- FindStat

Identifier

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

Images

0 => 0 => 0 => 0

1 => 1 => 1 => 1

00 => 00 => 00 => 00

01 => 10 => 01 => 10

10 => 01 => 10 => 01

11 => 11 => 11 => 11

000 => 000 => 000 => 000

001 => 010 => 010 => 100

010 => 100 => 001 => 010

011 => 101 => 101 => 110

100 => 001 => 100 => 001

101 => 110 => 011 => 101

110 => 011 => 110 => 011

111 => 111 => 111 => 111

0000 => 0000 => 0000 => 0000

0001 => 0010 => 0100 => 1000

0010 => 0100 => 0010 => 0100

0011 => 0101 => 1010 => 1100

0100 => 1000 => 0001 => 0010

0101 => 1010 => 0101 => 1010

0110 => 1001 => 1001 => 0110

0111 => 1011 => 1101 => 1110

1000 => 0001 => 1000 => 0001

1001 => 0110 => 0110 => 1001

1010 => 1100 => 0011 => 0101

1011 => 1101 => 1011 => 1101

1100 => 0011 => 1100 => 0011

1101 => 1110 => 0111 => 1011

1110 => 0111 => 1110 => 0111

1111 => 1111 => 1111 => 1111

00000 => 00000 => 00000 => 00000

00001 => 00010 => 01000 => 10000

00010 => 00100 => 00100 => 01000

00011 => 00101 => 10100 => 11000

00100 => 01000 => 00010 => 00100

00101 => 01010 => 01010 => 10100

00110 => 01001 => 10010 => 01100

00111 => 01011 => 11010 => 11100

01000 => 10000 => 00001 => 00010

01001 => 10010 => 01001 => 10010

01010 => 10100 => 00101 => 01010

01011 => 10101 => 10101 => 11010

01100 => 10001 => 10001 => 00110

01101 => 10110 => 01101 => 10110

01110 => 10011 => 11001 => 01110

01111 => 10111 => 11101 => 11110

10000 => 00001 => 10000 => 00001

10001 => 00110 => 01100 => 10001

10010 => 01100 => 00110 => 01001

10011 => 01101 => 10110 => 11001

10100 => 11000 => 00011 => 00101

10101 => 11010 => 01011 => 10101

10110 => 11001 => 10011 => 01101

10111 => 11011 => 11011 => 11101

11000 => 00011 => 11000 => 00011

11001 => 01110 => 01110 => 10011

11010 => 11100 => 00111 => 01011

11011 => 11101 => 10111 => 11011

11100 => 00111 => 11100 => 00111

11101 => 11110 => 01111 => 10111

11110 => 01111 => 11110 => 01111

11111 => 11111 => 11111 => 11111

000000 => 000000 => 000000 => 000000

000001 => 000010 => 010000 => 100000

000010 => 000100 => 001000 => 010000

000011 => 000101 => 101000 => 110000

000100 => 001000 => 000100 => 001000

000101 => 001010 => 010100 => 101000

000110 => 001001 => 100100 => 011000

000111 => 001011 => 110100 => 111000

001000 => 010000 => 000010 => 000100

001001 => 010010 => 010010 => 100100

001010 => 010100 => 001010 => 010100

001011 => 010101 => 101010 => 110100

001100 => 010001 => 100010 => 001100

001101 => 010110 => 011010 => 101100

001110 => 010011 => 110010 => 011100

001111 => 010111 => 111010 => 111100

010000 => 100000 => 000001 => 000010

010001 => 100010 => 010001 => 100010

010010 => 100100 => 001001 => 010010

010011 => 100101 => 101001 => 110010

010100 => 101000 => 000101 => 001010

010101 => 101010 => 010101 => 101010

010110 => 101001 => 100101 => 011010

010111 => 101011 => 110101 => 111010

011000 => 100001 => 100001 => 000110

011001 => 100110 => 011001 => 100110

011010 => 101100 => 001101 => 010110

011011 => 101101 => 101101 => 110110

011100 => 100011 => 110001 => 001110

011101 => 101110 => 011101 => 101110

011110 => 100111 => 111001 => 011110

011111 => 101111 => 111101 => 111110

100000 => 000001 => 100000 => 000001

100001 => 000110 => 011000 => 100001

100010 => 001100 => 001100 => 010001

100011 => 001101 => 101100 => 110001

100100 => 011000 => 000110 => 001001

100101 => 011010 => 010110 => 101001

100110 => 011001 => 100110 => 011001

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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.