Composition of an integer

{title2=$x_1+\cdots+x_k=N,\quad x_i\geq1$}

= Compositions of an integer
{synonym}

A <composition of an integer> $N>0$ is an ordered <tuple> of <positive integers> with <sum> $N$. Its length $k$ counts the parts. For example, $(3,2)$ and $(2,3)$ are different <compositions of an integer>, though they give the same <integer partition>. <Stars and bars> counts <compositions of an integer> with fixed length. https://math.mit.edu/~fgotti/docs/Courses/C.%20Combinatorial%20Analysis/6.%20Compositions/Compositions.pdf[Gotti, Lecture 6, definition of a composition]{ref}


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