- FindStat

Identifier

Mp00234: Binary words —valleys-to-peaks⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00280: Binary words —path rowmotion⟶ Binary words

Images

0 => 1 => 0 => 1

1 => 1 => 0 => 1

00 => 01 => 10 => 11

01 => 10 => 01 => 10

10 => 11 => 00 => 01

11 => 11 => 00 => 01

000 => 001 => 110 => 111

001 => 010 => 101 => 110

010 => 101 => 010 => 101

011 => 101 => 010 => 101

100 => 101 => 010 => 101

101 => 110 => 001 => 010

110 => 111 => 000 => 001

111 => 111 => 000 => 001

0000 => 0001 => 1110 => 1111

0001 => 0010 => 1101 => 1110

0010 => 0101 => 1010 => 1101

0011 => 0101 => 1010 => 1101

0100 => 1001 => 0110 => 1011

0101 => 1010 => 0101 => 1010

0110 => 1011 => 0100 => 1001

0111 => 1011 => 0100 => 1001

1000 => 1001 => 0110 => 1011

1001 => 1010 => 0101 => 1010

1010 => 1101 => 0010 => 0101

1011 => 1101 => 0010 => 0101

1100 => 1101 => 0010 => 0101

1101 => 1110 => 0001 => 0010

1110 => 1111 => 0000 => 0001

1111 => 1111 => 0000 => 0001

00000 => 00001 => 11110 => 11111

00001 => 00010 => 11101 => 11110

00010 => 00101 => 11010 => 11101

00011 => 00101 => 11010 => 11101

00100 => 01001 => 10110 => 11011

00101 => 01010 => 10101 => 11010

00110 => 01011 => 10100 => 11001

00111 => 01011 => 10100 => 11001

01000 => 10001 => 01110 => 10111

01001 => 10010 => 01101 => 10110

01010 => 10101 => 01010 => 10101

01011 => 10101 => 01010 => 10101

01100 => 10101 => 01010 => 10101

01101 => 10110 => 01001 => 10010

01110 => 10111 => 01000 => 10001

01111 => 10111 => 01000 => 10001

10000 => 10001 => 01110 => 10111

10001 => 10010 => 01101 => 10110

10010 => 10101 => 01010 => 10101

10011 => 10101 => 01010 => 10101

10100 => 11001 => 00110 => 01011

10101 => 11010 => 00101 => 01010

10110 => 11011 => 00100 => 01001

10111 => 11011 => 00100 => 01001

11000 => 11001 => 00110 => 01011

11001 => 11010 => 00101 => 01010

11010 => 11101 => 00010 => 00101

11011 => 11101 => 00010 => 00101

11100 => 11101 => 00010 => 00101

11101 => 11110 => 00001 => 00010

11110 => 11111 => 00000 => 00001

11111 => 11111 => 00000 => 00001

000000 => 000001 => 111110 => 111111

000001 => 000010 => 111101 => 111110

000010 => 000101 => 111010 => 111101

000011 => 000101 => 111010 => 111101

000100 => 001001 => 110110 => 111011

000101 => 001010 => 110101 => 111010

000110 => 001011 => 110100 => 111001

000111 => 001011 => 110100 => 111001

001000 => 010001 => 101110 => 110111

001001 => 010010 => 101101 => 110110

001010 => 010101 => 101010 => 110101

001011 => 010101 => 101010 => 110101

001100 => 010101 => 101010 => 110101

001101 => 010110 => 101001 => 110010

001110 => 010111 => 101000 => 110001

001111 => 010111 => 101000 => 110001

010000 => 100001 => 011110 => 101111

010001 => 100010 => 011101 => 101110

010010 => 100101 => 011010 => 101101

010011 => 100101 => 011010 => 101101

010100 => 101001 => 010110 => 101011

010101 => 101010 => 010101 => 101010

010110 => 101011 => 010100 => 101001

010111 => 101011 => 010100 => 101001

011000 => 101001 => 010110 => 101011

011001 => 101010 => 010101 => 101010

011010 => 101101 => 010010 => 100101

011011 => 101101 => 010010 => 100101

011100 => 101101 => 010010 => 100101

011101 => 101110 => 010001 => 100010

011110 => 101111 => 010000 => 100001

011111 => 101111 => 010000 => 100001

100000 => 100001 => 011110 => 101111

100001 => 100010 => 011101 => 101110

100010 => 100101 => 011010 => 101101

100011 => 100101 => 011010 => 101101

100100 => 101001 => 010110 => 101011

100101 => 101010 => 010101 => 101010

100110 => 101011 => 010100 => 101001

>>> Load all 1702 entries. <<<

Map

valleys-to-peaks

Description

Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak.

Map

complement

Description

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

Map

path rowmotion

Description

Return the rowmotion of the binary word, regarded as a lattice path.
Consider the binary word of length $n$ as a lattice path with $n$ steps, where a 1 corresponds to an up step and a 0 corresponds to a down step.
This map returns the path whose peaks are the valleys of the original path with an up step appended.