A Meaning of Slot-Naming Index Notation (tensor conversion)

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I'm studying the component representation of tensor algebra alone.
There is a exercise question but I cannot solve it, cannot deduce answer from the text. (text is concise, I think it assumes a bit of familiarity with the knowledge)

(a) Convert the following expressions and equations into geometric, index-free notation:
AαBγβ ;
AαBγβ ;
Sαβγ=Sγβα ;
AαBβ=AαBβgαβ

In this problem, I can't see any difference between first two expressions except for the index position, and my only solution for the expression of index position is using metric tensor g, which I think is included in slot-naming notation. Is "index-free" notation can express the difference?
Other expressions are similarly confusing for me.


(b) Convert T(_,S(R(C,_),_),_) into slot-naming index notation.

I think this notation would be not so universal notation. These problem are from http://www.pmaweb.caltech.edu/Courses/ph136/yr2012/1202.1.K.pdf (Ex 2.7)
and the help of anyone who is familiar with the notation would be appreciated.
 
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Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
 

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