maths.special_numbers.bell_numbers

Bell numbers represent the number of ways to partition a set into non-empty subsets. This module provides functions to calculate Bell numbers for sets of integers. In other words, the first (n + 1) Bell numbers.

For more information about Bell numbers, refer to: https://en.wikipedia.org/wiki/Bell_number

Functions

_binomial_coefficient(→ int)	Calculate the binomial coefficient C(total_elements, elements_to_choose)
bell_numbers(→ list[int])	Calculate Bell numbers for the sets of lengths from 0 to max_set_length.

Module Contents

maths.special_numbers.bell_numbers._binomial_coefficient(total_elements: int, elements_to_choose: int) → int

Calculate the binomial coefficient C(total_elements, elements_to_choose)

Args:

total_elements (int): The total number of elements. elements_to_choose (int): The number of elements to choose.

Returns:

int: The binomial coefficient C(total_elements, elements_to_choose).

Examples: >>> _binomial_coefficient(5, 2) 10 >>> _binomial_coefficient(6, 3) 20

maths.special_numbers.bell_numbers.bell_numbers(max_set_length: int) → list[int]

Calculate Bell numbers for the sets of lengths from 0 to max_set_length. In other words, calculate first (max_set_length + 1) Bell numbers.

Args:

max_set_length (int): The maximum length of the sets for which Bell numbers are calculated.

Returns:

list: A list of Bell numbers for sets of lengths from 0 to max_set_length.

Examples: >>> bell_numbers(0) [1] >>> bell_numbers(1) [1, 1] >>> bell_numbers(5) [1, 1, 2, 5, 15, 52]