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I've had this question more than once, and that is, when I'm referring to "something which belongs to something which belongs to something else".

For example, in the following phrase I'm referring to the implementation of the "delete" operation or function of the RBT (red-black tree):

improved the RBT's deletion operation's implementation

Is is correct to use double apostrophe 's? If it is, does it sound good? If not, how would you say it to make it sound better? If instead it's not correct English, why is it the case?

Examples of different situations are as usual welcome.

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As explained in the comments, the fragment is correct, but more difficult to understand.

A better construction is:

improved the implementation of the RBT's deletion operation

About using 's for genitive, you can find a discussion here.

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