SymPy | Partition.RGS_enum() in Python

Partition.RGS_enum() : RGS_enum() is a sympy Python library function that calculates the total number of restricted growth strings (string where a[i] is the block in which element i occurs) which is possible for a superset of size n.

Restricted growth strings – string in which each character, a_i results in the Block (B_i) in which the corresponding element belongs.

Syntax : sympy.combinatorics.partitions.Partition.RGS_enum()

Return : total number of restricted growth strings, possible for a superset of size n.

Code #1 : RGS_enum() Example

# Python code explaining
# SymPy.RGS_enum()

# importing SymPy libraries
from sympy.combinatorics.partitions import Partition
from sympy.combinatorics.partitions import RGS_enum

# Using from sympy.combinatorics.partitions.Partition.RGS_enum() method
p = RGS_enum(4)

q = RGS_enum(9)

print ("no. of strings possible for size  4: ", p)
print ("no. of strings possible for size  9: ", q)

Output :

no. of strings possible for size 4: 15
no. of strings possible for size 9: 203

Code #2 : RGS_enum() Example

# Python code explaining
# SymPy.RGS_enum()

# importing SymPy libraries
from sympy.combinatorics.partitions import Partition
from sympy.combinatorics.partitions import RGS_enum

# Using from sympy.combinatorics.partitions.Partition.RGS_enum() method
p = RGS_enum(20)

q = RGS_enum(-1)

print ("no. of strings possible for size  20 ", p)
print ("no. of strings possible for size  -1: ", q)

Output :

no. of strings possible for size 20 51724158235372
no. of strings possible for size -1: 0