Module count 

Exact combinatorial counting functions over num_bigint::BigUint.

Constants

MAX_BINOMIAL_INPUT

Largest effective k (min(k, n - k)) accepted by binomial_checked before CombError::LimitExceeded.

MAX_FACTORIAL_INPUT

Largest n accepted by factorial_checked before CombError::LimitExceeded.

MAX_PARTITION_INPUT

Largest n accepted by integer_partition_count_checked before CombError::LimitExceeded.

Functions

bell_number

The Bell number B(n) = sum_k S(n, k): total partitions of an n-set.

binomial

n choose k via the multiplicative formula (0 when k > n).

binomial_checked

n choose k with an explicit ceiling on the effective loop length (min(k, n - k)).

factorial

n! (with factorial(0) == 1).

factorial_checked

n! with an explicit input ceiling (MAX_FACTORIAL_INPUT).

falling_factorial

The falling factorial n * (n-1) * ... * (n-k+1) (0 when k > n).

integer_partition_count

The partition count p(n): ways to write n as a sum of positive integers, order ignored.

integer_partition_count_checked

p(n) with an explicit input ceiling (MAX_PARTITION_INPUT).

multinomial

The multinomial coefficient (sum parts)! / prod(part!).

permutation_count

The number of k-permutations of n, nPk (0 when k > n).

stirling2

Stirling numbers of the second kind S(n, k): partitions of an n-set into k non-empty unlabeled blocks.