Math.Combinat.Compositions

Description

Compositions. This module is equivalent to the module Combinations, but it turns out that "compositions" is the accepted name. I will remove the Combinations module in the future.

Synopsis

Documentation

compositions'Source

Arguments

:: [Int]	shape
-> Int	sum
-> [[Int]]

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

countCompositions' :: [Int] -> Int -> Integer Source

allCompositions' :: [Int] -> [[[Int]]]Source

All compositions fitting into a given shape.

compositions Source

Arguments

:: Integral a
=> a	length
-> a	sum
-> [[Int]]

Compositions of a given length.

countCompositions :: Integral a => a -> a -> Integer Source

# = \binom { len+d-1 } { len-1 }

compositions1 Source

Arguments

:: Integral a
=> a	length
-> a	sum
-> [[Int]]

Positive compositions of a given length.

countCompositions1 :: Integral a => a -> a -> Integer Source