1] => 0001111
[4,4,3,3,2] => 00110
[4,4,3,3,1,1] => 001111
[4,4,3,2,2,1] => 001001
[4,4,3,2,1,1,1] => 0010111
[4,4,3,1,1,1,1,1] => 00111111
[4,4,2,2,2,2] => 000000
[4,4,2,2,2,1,1] => 0000011
[4,4,2,2,1,1,1,1] => 00001111
[4,4,2,1,1,1,1,1,1] => 000111111
[4,4,1,1,1,1,1,1,1,1] => 0011111111
[4,3,3,3,3] => 01111
[4,3,3,3,2,1] => 011101
[4,3,3,3,1,1,1] => 0111111
[4,3,3,2,2,2] => 011000
[4,3,3,2,2,1,1] => 0110011
[4,3,3,2,1,1,1,1] => 01101111
[4,3,3,1,1,1,1,1,1] => 011111111
[4,3,2,2,2,2,1] => 0100001
[4,3,2,2,2,1,1,1] => 01000111
[4,3,2,2,1,1,1,1,1] => 010011111
[4,3,2,1,1,1,1,1,1,1] => 0101111111
[4,3,1,1,1,1,1,1,1,1,1] => 01111111111
[4,2,2,2,2,2,2] => 0000000
[4,2,2,2,2,2,1,1] => 00000011
[4,2,2,2,2,1,1,1,1] => 000001111
[4,2,2,2,1,1,1,1,1,1] => 0000111111
[4,2,2,1,1,1,1,1,1,1,1] => 00011111111
[4,2,1,1,1,1,1,1,1,1,1,1] => 001111111111
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 0111111111111
[3,3,3,3,3,1] => 111111
[3,3,3,3,2,2] => 111100
[3,3,3,3,2,1,1] => 1111011
[3,3,3,3,1,1,1,1] => 11111111
[3,3,3,2,2,2,1] => 1110001
[3,3,3,2,2,1,1,1] => 11100111
[3,3,3,2,1,1,1,1,1] => 111011111
[3,3,3,1,1,1,1,1,1,1] => 1111111111
[3,3,2,2,2,2,2] => 1100000
[3,3,2,2,2,2,1,1] => 11000011
[3,3,2,2,2,1,1,1,1] => 110001111
[3,3,2,2,1,1,1,1,1,1] => 1100111111
[3,3,2,1,1,1,1,1,1,1,1] => 11011111111
[3,3,1,1,1,1,1,1,1,1,1,1] => 111111111111
[3,2,2,2,2,2,2,1] => 10000001
[3,2,2,2,2,2,1,1,1] => 100000111
[3,2,2,2,2,1,1,1,1,1] => 1000011111
[3,2,2,2,1,1,1,1,1,1,1] => 10001111111
[3,2,2,1,1,1,1,1,1,1,1,1] => 100111111111
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 1011111111111
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 11111111111111
[2,2,2,2,2,2,2,2] => 00000000
[2,2,2,2,2,2,2,1,1] => 000000011
[2,2,2,2,2,2,1,1,1,1] => 0000001111
[2,2,2,2,2,1,1,1,1,1,1] => 00000111111
[2,2,2,2,1,1,1,1,1,1,1,1] => 000011111111
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 0001111111111
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 00111111111111
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 011111111111111
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1111111111111111
[17] => 1
[16,1] => 01
[15,2] => 10
[15,1,1] => 111
[14,3] => 01
[14,2,1] => 001
[14,1,1,1] => 0111
[13,4] => 10
[13,3,1] => 111
[13,2,2] => 100
[13,2,1,1] => 1011
[13,1,1,1,1] => 11111
[12,5] => 01
[12,4,1] => 001
[12,3,2] => 010
[12,3,1,1] => 0111
[12,2,2,1] => 0001
[12,2,1,1,1] => 00111
[12,1,1,1,1,1] => 011111
[11,6] => 10
[11,5,1] => 111
[11,4,2] => 100
[11,4,1,1] => 1011
[11,3,3] => 111
[11,3,2,1] => 1101
[11,3,1,1,1] => 11111
[11,2,2,2] => 1000
[11,2,2,1,1] => 10011
