I've encountered lots of other 'ways' of expressing a sum that are different to

$\displaystyle \sum_{k=1}^n$

Sometimes people put $\displaystyle \sum_{cyc}$, $\displaystyle \sum_{sym}$, $\displaystyle \sum_{a,b,c}$, and sometimes they just put $\displaystyle \sum $. What does this all mean?? Thanks!