- FindStat

Identifier

Mp00271: Signed permutations —flag negatives to negatives⟶ Signed permutations
Mp00267: Signed permutations —signs⟶ Binary words

Images

[1] => [1] => 0

[-1] => [-1] => 1

[1,2] => [1,2] => 00

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

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

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

[2,1] => [2,1] => 00

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 4282 entries. <<<

Map

flag negatives to negatives

Description

A map sending the number of flag negative entries to the number of negative entries.
For a signed permutation

$\pi\in\mathfrak H_n$ , a flag negative entry is a positive entry followed by a negative entry in the sequence

$\pi(-n),\dots,\pi(-1),\pi(1),\dots,\pi(n)$ , see St001870The number of positive entries followed by a negative entry in a signed permutation..
This map leaves the underlying permutation intact, and uses Mp00269flag zeros to zeros on the sequence of signs.

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

$\pi(i) > 0$ .