- FindStat

Identifier

Mp00267: Signed permutations —signs⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words

Images

[1] => 0 => 0

[-1] => 1 => 1

[1,2] => 00 => 00

[1,-2] => 01 => 10

[-1,2] => 10 => 01

[-1,-2] => 11 => 11

[2,1] => 00 => 00

[2,-1] => 01 => 10

[-2,1] => 10 => 01

[-2,-1] => 11 => 11

[1,2,3] => 000 => 000

[1,2,-3] => 001 => 100

[1,-2,3] => 010 => 001

[1,-2,-3] => 011 => 101

[-1,2,3] => 100 => 010

[-1,2,-3] => 101 => 110

[-1,-2,3] => 110 => 011

[-1,-2,-3] => 111 => 111

[1,3,2] => 000 => 000

[1,3,-2] => 001 => 100

[1,-3,2] => 010 => 001

[1,-3,-2] => 011 => 101

[-1,3,2] => 100 => 010

[-1,3,-2] => 101 => 110

[-1,-3,2] => 110 => 011

[-1,-3,-2] => 111 => 111

[2,1,3] => 000 => 000

[2,1,-3] => 001 => 100

[2,-1,3] => 010 => 001

[2,-1,-3] => 011 => 101

[-2,1,3] => 100 => 010

[-2,1,-3] => 101 => 110

[-2,-1,3] => 110 => 011

[-2,-1,-3] => 111 => 111

[2,3,1] => 000 => 000

[2,3,-1] => 001 => 100

[2,-3,1] => 010 => 001

[2,-3,-1] => 011 => 101

[-2,3,1] => 100 => 010

[-2,3,-1] => 101 => 110

[-2,-3,1] => 110 => 011

[-2,-3,-1] => 111 => 111

[3,1,2] => 000 => 000

[3,1,-2] => 001 => 100

[3,-1,2] => 010 => 001

[3,-1,-2] => 011 => 101

[-3,1,2] => 100 => 010

[-3,1,-2] => 101 => 110

[-3,-1,2] => 110 => 011

[-3,-1,-2] => 111 => 111

[3,2,1] => 000 => 000

[3,2,-1] => 001 => 100

[3,-2,1] => 010 => 001

[3,-2,-1] => 011 => 101

[-3,2,1] => 100 => 010

[-3,2,-1] => 101 => 110

[-3,-2,1] => 110 => 011

[-3,-2,-1] => 111 => 111

[1,2,3,4] => 0000 => 0000

[1,2,3,-4] => 0001 => 1000

[1,2,-3,4] => 0010 => 0001

[1,2,-3,-4] => 0011 => 1001

[1,-2,3,4] => 0100 => 0010

[1,-2,3,-4] => 0101 => 1010

[1,-2,-3,4] => 0110 => 0011

[1,-2,-3,-4] => 0111 => 1011

[-1,2,3,4] => 1000 => 0100

[-1,2,3,-4] => 1001 => 1100

[-1,2,-3,4] => 1010 => 0101

[-1,2,-3,-4] => 1011 => 1101

[-1,-2,3,4] => 1100 => 0110

[-1,-2,3,-4] => 1101 => 1110

[-1,-2,-3,4] => 1110 => 0111

[-1,-2,-3,-4] => 1111 => 1111

[1,2,4,3] => 0000 => 0000

[1,2,4,-3] => 0001 => 1000

[1,2,-4,3] => 0010 => 0001

[1,2,-4,-3] => 0011 => 1001

[1,-2,4,3] => 0100 => 0010

[1,-2,4,-3] => 0101 => 1010

[1,-2,-4,3] => 0110 => 0011

[1,-2,-4,-3] => 0111 => 1011

[-1,2,4,3] => 1000 => 0100

[-1,2,4,-3] => 1001 => 1100

[-1,2,-4,3] => 1010 => 0101

[-1,2,-4,-3] => 1011 => 1101

[-1,-2,4,3] => 1100 => 0110

[-1,-2,4,-3] => 1101 => 1110

[-1,-2,-4,3] => 1110 => 0111

[-1,-2,-4,-3] => 1111 => 1111

[1,3,2,4] => 0000 => 0000

[1,3,2,-4] => 0001 => 1000

[1,3,-2,4] => 0010 => 0001

[1,3,-2,-4] => 0011 => 1001

[1,-3,2,4] => 0100 => 0010

[1,-3,2,-4] => 0101 => 1010

[1,-3,-2,4] => 0110 => 0011

[1,-3,-2,-4] => 0111 => 1011

[-1,3,2,4] => 1000 => 0100

[-1,3,2,-4] => 1001 => 1100

[-1,3,-2,4] => 1010 => 0101

>>> Load all 6397 entries. <<<

Map

signs

Description

The binary word recording the signs of a signed permutation.
This map sends a signed permutation $\pi\in\mathfrak H_n$ to the binary word $w$ of length $n$ such that $w_i = 0$ if $\pi(i) > 0$.

Map

rotate back-to-front

Description

The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.