Ranks k-composites that sum to n

composite_rank.py

def gam_to_lam(c, n):
    i, m = 0, 0
    L = [0] * n

    while 1:
        i = i+1
        if c[i-1] > 0:
            for j in range(1, c[i-1] + 1):
                m = m + 1
                L[m-1] = i
        if m == n: return L

def lam_to_k(L, n):
    K = [0] * n
    for i in range(0, n):
        K[i] = L[i] + i
    return K

def rank_combination(a, k, n):
    r = 0
    for j in range(1, k+1):
        r += binomial(n - a[j-1], k - j + 1)
    return r

def rank_class(a, k, n):
    c = gam_to_lam(a, n)
    c = lam_to_k(c, n)
    r = rank_combination(c, n, n+k-1)
    return r