[11,2,1,1,1,1] => 101111
[11,1,1,1,1,1,1] => 1111111
[10,7] => 01
[10,6,1] => 001
[10,5,2] => 010
[10,5,1,1] => 0111
[10,4,3] => 001
[10,4,2,1] => 0001
[10,4,1,1,1] => 00111
[10,3,3,1] => 0111
[10,3,2,2] => 0100
[10,3,2,1,1] => 01011
[10,3,1,1,1,1] => 011111
[10,2,2,2,1] => 00001
[10,2,2,1,1,1] => 000111
[10,2,1,1,1,1,1] => 0011111
[10,1,1,1,1,1,1,1] => 01111111
[9,8] => 10
[9,7,1] => 111
[9,6,2] => 100
[9,6,1,1] => 1011
[9,5,3] => 111
[9,5,2,1] => 1101
[9,5,1,1,1] => 11111
[9,4,4] => 100
[9,4,3,1] => 1011
[9,4,2,2] => 1000
[9,4,2,1,1] => 10011
[9,4,1,1,1,1] => 101111
[9,3,3,2] => 1110
[9,3,3,1,1] => 11111
[9,3,2,2,1] => 11001
[9,3,2,1,1,1] => 110111
[9,3,1,1,1,1,1] => 1111111
[9,2,2,2,2] => 10000
[9,2,2,2,1,1] => 100011
[9,2,2,1,1,1,1] => 1001111
[9,2,1,1,1,1,1,1] => 10111111
[9,1,1,1,1,1,1,1,1] => 111111111
[8,8,1] => 001
[8,7,2] => 010
[8,7,1,1] => 0111
[8,6,3] => 001
[8,6,2,1] => 0001
[8,6,1,1,1] => 00111
[8,5,4] => 010
[8,5,3,1] => 0111
[8,5,2,2] => 0100
[8,5,2,1,1] => 01011
[8,5,1,1,1,1] => 011111
[8,4,4,1] => 0001
[8,4,3,2] => 0010
[8,4,3,1,1] => 00111
[8,4,2,2,1] => 00001
[8,4,2,1,1,1] => 000111
[8,4,1,1,1,1,1] => 0011111
[8,3,3,3] => 0111
[8,3,3,2,1] => 01101
[8,3,3,1,1,1] => 011111
[8,3,2,2,2] => 01000
[8,3,2,2,1,1] => 010011
[8,3,2,1,1,1,1] => 0101111
[8,3,1,1,1,1,1,1] => 01111111
[8,2,2,2,2,1] => 000001
[8,2,2,2,1,1,1] => 0000111
[8,2,2,1,1,1,1,1] => 00011111
[8,2,1,1,1,1,1,1,1] => 001111111
[8,1,1,1,1,1,1,1,1,1] => 0111111111
[7,7,3] => 111
[7,7,2,1] => 1101
[7,7,1,1,1] => 11111
[7,6,4] => 100
[7,6,3,1] => 1011
[7,6,2,2] => 1000
[7,6,2,1,1] => 10011
[7,6,1,1,1,1] => 101111
[7,5,5] => 111
[7,5,4,1] => 1101
[7,5,3,2] => 1110
[7,5,3,1,1] => 11111
[7,5,2,2,1] => 11001
[7,5,2,1,1,1] => 110111
[7,5,1,1,1,1,1] => 1111111
[7,4,4,2] => 1000
[7,4,4,1,1] => 10011
[7,4,3,3] => 1011
[7,4,3,2,1] => 10101
[7,4,3,1,1,1] => 101111
[7,4,2,2,2] => 10000
[7,4,2,2,1,1] => 100011
[7,4,2,1,1,1,1] => 1001111
[7,4,1,1,1,1,1,1] => 10111111
[7,3,3,3,1] => 11111
[7,3,3,2,2] => 11100
[7,3,3,2,1,1] => 111011
[7,3,3,1,1,1,1] => 1111111
[7,3,2,2,2,1] => 110001
[7,3,2,2,1,1,1] => 1100111
[7,3,2,1,1,1,1,1] => 11011111
[7,3,1,1,1,1,1,1,1] => 111111111
[7,2,2,2,2,2] => 100000
[7,2,2,2,2,1,1] => 1000011
[7,2,2,2,1,1,1,1] => 10001111
[7,2,2,1,1,1,1,1,1] => 100111111
[7,2,1,1,1,1,1,1,1,1] => 1011111111
[7,1,1,1,1,1,1,1,1,1,1] => 11111111111
[6,6,5] => 001
[6,6,4,1] => 0001
[6,6,3,2] => 0010
[6,6,3,1,1] => 00111
[6,6,2,2,1] => 00001
[6,6,2,1,1,1] => 000111
[6,6,1,1,1,1,1] => 0011111
[6,5,5,1] => 0111
[6,5,4,2] => 0100
[6,5,4,1,1] => 01011
[6,5,3,3] => 0111
[6,5,3,2,1] => 01101
