Notation for "Nested" Sequences? Let $X$ and $Y$ be two ordered pairs $X = (A,B)$ and $Y = (A,B)$. Then let $A$ and $B$ be two sequences "nested" in the pairs $A = \langle A_1,A_2,...,A_n \rangle$ and $B = \langle B_1,B_2,...B_n \rangle$ (the elements of the sequences in $X$ and $Y$ can be different). Finally, let each element of $A$ and $B$ also be a sequence $A_i = \langle a_1,a_2,...,a_n \rangle$ and $B_i = \langle b_1,b_2,...b_n \rangle$.
1) Which is the best notation to reference the elements inside the sequence of each pair? $X_{A_{1}}$?
2) Which is the best notation to reference the elements in the sequences of the sequences $A$ and $B$ ? $X_{{A_{1_{a_1}}}}$ and $X_{{B_{1_{b_1}}}}$?
I would like to avoid the excessive use of subscripts that makes it nearly impossible to read because of the size. Any suggestion?

It depends very much on what your purposes are.  I would be disinclined to 'share' letters between the ordered pairs in e.g. a proof and would much prefer something like 'let $X=(A,B)$ and $Y=(C,D)$'; this saves you from having to disambiguate between $X$ and $Y$ in your subsequences in the first place.  Then I would say $A=\langle A_1, A_2, \ldots, A_n\rangle$ where $A_1=\langle a_{1,1}, a_{1,2}, \ldots, a_{1,m}\rangle$, etc; if the two indices need to be more strongly distinguished then $a_{i;j}$ is also fine notation.  Ideally, though, I would encourage restructuring your argument so that you don't need quite so much nesting to whatever extent possible — it may be inevitable that you have to compare, e.g., $a_{2,4}$ with $d_{5,3}$ but it's generally a sign that the overall structure of whatever you're talking about could be substantially cleaned up.
