Identifier
Mp00170:
Permutations
—to signed permutation⟶
Signed permutations
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Mp00260: Signed permutations —Demazure product with inverse⟶ Signed permutations
Images
=>
[1]=>[1]=>[1]
[1,2]=>[1,2]=>[1,2]
[2,1]=>[2,1]=>[2,1]
[1,2,3]=>[1,2,3]=>[1,2,3]
[1,3,2]=>[1,3,2]=>[1,3,2]
[2,1,3]=>[2,1,3]=>[2,1,3]
[2,3,1]=>[2,3,1]=>[3,2,1]
[3,1,2]=>[3,1,2]=>[3,2,1]
[3,2,1]=>[3,2,1]=>[3,2,1]
[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]
[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]
[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]
[1,3,4,2]=>[1,3,4,2]=>[1,4,3,2]
[1,4,2,3]=>[1,4,2,3]=>[1,4,3,2]
[1,4,3,2]=>[1,4,3,2]=>[1,4,3,2]
[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]
[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]
[2,3,1,4]=>[2,3,1,4]=>[3,2,1,4]
[2,3,4,1]=>[2,3,4,1]=>[4,2,3,1]
[2,4,1,3]=>[2,4,1,3]=>[4,2,3,1]
[2,4,3,1]=>[2,4,3,1]=>[4,2,3,1]
[3,1,2,4]=>[3,1,2,4]=>[3,2,1,4]
[3,1,4,2]=>[3,1,4,2]=>[3,4,1,2]
[3,2,1,4]=>[3,2,1,4]=>[3,2,1,4]
[3,2,4,1]=>[3,2,4,1]=>[4,3,2,1]
[3,4,1,2]=>[3,4,1,2]=>[4,3,2,1]
[3,4,2,1]=>[3,4,2,1]=>[4,3,2,1]
[4,1,2,3]=>[4,1,2,3]=>[4,2,3,1]
[4,1,3,2]=>[4,1,3,2]=>[4,3,2,1]
[4,2,1,3]=>[4,2,1,3]=>[4,2,3,1]
[4,2,3,1]=>[4,2,3,1]=>[4,3,2,1]
[4,3,1,2]=>[4,3,1,2]=>[4,3,2,1]
[4,3,2,1]=>[4,3,2,1]=>[4,3,2,1]
[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]
[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]
[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]
[1,2,4,5,3]=>[1,2,4,5,3]=>[1,2,5,4,3]
[1,2,5,3,4]=>[1,2,5,3,4]=>[1,2,5,4,3]
[1,2,5,4,3]=>[1,2,5,4,3]=>[1,2,5,4,3]
[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]
[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]
[1,3,4,2,5]=>[1,3,4,2,5]=>[1,4,3,2,5]
[1,3,4,5,2]=>[1,3,4,5,2]=>[1,5,3,4,2]
[1,3,5,2,4]=>[1,3,5,2,4]=>[1,5,3,4,2]
[1,3,5,4,2]=>[1,3,5,4,2]=>[1,5,3,4,2]
[1,4,2,3,5]=>[1,4,2,3,5]=>[1,4,3,2,5]
[1,4,2,5,3]=>[1,4,2,5,3]=>[1,4,5,2,3]
[1,4,3,2,5]=>[1,4,3,2,5]=>[1,4,3,2,5]
[1,4,3,5,2]=>[1,4,3,5,2]=>[1,5,4,3,2]
[1,4,5,2,3]=>[1,4,5,2,3]=>[1,5,4,3,2]
[1,4,5,3,2]=>[1,4,5,3,2]=>[1,5,4,3,2]
[1,5,2,3,4]=>[1,5,2,3,4]=>[1,5,3,4,2]
