Numeric.Combinatorics

This provides facilities for working with common combinatorial functions.

Documentation

choose :: Int -> Int -> Integer

\( \binom{n}{k} \)

doubleFactorial :: Int -> Integer

\( n!! \)

catalan :: Int -> Integer

The nth Catalan number, with indexing beginning at 0.

λ:> catalan <$> [0..9]
[1,1,2,5,14,42,132,429,1430,4862]

factorial :: Int -> Integer

derangement :: Int -> Integer

\( !n \)

λ:> derangement <$> [0..10]
[1,0,1,2,9,44,265,1854,14833,133496,1334961]

permutations :: Int -> Int -> Integer

maxRegions

Arguments

:: Int

\( n \)

-> Integer

Compute the maximal number of regions obtained by joining \( n \) points about a circle by straight lines. See here.

stirling2 :: Int -> Int -> Integer

Stirling numbers of the second kind.