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I want to put the following in formula-form: "$ T_i$ should be the sum of the $ b $ smallest durations out of all durations of the predecessors of $i$ (which is the set $P_i$)"

Does a mathematical formulation exist to describe the "$n$-th smallest element of a set"?

This was my trial:

$$T_i = \sum\limits_{n=0}^{b} \min\limits_{n}\{ t_j \mid j \in P_i \} $$

Thank you in advance!

Xander Henderson
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Lisa
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    I am not clear on the idea that you are trying to express. Why not simply order the $t_j$'s in increasing order, then add up the first $b$ of them? Or are you trying to order the $P_i$'s? I'm quite confused... – Xander Henderson May 19 '19 at 14:35
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    Those are called order statistics. Notation, like all language, works in context. You can borrow the notation in that link, which will work for those who use it. Include its definition for those who don't. – logarithm May 19 '19 at 14:36

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