Multicombinations.jl

An iterator for k-combinations with repetitions, k-multicombinations, k-multisubsets or whatever you want to call them.

Install this package with Pkg.clone("git://github.com/jlep/Multicombinations.jl")

• multichoose(n, k)

  Return the number of multisets of length k on n symbols.

  Examples

  multichoose(3,2)

  yields

  6
  

• multicombinations(xs, k)

  Iterate over every k-size multisubset of a collection xs.

  Example:

  for i in multicombinations([1,2,3],2)
      @show i
  end

  yields

  i => [1,1]
  i => [1,2]
  i => [1,3]
  i => [2,2]
  i => [2,3]
  i => [3,3]
  

• integersums(n, k)

  Iterate over every nonnegative integer solution of the equation: x₁ + x₂ + ... + x_n = k.

  The order in which the solutions are given corresponds to the order of subsets given by multicombinations(xs, k).

  Example:

  for i in integersums(3,2)
      @show i
  end

  yields

  i => [2,0,0]
  i => [1,1,0]
  i => [1,0,1]
  i => [0,2,0]
  i => [0,1,1]
  i => [0,0,2]
  

• is2mc(s)

  Convert a solution array given by integersums(n, k) to the corresponding multicombination index array.

  Example:

  for i in integersums(3,2)
      @show is2mc(i)
  end

  yields

  is2mc(i) => [1,1]
  is2mc(i) => [1,2]
  is2mc(i) => [1,3]
  is2mc(i) => [2,2]
  is2mc(i) => [2,3]
  is2mc(i) => [3,3]