Grouping unordered sets by how many times one chosen letter appears
gives N_U_n = sum_{j=0}^{n} (N-1)_U_j – eq (1.54) in general,
eq (1.51) for n=4, N=3 and eq (1.52) for general n with N=3.
Eq (1.55) rewrites each term with eq (1.16); the sum is returned
beside the closed form.
Arguments
- n
number of picks.
- N
number of distinct types, N >= 2.
Value
list(n_picks, n_types, recursion_sum, closed_form, n_terms,
forms_agree).
References
Morin, D. J. (2016). Probability: For the Enthusiastic
Beginner. Createspace. Eqs. (1.51)-(1.52), (1.54)-(1.55).
Examples
StarBRec(4, 3)$recursion_sum
#> [1] 15
