co.combinatorics - Strings and "co-subsequences"

Since you are taking the complement of a substring, and it appears that there may be no firmly established terminology, I propose:

• a substring complement is what remains after deleting a substring,


• and more generally, a subsequence complement is what remains after deleting a subsequence.

Thus, one may refer to the substring complement of s in t, and use the notation t - s, or $t setminus s$, with the same notation for the subsequence.

I would prefer this natural language terminology over the alternative co-substring and co-subsequence, which sound unnecessarily technical to my ear, but this difference may be slight.

It does seem worthwhile, however, to distinguish between the two cases, and so I would argue against using the term co-subsequence, as you suggested in your question, to refer to the substring complement.