Efficient, parallelization-friendly combination generator

combination.py

import typing as t
import math


def combination(n: int, k: int, m: int) -> t.Generator[int, None, None]:
    """
    Return the m-th combination (in lexicographic order) of the n integers from 0 to
    n-1, taken k at a time.
    """
    a, b, x = n, k + 1, math.comb(n, k)
    comb_a_b = x * (n - k) // b
    x -= m + 1
    for b in range(k, 0, -1):
        comb_a_b = comb_a_b * (b + 1) // a
        a -= 1
        while comb_a_b > x:
            comb_a_b = comb_a_b * (a - b) // a
            a -= 1
        x -= comb_a_b
        yield n - 1 - a

The code is adapted from this project, with additional tricks to avoid multiple evaluations of math.comb.