[6,5,3,1,1,1] => 011111
[6,5,2,2,2] => 01000
[6,5,2,2,1,1] => 010011
[6,5,2,1,1,1,1] => 0101111
[6,5,1,1,1,1,1,1] => 01111111
[6,4,4,3] => 0001
[6,4,4,2,1] => 00001
[6,4,4,1,1,1] => 000111
[6,4,3,3,1] => 00111
[6,4,3,2,2] => 00100
[6,4,3,2,1,1] => 001011
[6,4,3,1,1,1,1] => 0011111
[6,4,2,2,2,1] => 000001
[6,4,2,2,1,1,1] => 0000111
[6,4,2,1,1,1,1,1] => 00011111
[6,4,1,1,1,1,1,1,1] => 001111111
[6,3,3,3,2] => 01110
[6,3,3,3,1,1] => 011111
[6,3,3,2,2,1] => 011001
[6,3,3,2,1,1,1] => 0110111
[6,3,3,1,1,1,1,1] => 01111111
[6,3,2,2,2,2] => 010000
[6,3,2,2,2,1,1] => 0100011
[6,3,2,2,1,1,1,1] => 01001111
[6,3,2,1,1,1,1,1,1] => 010111111
[6,3,1,1,1,1,1,1,1,1] => 0111111111
[6,2,2,2,2,2,1] => 0000001
[6,2,2,2,2,1,1,1] => 00000111
[6,2,2,2,1,1,1,1,1] => 000011111
[6,2,2,1,1,1,1,1,1,1] => 0001111111
[6,2,1,1,1,1,1,1,1,1,1] => 00111111111
[6,1,1,1,1,1,1,1,1,1,1,1] => 011111111111
[5,5,5,2] => 1110
[5,5,5,1,1] => 11111
[5,5,4,3] => 1101
[5,5,4,2,1] => 11001
[5,5,4,1,1,1] => 110111
[5,5,3,3,1] => 11111
[5,5,3,2,2] => 11100
[5,5,3,2,1,1] => 111011
[5,5,3,1,1,1,1] => 1111111
[5,5,2,2,2,1] => 110001
[5,5,2,2,1,1,1] => 1100111
[5,5,2,1,1,1,1,1] => 11011111
[5,5,1,1,1,1,1,1,1] => 111111111
[5,4,4,4] => 1000
[5,4,4,3,1] => 10011
[5,4,4,2,2] => 10000
[5,4,4,2,1,1] => 100011
[5,4,4,1,1,1,1] => 1001111
[5,4,3,3,2] => 10110
[5,4,3,3,1,1] => 101111
[5,4,3,2,2,1] => 101001
[5,4,3,2,1,1,1] => 1010111
[5,4,3,1,1,1,1,1] => 10111111
[5,4,2,2,2,2] => 100000
[5,4,2,2,2,1,1] => 1000011
[5,4,2,2,1,1,1,1] => 10001111
[5,4,2,1,1,1,1,1,1] => 100111111
[5,4,1,1,1,1,1,1,1,1] => 1011111111
[5,3,3,3,3] => 11111
[5,3,3,3,2,1] => 111101
[5,3,3,3,1,1,1] => 1111111
[5,3,3,2,2,2] => 111000
[5,3,3,2,2,1,1] => 1110011
[5,3,3,2,1,1,1,1] => 11101111
[5,3,3,1,1,1,1,1,1] => 111111111
[5,3,2,2,2,2,1] => 1100001
[5,3,2,2,2,1,1,1] => 11000111
[5,3,2,2,1,1,1,1,1] => 110011111
[5,3,2,1,1,1,1,1,1,1] => 1101111111
[5,3,1,1,1,1,1,1,1,1,1] => 11111111111
[5,2,2,2,2,2,2] => 1000000
[5,2,2,2,2,2,1,1] => 10000011
[5,2,2,2,2,1,1,1,1] => 100001111
[5,2,2,2,1,1,1,1,1,1] => 1000111111
[5,2,2,1,1,1,1,1,1,1,1] => 10011111111
[5,2,1,1,1,1,1,1,1,1,1,1] => 101111111111
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 1111111111111
[4,4,4,4,1] => 00001
[4,4,4,3,2] => 00010
[4,4,4,3,1,1] => 000111
[4,4,4,2,2,1] => 000001
[4,4,4,2,1,1,1] => 0000111
[4,4,4,1,1,1,1,1] => 00011111
[4,4,3,3,3] => 00111
[4,4,3,3,2,1] => 001101
[4,4,3,3,1,1,1] => 0011111
[4,4,3,2,2,2] => 001000
[4,4,3,2,2,1,1] => 0010011
[4,4,3,2,1,1,1,1] => 00101111
[4,4,3,1,1,1,1,1,1] => 001111111
[4,4,2,2,2,2,1] => 0000001
[4,4,2,2,2,1,1,1] => 00000111