[1,5,2,4,3]=>[1,5,2,4,3]=>[1,5,4,3,2]
[1,5,3,2,4]=>[1,5,3,2,4]=>[1,5,3,4,2]
[1,5,3,4,2]=>[1,5,3,4,2]=>[1,5,4,3,2]
[1,5,4,2,3]=>[1,5,4,2,3]=>[1,5,4,3,2]
[1,5,4,3,2]=>[1,5,4,3,2]=>[1,5,4,3,2]
[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]
[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,3,5,4]
[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,4,3,5]
[2,1,4,5,3]=>[2,1,4,5,3]=>[2,1,5,4,3]
[2,1,5,3,4]=>[2,1,5,3,4]=>[2,1,5,4,3]
[2,1,5,4,3]=>[2,1,5,4,3]=>[2,1,5,4,3]
[2,3,1,4,5]=>[2,3,1,4,5]=>[3,2,1,4,5]
[2,3,1,5,4]=>[2,3,1,5,4]=>[3,2,1,5,4]
[2,3,4,1,5]=>[2,3,4,1,5]=>[4,2,3,1,5]
[2,3,4,5,1]=>[2,3,4,5,1]=>[5,2,3,4,1]
[2,3,5,1,4]=>[2,3,5,1,4]=>[5,2,3,4,1]
[2,3,5,4,1]=>[2,3,5,4,1]=>[5,2,3,4,1]
[2,4,1,3,5]=>[2,4,1,3,5]=>[4,2,3,1,5]
[2,4,1,5,3]=>[2,4,1,5,3]=>[4,2,5,1,3]
[2,4,3,1,5]=>[2,4,3,1,5]=>[4,2,3,1,5]
[2,4,3,5,1]=>[2,4,3,5,1]=>[5,2,4,3,1]
[2,4,5,1,3]=>[2,4,5,1,3]=>[5,2,4,3,1]
[2,4,5,3,1]=>[2,4,5,3,1]=>[5,2,4,3,1]
[2,5,1,3,4]=>[2,5,1,3,4]=>[5,2,3,4,1]
[2,5,1,4,3]=>[2,5,1,4,3]=>[5,2,4,3,1]
[2,5,3,1,4]=>[2,5,3,1,4]=>[5,2,3,4,1]
[2,5,3,4,1]=>[2,5,3,4,1]=>[5,2,4,3,1]
[2,5,4,1,3]=>[2,5,4,1,3]=>[5,2,4,3,1]
[2,5,4,3,1]=>[2,5,4,3,1]=>[5,2,4,3,1]
[3,1,2,4,5]=>[3,1,2,4,5]=>[3,2,1,4,5]
[3,1,2,5,4]=>[3,1,2,5,4]=>[3,2,1,5,4]
[3,1,4,2,5]=>[3,1,4,2,5]=>[3,4,1,2,5]
[3,1,4,5,2]=>[3,1,4,5,2]=>[3,5,1,4,2]
[3,1,5,2,4]=>[3,1,5,2,4]=>[3,5,1,4,2]
[3,1,5,4,2]=>[3,1,5,4,2]=>[3,5,1,4,2]
[3,2,1,4,5]=>[3,2,1,4,5]=>[3,2,1,4,5]
[3,2,1,5,4]=>[3,2,1,5,4]=>[3,2,1,5,4]
[3,2,4,1,5]=>[3,2,4,1,5]=>[4,3,2,1,5]
[3,2,4,5,1]=>[3,2,4,5,1]=>[5,3,2,4,1]
[3,2,5,1,4]=>[3,2,5,1,4]=>[5,3,2,4,1]
[3,2,5,4,1]=>[3,2,5,4,1]=>[5,3,2,4,1]
[3,4,1,2,5]=>[3,4,1,2,5]=>[4,3,2,1,5]
[3,4,1,5,2]=>[3,4,1,5,2]=>[4,5,3,1,2]
[3,4,2,1,5]=>[3,4,2,1,5]=>[4,3,2,1,5]
[3,4,2,5,1]=>[3,4,2,5,1]=>[5,4,3,2,1]
[3,4,5,1,2]=>[3,4,5,1,2]=>[5,4,3,2,1]
[3,4,5,2,1]=>[3,4,5,2,1]=>[5,4,3,2,1]
[3,5,1,2,4]=>[3,5,1,2,4]=>[5,3,2,4,1]
[3,5,1,4,2]=>[3,5,1,4,2]=>[5,4,3,2,1]
[3,5,2,1,4]=>[3,5,2,1,4]=>[5,3,2,4,1]
[3,5,2,4,1]=>[3,5,2,4,1]=>[5,4,3,2,1]
[3,5,4,1,2]=>[3,5,4,1,2]=>[5,4,3,2,1]
[3,5,4,2,1]=>[3,5,4,2,1]=>[5,4,3,2,1]
[4,1,2,3,5]=>[4,1,2,3,5]=>[4,2,3,1,5]
[4,1,2,5,3]=>[4,1,2,5,3]=>[4,2,5,1,3]
