Composition (number Theory) - Examples

Examples

The sixteen compositions of 5 are:

  • 5
  • 4+1
  • 3+2
  • 3+1+1
  • 2+3
  • 2+2+1
  • 2+1+2
  • 2+1+1+1
  • 1+4
  • 1+3+1
  • 1+2+2
  • 1+2+1+1
  • 1+1+3
  • 1+1+2+1
  • 1+1+1+2
  • 1+1+1+1+1.

Compare this with the seven partitions of 5:

  • 5
  • 4+1
  • 3+2
  • 3+1+1
  • 2+2+1
  • 2+1+1+1
  • 1+1+1+1+1.

It is possible to put constraints on the parts of the compositions. For example the five compositions of 5 into distinct terms are:

  • 5
  • 4+1
  • 3+2
  • 2+3
  • 1+4.

Compare this with the three partitions of 5 into distinct terms:

  • 5
  • 4+1
  • 3+2.

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