Python | SymPy Permutation.inversion_vector()

Permutation.inversion_vector() : inversion_vector() is a sympy Python library function that returns the inversion_vector value of the permutation in argument.
The inversion vector includes those elements whose value indicates the no. of elements in the permutation that are < it and lie on its right hand side.

Syntax :
sympy.combinatorics.permutations.Permutation.inversion_vector()

Return :
inversion_vector value of the permutation

Code #1 : inversion_vector() Example

# Python code explaining
# SymPy.Permutation.inversion_vector()

# importing SymPy libraries
from sympy.combinatorics.partitions import Partition
from sympy.combinatorics.permutations import Permutation

# Using from sympy.combinatorics.permutations.Permutation.inversion_vector() method

# creating Permutation
a = Permutation([[2, 0], [3, 1]])

b = Permutation([1, 3, 5, 4, 2, 0])


print ("Permutation a - inversion_vector form : ", a.inversion_vector())
print ("Permutation b - inversion_vector form : ", b.inversion_vector())

Output :

Permutation a – inversion_vector form : [2, 2, 0]
Permutation b – inversion_vector form : [1, 2, 3, 2, 1]

Code #2 : inversion_vector() Example – 2D Permutation

# Python code explaining
# SymPy.Permutation.inversion_vector()

# importing SymPy libraries
from sympy.combinatorics.partitions import Partition
from sympy.combinatorics.permutations import Permutation

# Using from sympy.combinatorics.permutations.Permutation.inversion_vector() method

# creating Permutation
a = Permutation([[2, 4, 0],
                 [3, 1, 2],
                 [1, 5, 6]])


print ("Permutation a - inversion_vector form : ", a.inversion_vector())

Output :

Permutation a – inversion_vector form : [3, 2, 2, 2, 0, 1]