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In the non-printing characters documentation, I see two named characters that are largely undocumented: \[InvisiblePrefixScriptBase] and \[InvisiblePostfixScriptBase].

Interestingly, they have input aliases defined: [Esc]i-[Esc] and [Esc]-i[Esc].

What are they used for?

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Related (possible dupe): I'd say that they're mostly for typesetting purposes and for finer control of the placements and positioning of subscripts/superscripts. You might probably use one of these when you need a subscript/superscript that's not attached to any symbol. – R. M. Dec 6 '12 at 7:20
Two examples of the first one are (1) TraditionalForm[Hypergeometric2F1[a, b, c, d]], and (2) this Q/A where it is used to typset $_{n}C_{r}$ – kglr Dec 6 '12 at 7:26
@kguler: So it seems like the Prefix one is meant as an invisible base character for sub-/superscripts that are typeset before the conceptual base character. But the Postfix one is still a mystery. – Mechanical snail Dec 6 '12 at 9:53
I have not come across any usage examples of \[InvisiblePostfixScriptBase] -- who knows? Maybe for right-to-left scripts it works similar to the Prefix one? – kglr Dec 6 '12 at 11:32
I use \[InvisiblePostfixScriptBase] to emulate the spaces and alignments in some tensor notions. In LaTeX it's usually done by \phantom command. Compare RowBox[{SubscriptBox["F","a"],SubsuperscriptBox["\[InvisiblePostfixScriptBase]"‌​,"b","c"]}]//DisplayForm to LaTeX code F_{ab}^{\phantom{a}c}. – Silvia Dec 6 '12 at 12:07

As the comments to OP described, those invisible marks are usually used as placeholder / anchor for typesetting.

For example, we can use \[InvisiblePostfixScriptBase] to emulate the spaces and alignments in some tensor notions. In LaTeX it's usually done by the \phantom command: Compare RowBox[{SubscriptBox["F", "a"],SubsuperscriptBox["\[InvisiblePostfixScriptBase]"‌, "b", "c"]}] // DisplayForm to LaTeX code F_{ab}^{ \phantom{a} c }.

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