[4,4,2,2,1,1,1,1,1] => 000011111
[4,4,2,1,1,1,1,1,1,1] => 0001111111
[4,4,1,1,1,1,1,1,1,1,1] => 00111111111
[4,3,3,3,3,1] => 011111
[4,3,3,3,2,2] => 011100
[4,3,3,3,2,1,1] => 0111011
[4,3,3,3,1,1,1,1] => 01111111
[4,3,3,2,2,2,1] => 0110001
[4,3,3,2,2,1,1,1] => 01100111
[4,3,3,2,1,1,1,1,1] => 011011111
[4,3,3,1,1,1,1,1,1,1] => 0111111111
[4,3,2,2,2,2,2] => 0100000
[4,3,2,2,2,2,1,1] => 01000011
[4,3,2,2,2,1,1,1,1] => 010001111
[4,3,2,2,1,1,1,1,1,1] => 0100111111
[4,3,2,1,1,1,1,1,1,1,1] => 01011111111
[4,3,1,1,1,1,1,1,1,1,1,1] => 011111111111
[4,2,2,2,2,2,2,1] => 00000001
[4,2,2,2,2,2,1,1,1] => 000000111
[4,2,2,2,2,1,1,1,1,1] => 0000011111
[4,2,2,2,1,1,1,1,1,1,1] => 00001111111
[4,2,2,1,1,1,1,1,1,1,1,1] => 000111111111
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 0011111111111
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 01111111111111
[3,3,3,3,3,2] => 111110
[3,3,3,3,3,1,1] => 1111111
[3,3,3,3,2,2,1] => 1111001
[3,3,3,3,2,1,1,1] => 11110111
[3,3,3,3,1,1,1,1,1] => 111111111
[3,3,3,2,2,2,2] => 1110000
[3,3,3,2,2,2,1,1] => 11100011
[3,3,3,2,2,1,1,1,1] => 111001111
[3,3,3,2,1,1,1,1,1,1] => 1110111111
[3,3,3,1,1,1,1,1,1,1,1] => 11111111111
[3,3,2,2,2,2,2,1] => 11000001
[3,3,2,2,2,2,1,1,1] => 110000111
[3,3,2,2,2,1,1,1,1,1] => 1100011111
[3,3,2,2,1,1,1,1,1,1,1] => 11001111111
[3,3,2,1,1,1,1,1,1,1,1,1] => 110111111111
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 1111111111111
[3,2,2,2,2,2,2,2] => 10000000
[3,2,2,2,2,2,2,1,1] => 100000011
[3,2,2,2,2,2,1,1,1,1] => 1000001111
[3,2,2,2,2,1,1,1,1,1,1] => 10000111111
[3,2,2,2,1,1,1,1,1,1,1,1] => 100011111111
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 1001111111111
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => 10111111111111
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 111111111111111
[2,2,2,2,2,2,2,2,1] => 000000001
[2,2,2,2,2,2,2,1,1,1] => 0000000111
[2,2,2,2,2,2,1,1,1,1,1] => 00000011111
[2,2,2,2,2,1,1,1,1,1,1,1] => 000001111111
[2,2,2,2,1,1,1,1,1,1,1,1,1] => 0000111111111
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => 00011111111111
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 001111111111111
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0111111111111111
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 11111111111111111
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
Return the binary word indicating which parts of the partition are odd.
Properties
surjective
Sage code
def mapping(pi):
    return Word([p % 2 for p in pi])
Weight
40
Created
Nov 09, 2023 at 10:45 by Martin Rubey
Updated
Nov 09, 2023 at 10:45 by Martin Rubey