> \Sum_{e \in S} e_i

I'm tempted to call that notation simply wrong instead of abusive. Generally "abusive" notation, while technically wrong, has some redeeming feature in intuition or consicebess.

In this case, the alternative notation would be to simply drop the index and write "\Sum_{e \in S} e", which seems to be all around better.

From having spent way too much time doing technical writing; I'm tempted to say the notation you are recalling really was a mistake. They probably started out with "\Sum_{e \in S} e", then decided to make all summations be index based instead of set based. Unless you spend a lot of time proofreading, that type of style change can easily lead to half translated expressions like what you recall.