[4,1,3,2,5]=>[4,1,3,2,5]=>[4,3,2,1,5]
[4,1,3,5,2]=>[4,1,3,5,2]=>[4,5,3,1,2]
[4,1,5,2,3]=>[4,1,5,2,3]=>[4,5,3,1,2]
[4,1,5,3,2]=>[4,1,5,3,2]=>[4,5,3,1,2]
[4,2,1,3,5]=>[4,2,1,3,5]=>[4,2,3,1,5]
[4,2,1,5,3]=>[4,2,1,5,3]=>[4,2,5,1,3]
[4,2,3,1,5]=>[4,2,3,1,5]=>[4,3,2,1,5]
[4,2,3,5,1]=>[4,2,3,5,1]=>[5,4,3,2,1]
[4,2,5,1,3]=>[4,2,5,1,3]=>[5,4,3,2,1]
[4,2,5,3,1]=>[4,2,5,3,1]=>[5,4,3,2,1]
[4,3,1,2,5]=>[4,3,1,2,5]=>[4,3,2,1,5]
[4,3,1,5,2]=>[4,3,1,5,2]=>[4,5,3,1,2]
[4,3,2,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]
[4,3,2,5,1]=>[4,3,2,5,1]=>[5,4,3,2,1]
[4,3,5,1,2]=>[4,3,5,1,2]=>[5,4,3,2,1]
[4,3,5,2,1]=>[4,3,5,2,1]=>[5,4,3,2,1]
[4,5,1,2,3]=>[4,5,1,2,3]=>[5,4,3,2,1]
[4,5,1,3,2]=>[4,5,1,3,2]=>[5,4,3,2,1]
[4,5,2,1,3]=>[4,5,2,1,3]=>[5,4,3,2,1]
[4,5,2,3,1]=>[4,5,2,3,1]=>[5,4,3,2,1]
[4,5,3,1,2]=>[4,5,3,1,2]=>[5,4,3,2,1]
[4,5,3,2,1]=>[4,5,3,2,1]=>[5,4,3,2,1]
[5,1,2,3,4]=>[5,1,2,3,4]=>[5,2,3,4,1]
[5,1,2,4,3]=>[5,1,2,4,3]=>[5,2,4,3,1]
[5,1,3,2,4]=>[5,1,3,2,4]=>[5,3,2,4,1]
[5,1,3,4,2]=>[5,1,3,4,2]=>[5,4,3,2,1]
[5,1,4,2,3]=>[5,1,4,2,3]=>[5,4,3,2,1]
[5,1,4,3,2]=>[5,1,4,3,2]=>[5,4,3,2,1]
[5,2,1,3,4]=>[5,2,1,3,4]=>[5,2,3,4,1]
[5,2,1,4,3]=>[5,2,1,4,3]=>[5,2,4,3,1]
[5,2,3,1,4]=>[5,2,3,1,4]=>[5,3,2,4,1]
[5,2,3,4,1]=>[5,2,3,4,1]=>[5,4,3,2,1]
[5,2,4,1,3]=>[5,2,4,1,3]=>[5,4,3,2,1]
[5,2,4,3,1]=>[5,2,4,3,1]=>[5,4,3,2,1]
[5,3,1,2,4]=>[5,3,1,2,4]=>[5,3,2,4,1]
[5,3,1,4,2]=>[5,3,1,4,2]=>[5,4,3,2,1]
[5,3,2,1,4]=>[5,3,2,1,4]=>[5,3,2,4,1]
[5,3,2,4,1]=>[5,3,2,4,1]=>[5,4,3,2,1]
[5,3,4,1,2]=>[5,3,4,1,2]=>[5,4,3,2,1]
[5,3,4,2,1]=>[5,3,4,2,1]=>[5,4,3,2,1]
[5,4,1,2,3]=>[5,4,1,2,3]=>[5,4,3,2,1]
[5,4,1,3,2]=>[5,4,1,3,2]=>[5,4,3,2,1]
[5,4,2,1,3]=>[5,4,2,1,3]=>[5,4,3,2,1]
[5,4,2,3,1]=>[5,4,2,3,1]=>[5,4,3,2,1]
[5,4,3,1,2]=>[5,4,3,1,2]=>[5,4,3,2,1]
[5,4,3,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on signed permutations.
This map is a surjection onto the set of involutions, i.e., the set of signed permutations $\pi$ for which $\pi = \pi^{-1}$.
This map is a surjection onto the set of involutions, i.e., the set of signed permutations $\pi$ for which $\pi = \pi^{-1}$.
searching the database
Sorry, this map was not found in the database.