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SymPy | Permutation.rank () in Python

Permutation.rank (): rank () — nice Python library function that returns the lexicographic rank of a permutation.

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

Return: lexicographic rank of the permutation

Code # 1: rank () Example

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

 
# import SymPy libraries

from sympy.combinatorics.partitions import Partition

from sympy.combinatorics.permutations import Permutation

  
# Using the sympy.combinatorics.permutations.Permutation.rank () method

 
# create permutation

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

  

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

 

 

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

print ( "Permutation b - rank form:" , b.rank ())

Output:

Permutation a - rank form: 16
Permutation b - rank form: 191

Code # 2: rank () Example — 2D permutation

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

 
# import SymPy libraries

from sympy.combinatorics.partitions import Partition

from sympy.combinatorics.permutations import Permutation

 
# Using the sympy.combinatorics.permutations.Permutation.rank () method

 
# create permutation

a = Permutation ([[ 2 , 4 , 0 ], 

  [ 3 , 1 , 2 ],

  [ 1 , 5 , 6 ]])

 

 

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

Output:

Permutation a - rank form: 2461

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