A question about meaning of a notation

Question

When we have a sum of the form

$$ \sum_{cyc} \dfrac{ (a+b)(a+c) - bc }{(b-c)(b^3-c^3)} $$

Does this mean:

$$ \dfrac{ (a+b)(a+c) - bc }{(b-c)(b^3-c^3)} + \dfrac{ (b+c)(b+a) - ac }{(a-c)(a^3-c^3)} + \dfrac{ (c+b)(c+a) - ba }{(b-a)(b^3-a^3)} $$

?

Answer 1

It means that you take the sum over the cycles based on $(a \ b \ c)$ which are $$\begin{cases} (a \ b \ c) \to (a \ b \ c)\\ (a \ b \ c) \to (b \ c \ a)\\ (a \ b \ c) \to (c \ a \ b) \end{cases}$$