How does one schematically represent a sequence that differs from another sequence only in that it is missing just one element, without specifying which element is missing?
Say I represent a sequence $S_1$ of $n$ elements where $n\ge 2$ as $(i_1, \dotsc, i_n)$. Now I want to represent another sequence $S_2$ which differs from $S_1$ only in that it is missing one element, represented as $i_j$. It is the $j$-th element in the sequence $S_1$, but I want to allow $j$ to have any value $1\le j \le n$. Is there a notation for schematically representing $(i_1,\dotsc,i_n)$ without $i_j$?
(Note: I am not a mathematician, so if I have misused any terms here, feel free to correct me.)
In his text Algebraic Topology (page 105), Hatcher uses a "hat" (or circumflex) to denote an $(n-1)$-tuple which is produced by removing the "hatted" element from an $n$-tuple. For example, $$ (i_1, \dotsc, \hat{i}_j, \dotsc, i_n) = (i_1, \dotsc, i_{j-1}, i_{j+1}, \dotsc, i_n), $$ where $j$ is any index between $1$ and $n$, inclusive. I would not say that this is universally standard notation, but Hatcher is a popular text on the topic, so folk are likely to have at least seen the notation at some point in their lives (assuming that they went to grad school in mathematics...?). If you desire something more compact, perhaps define a function $\delta$ (the Greek letter delta, for "delete") on the space of finite tuples by $$ \delta_j(i_1, \dotsc, i_n) := (i_1, \dotsc, \hat{i}_j, \dotsc, i_n) $$ would be appropriate (where the hat notation is as defined above)? In the example given in the question, this notation gives $ \delta_j(S_1) = S_2$.
Whatever notation you use, it will almost certainly be a little non-standard, so make sure that you give a clear definition before you start using it.