Is $\sum_{i=1}^n t_i=1$ equivalent to $t = \frac{1}{n}$?

Question

I have encountered this in a text book: "weight value $t$ for $n$ partitions is such that $\sum_{i=1}^n t_i=1$"

Do I understand it right that it's saying the same as: $t = \frac{1}{n}$ ? Or am I completely misunderstanding something here?

Answer 1

No.

Note that the summand is $t_i$ (which may differ depending on $i$) and not $t$. So for example, we might have $n=3$, $t_1=\frac12$, $t_2=\frac13$, and $t_3=\frac16$ as $\frac12+\frac13+\frac16=1$.