= Weak composition of an integer
{title2=$x_1+\cdots+x_k=N,\quad x_i\geq0$}
= Weak compositions of an integer
{synonym}
A <weak composition of an integer> $N\geq0$ into $k\geq1$ parts is an ordered <tuple> of <nonnegative integers> with <sum> $N$. Zero parts retain their positions: $(0,2,3)$ and $(2,0,3)$ differ. Fixing the length $k$ is essential when applying <stars and bars>, since inserting extra zero parts creates further <tuples>. https://math.mit.edu/~fgotti/docs/Courses/C.%20Combinatorial%20Analysis/6.%20Compositions/Compositions.pdf[Gotti, Lecture 6, definition and discussion of weak compositions]{ref}
Back to article page
