- FindStat

Identifier

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

Images

0 => 0 => 1 => 1

1 => 1 => 0 => 0

00 => 00 => 11 => 11

01 => 10 => 01 => 10

10 => 01 => 10 => 01

11 => 11 => 00 => 00

000 => 000 => 111 => 111

001 => 010 => 101 => 110

010 => 100 => 011 => 101

011 => 101 => 010 => 100

100 => 001 => 110 => 011

101 => 110 => 001 => 010

110 => 011 => 100 => 001

111 => 111 => 000 => 000

0000 => 0000 => 1111 => 1111

0001 => 0010 => 1101 => 1110

0010 => 0100 => 1011 => 1101

0011 => 0101 => 1010 => 1100

0100 => 1000 => 0111 => 1011

0101 => 1010 => 0101 => 1010

0110 => 1001 => 0110 => 1001

0111 => 1011 => 0100 => 1000

1000 => 0001 => 1110 => 0111

1001 => 0110 => 1001 => 0110

1010 => 1100 => 0011 => 0101

1011 => 1101 => 0010 => 0100

1100 => 0011 => 1100 => 0011

1101 => 1110 => 0001 => 0010

1110 => 0111 => 1000 => 0001

1111 => 1111 => 0000 => 0000

00000 => 00000 => 11111 => 11111

00001 => 00010 => 11101 => 11110

00010 => 00100 => 11011 => 11101

00011 => 00101 => 11010 => 11100

00100 => 01000 => 10111 => 11011

00101 => 01010 => 10101 => 11010

00110 => 01001 => 10110 => 11001

00111 => 01011 => 10100 => 11000

01000 => 10000 => 01111 => 10111

01001 => 10010 => 01101 => 10110

01010 => 10100 => 01011 => 10101

01011 => 10101 => 01010 => 10100

01100 => 10001 => 01110 => 10011

01101 => 10110 => 01001 => 10010

01110 => 10011 => 01100 => 10001

01111 => 10111 => 01000 => 10000

10000 => 00001 => 11110 => 01111

10001 => 00110 => 11001 => 01110

10010 => 01100 => 10011 => 01101

10011 => 01101 => 10010 => 01100

10100 => 11000 => 00111 => 01011

10101 => 11010 => 00101 => 01010

10110 => 11001 => 00110 => 01001

10111 => 11011 => 00100 => 01000

11000 => 00011 => 11100 => 00111

11001 => 01110 => 10001 => 00110

11010 => 11100 => 00011 => 00101

11011 => 11101 => 00010 => 00100

11100 => 00111 => 11000 => 00011

11101 => 11110 => 00001 => 00010

11110 => 01111 => 10000 => 00001

11111 => 11111 => 00000 => 00000

000000 => 000000 => 111111 => 111111

000001 => 000010 => 111101 => 111110

000010 => 000100 => 111011 => 111101

000011 => 000101 => 111010 => 111100

000100 => 001000 => 110111 => 111011

000101 => 001010 => 110101 => 111010

000110 => 001001 => 110110 => 111001

000111 => 001011 => 110100 => 111000

001000 => 010000 => 101111 => 110111

001001 => 010010 => 101101 => 110110

001010 => 010100 => 101011 => 110101

001011 => 010101 => 101010 => 110100

001100 => 010001 => 101110 => 110011

001101 => 010110 => 101001 => 110010

001110 => 010011 => 101100 => 110001

001111 => 010111 => 101000 => 110000

010000 => 100000 => 011111 => 101111

010001 => 100010 => 011101 => 101110

010010 => 100100 => 011011 => 101101

010011 => 100101 => 011010 => 101100

010100 => 101000 => 010111 => 101011

010101 => 101010 => 010101 => 101010

010110 => 101001 => 010110 => 101001

010111 => 101011 => 010100 => 101000

011000 => 100001 => 011110 => 100111

011001 => 100110 => 011001 => 100110

011010 => 101100 => 010011 => 100101

011011 => 101101 => 010010 => 100100

011100 => 100011 => 011100 => 100011

011101 => 101110 => 010001 => 100010

011110 => 100111 => 011000 => 100001

011111 => 101111 => 010000 => 100000

100000 => 000001 => 111110 => 011111

100001 => 000110 => 111001 => 011110

100010 => 001100 => 110011 => 011101

100011 => 001101 => 110010 => 011100

100100 => 011000 => 100111 => 011011

100101 => 011010 => 100101 => 011010

100110 => 011001 => 100110 => 011001

>>> Load all 1677 entries. <<<

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].

Map

complement

Description

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