- FindStat

Identifier

Mp00105: Binary words —complement⟶ Binary words
Mp00278: Binary words —rowmotion⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words

Images

0 => 1 => 1 => 1

1 => 0 => 0 => 0

00 => 11 => 11 => 11

01 => 10 => 01 => 10

10 => 01 => 10 => 01

11 => 00 => 00 => 00

000 => 111 => 111 => 111

001 => 110 => 011 => 110

010 => 101 => 110 => 011

011 => 100 => 001 => 100

100 => 011 => 101 => 101

101 => 010 => 100 => 001

110 => 001 => 010 => 010

111 => 000 => 000 => 000

0000 => 1111 => 1111 => 1111

0001 => 1110 => 0111 => 1110

0010 => 1101 => 1110 => 0111

0011 => 1100 => 0011 => 1100

0100 => 1011 => 1101 => 1011

0101 => 1010 => 1100 => 0011

0110 => 1001 => 0110 => 0110

0111 => 1000 => 0001 => 1000

1000 => 0111 => 1011 => 1101

1001 => 0110 => 1001 => 1001

1010 => 0101 => 1010 => 0101

1011 => 0100 => 1000 => 0001

1100 => 0011 => 0101 => 1010

1101 => 0010 => 0100 => 0010

1110 => 0001 => 0010 => 0100

1111 => 0000 => 0000 => 0000

00000 => 11111 => 11111 => 11111

00001 => 11110 => 01111 => 11110

00010 => 11101 => 11110 => 01111

00011 => 11100 => 00111 => 11100

00100 => 11011 => 11101 => 10111

00101 => 11010 => 11100 => 00111

00110 => 11001 => 01110 => 01110

00111 => 11000 => 00011 => 11000

01000 => 10111 => 11011 => 11011

01001 => 10110 => 11001 => 10011

01010 => 10101 => 11010 => 01011

01011 => 10100 => 11000 => 00011

01100 => 10011 => 01101 => 10110

01101 => 10010 => 01100 => 00110

01110 => 10001 => 00110 => 01100

01111 => 10000 => 00001 => 10000

10000 => 01111 => 10111 => 11101

10001 => 01110 => 10011 => 11001

10010 => 01101 => 10110 => 01101

10011 => 01100 => 10001 => 10001

10100 => 01011 => 10101 => 10101

10101 => 01010 => 10100 => 00101

10110 => 01001 => 10010 => 01001

10111 => 01000 => 10000 => 00001

11000 => 00111 => 01011 => 11010

11001 => 00110 => 01001 => 10010

11010 => 00101 => 01010 => 01010

11011 => 00100 => 01000 => 00010

11100 => 00011 => 00101 => 10100

11101 => 00010 => 00100 => 00100

11110 => 00001 => 00010 => 01000

11111 => 00000 => 00000 => 00000

000000 => 111111 => 111111 => 111111

000001 => 111110 => 011111 => 111110

000010 => 111101 => 111110 => 011111

000011 => 111100 => 001111 => 111100

000100 => 111011 => 111101 => 101111

000101 => 111010 => 111100 => 001111

000110 => 111001 => 011110 => 011110

000111 => 111000 => 000111 => 111000

001000 => 110111 => 111011 => 110111

001001 => 110110 => 111001 => 100111

001010 => 110101 => 111010 => 010111

001011 => 110100 => 111000 => 000111

001100 => 110011 => 011101 => 101110

001101 => 110010 => 011100 => 001110

001110 => 110001 => 001110 => 011100

001111 => 110000 => 000011 => 110000

010000 => 101111 => 110111 => 111011

010001 => 101110 => 110011 => 110011

010010 => 101101 => 110110 => 011011

010011 => 101100 => 110001 => 100011

010100 => 101011 => 110101 => 101011

010101 => 101010 => 110100 => 001011

010110 => 101001 => 110010 => 010011

010111 => 101000 => 110000 => 000011

011000 => 100111 => 011011 => 110110

011001 => 100110 => 011001 => 100110

011010 => 100101 => 011010 => 010110

011011 => 100100 => 011000 => 000110

011100 => 100011 => 001101 => 101100

011101 => 100010 => 001100 => 001100

011110 => 100001 => 000110 => 011000

011111 => 100000 => 000001 => 100000

100000 => 011111 => 101111 => 111101

100001 => 011110 => 100111 => 111001

100010 => 011101 => 101110 => 011101

100011 => 011100 => 100011 => 110001

100100 => 011011 => 101101 => 101101

100101 => 011010 => 101100 => 001101

100110 => 011001 => 100110 => 011001

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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].

Map

reverse

Description

Return the reversal of a binary word.