| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Math.Combinat.Compositions
Description
Compositions.
See eg. http://en.wikipedia.org/wiki/Composition_%28combinatorics%29
Synopsis
- type Composition = [Int]
- compositions' :: [Int] -> Int -> [[Int]]
- countCompositions' :: [Int] -> Int -> Integer
- allCompositions1 :: Int -> [[Composition]]
- allCompositions' :: [Int] -> [[Composition]]
- compositions :: Integral a => a -> a -> [[Int]]
- countCompositions :: Integral a => a -> a -> Integer
- compositions1 :: Integral a => a -> a -> [[Int]]
- countCompositions1 :: Integral a => a -> a -> Integer
- randomComposition :: RandomGen g => Int -> Int -> g -> ([Int], g)
- randomComposition1 :: RandomGen g => Int -> Int -> g -> ([Int], g)
generating all compositions
type Composition = [Int] Source #
A composition of an integer n into k parts is an ordered k-tuple of nonnegative (sometimes positive) integers
whose sum is n.
Compositions fitting into a given shape and having a given degree. The order is lexicographic, that is,
sort cs == cs where cs = compositions' shape k
allCompositions1 :: Int -> [[Composition]] Source #
All positive compositions of a given number (filtrated by the length).
Total number of these is 2^(n-1)
allCompositions' :: [Int] -> [[Composition]] Source #
All compositions fitting into a given shape.
Nonnegative compositions of a given length.
countCompositions :: Integral a => a -> a -> Integer Source #
# = \binom { len+d-1 } { len-1 }
Positive compositions of a given length.
countCompositions1 :: Integral a => a -> a -> Integer Source #