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combinat::composition -- k-composition of an integer

Introduction

combinat::composition computes a list of all distinct ordered k-tupels (k_1, ..., k_n) such that n_1 + ... + n_k = n and n_i >= 1, i=1..k.

Call(s)

combinat::composition(n,k)

Parameters

n, k - integer

Returns

A list of type DOM_LIST containing every computed k-tupel also as a list of type DOM_LIST. If there exist no k-tupel the empty list is returned.

Details

Example 1

How can one write 5 as a sum of two other positive integers?

>> combinat::composition(5,2) 
                     [[1, 4], [2, 3], [3, 2], [4, 1]]

Example 2

There is no way to write 2 as the sum of 5 positive integers.

>> combinat::composition(2,5) 
                                    []

Example 3

combinat::composition does not handle symbolic expressions.

>> combinat::composition(xx,2) 
      Error: arguments must be integers [combinat::composition]

Changes




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