- FindStat

Identifier

Mp00105: Binary words —complement⟶ Binary words
Mp00278: Binary words —rowmotion⟶ Binary words

Images

0 => 1 => 1

1 => 0 => 0

00 => 11 => 11

01 => 10 => 01

10 => 01 => 10

11 => 00 => 00

000 => 111 => 111

001 => 110 => 011

010 => 101 => 110

011 => 100 => 001

100 => 011 => 101

101 => 010 => 100

110 => 001 => 010

111 => 000 => 000

0000 => 1111 => 1111

0001 => 1110 => 0111

0010 => 1101 => 1110

0011 => 1100 => 0011

0100 => 1011 => 1101

0101 => 1010 => 1100

0110 => 1001 => 0110

0111 => 1000 => 0001

1000 => 0111 => 1011

1001 => 0110 => 1001

1010 => 0101 => 1010

1011 => 0100 => 1000

1100 => 0011 => 0101

1101 => 0010 => 0100

1110 => 0001 => 0010

1111 => 0000 => 0000

00000 => 11111 => 11111

00001 => 11110 => 01111

00010 => 11101 => 11110

00011 => 11100 => 00111

00100 => 11011 => 11101

00101 => 11010 => 11100

00110 => 11001 => 01110

00111 => 11000 => 00011

01000 => 10111 => 11011

01001 => 10110 => 11001

01010 => 10101 => 11010

01011 => 10100 => 11000

01100 => 10011 => 01101

01101 => 10010 => 01100

01110 => 10001 => 00110

01111 => 10000 => 00001

10000 => 01111 => 10111

10001 => 01110 => 10011

10010 => 01101 => 10110

10011 => 01100 => 10001

10100 => 01011 => 10101

10101 => 01010 => 10100

10110 => 01001 => 10010

10111 => 01000 => 10000

11000 => 00111 => 01011

11001 => 00110 => 01001

11010 => 00101 => 01010

11011 => 00100 => 01000

11100 => 00011 => 00101

11101 => 00010 => 00100

11110 => 00001 => 00010

11111 => 00000 => 00000

000000 => 111111 => 111111

000001 => 111110 => 011111

000010 => 111101 => 111110

000011 => 111100 => 001111

000100 => 111011 => 111101

000101 => 111010 => 111100

000110 => 111001 => 011110

000111 => 111000 => 000111

001000 => 110111 => 111011

001001 => 110110 => 111001

001010 => 110101 => 111010

001011 => 110100 => 111000

001100 => 110011 => 011101

001101 => 110010 => 011100

001110 => 110001 => 001110

001111 => 110000 => 000011

010000 => 101111 => 110111

010001 => 101110 => 110011

010010 => 101101 => 110110

010011 => 101100 => 110001

010100 => 101011 => 110101

010101 => 101010 => 110100

010110 => 101001 => 110010

010111 => 101000 => 110000

011000 => 100111 => 011011

011001 => 100110 => 011001

011010 => 100101 => 011010

011011 => 100100 => 011000

011100 => 100011 => 001101

011101 => 100010 => 001100

011110 => 100001 => 000110

011111 => 100000 => 000001

100000 => 011111 => 101111

100001 => 011110 => 100111

100010 => 011101 => 101110

100011 => 011100 => 100011

100100 => 011011 => 101101

100101 => 011010 => 101100

100110 => 011001 => 100110

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Map

complement

Description

Send a binary word to the word obtained by interchanging the two letters.

Map

rowmotion

Description

Return the rowmotion of the binary word, regarded as an order ideal in the product of two chains.
In particular, this operation preserves the number of ones, and its order is the length of the word, see section 3.3 of [1].