In number theory, the composition , or decomposition , of a natural number is its representation in the form of an ordered sum of natural terms. The terms included in the composition are called parts , and their number is called the length of the composition.
Unlike composition, splitting a number does not take into account the order of the parts. Therefore, the number of splits of the number never exceeds the number of compositions.
With a fixed length of compositions, zero parts are also sometimes allowed in them.
There are 16 compositions of the number 5:
Number of Songs
In general, there is compositions of n , of which exactly have length k .
If zero compositions are allowed in compositions of number n of length k , then the number of such compositions will be equal to , since adding 1 to each part gives the composition of the number n + k already without zero parts. The question of the total number of compositions of n with possible zero parts is meaningless, since it is infinite.
- Number splitting
- Sachkov V. N. Combinatorial methods of discrete mathematics. - M .: Nauka, 1977 .-- S. 241. - 319 p.