- FindStat

Identifier

Mp00104: Binary words —reverse⟶ 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 => 100 => 011 => 101

010 => 010 => 101 => 110

011 => 110 => 001 => 010

100 => 001 => 110 => 011

101 => 101 => 010 => 100

110 => 011 => 100 => 001

111 => 111 => 000 => 000

0000 => 0000 => 1111 => 1111

0001 => 1000 => 0111 => 1011

0010 => 0100 => 1011 => 1101

0011 => 1100 => 0011 => 0101

0100 => 0010 => 1101 => 1110

0101 => 1010 => 0101 => 1010

0110 => 0110 => 1001 => 0110

0111 => 1110 => 0001 => 0010

1000 => 0001 => 1110 => 0111

1001 => 1001 => 0110 => 1001

1010 => 0101 => 1010 => 1100

1011 => 1101 => 0010 => 0100

1100 => 0011 => 1100 => 0011

1101 => 1011 => 0100 => 1000

1110 => 0111 => 1000 => 0001

1111 => 1111 => 0000 => 0000

00000 => 00000 => 11111 => 11111

00001 => 10000 => 01111 => 10111

00010 => 01000 => 10111 => 11011

00011 => 11000 => 00111 => 01011

00100 => 00100 => 11011 => 11101

00101 => 10100 => 01011 => 10101

00110 => 01100 => 10011 => 01101

00111 => 11100 => 00011 => 00101

01000 => 00010 => 11101 => 11110

01001 => 10010 => 01101 => 10110

01010 => 01010 => 10101 => 11010

01011 => 11010 => 00101 => 01010

01100 => 00110 => 11001 => 01110

01101 => 10110 => 01001 => 10010

01110 => 01110 => 10001 => 00110

01111 => 11110 => 00001 => 00010

10000 => 00001 => 11110 => 01111

10001 => 10001 => 01110 => 10011

10010 => 01001 => 10110 => 11001

10011 => 11001 => 00110 => 01001

10100 => 00101 => 11010 => 11100

10101 => 10101 => 01010 => 10100

10110 => 01101 => 10010 => 01100

10111 => 11101 => 00010 => 00100

11000 => 00011 => 11100 => 00111

11001 => 10011 => 01100 => 10001

11010 => 01011 => 10100 => 11000

11011 => 11011 => 00100 => 01000

11100 => 00111 => 11000 => 00011

11101 => 10111 => 01000 => 10000

11110 => 01111 => 10000 => 00001

11111 => 11111 => 00000 => 00000

000000 => 000000 => 111111 => 111111

000001 => 100000 => 011111 => 101111

000010 => 010000 => 101111 => 110111

000011 => 110000 => 001111 => 010111

000100 => 001000 => 110111 => 111011

000101 => 101000 => 010111 => 101011

000110 => 011000 => 100111 => 011011

000111 => 111000 => 000111 => 001011

001000 => 000100 => 111011 => 111101

001001 => 100100 => 011011 => 101101

001010 => 010100 => 101011 => 110101

001011 => 110100 => 001011 => 010101

001100 => 001100 => 110011 => 011101

001101 => 101100 => 010011 => 100101

001110 => 011100 => 100011 => 001101

001111 => 111100 => 000011 => 000101

010000 => 000010 => 111101 => 111110

010001 => 100010 => 011101 => 101110

010010 => 010010 => 101101 => 110110

010011 => 110010 => 001101 => 010110

010100 => 001010 => 110101 => 111010

010101 => 101010 => 010101 => 101010

010110 => 011010 => 100101 => 011010

010111 => 111010 => 000101 => 001010

011000 => 000110 => 111001 => 011110

011001 => 100110 => 011001 => 100110

011010 => 010110 => 101001 => 110010

011011 => 110110 => 001001 => 010010

011100 => 001110 => 110001 => 001110

011101 => 101110 => 010001 => 100010

011110 => 011110 => 100001 => 000110

011111 => 111110 => 000001 => 000010

100000 => 000001 => 111110 => 011111

100001 => 100001 => 011110 => 100111

100010 => 010001 => 101110 => 110011

100011 => 110001 => 001110 => 010011

100100 => 001001 => 110110 => 111001

100101 => 101001 => 010110 => 101001

100110 => 011001 => 100110 => 011001

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Map

reverse

Description

Return the reversal of a binary word.

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].