This line is causing the syntax error:

        my @third_fragments = grep -v ($rsite3), $second_fragments[$i]
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Generally, Perl statements end with a semicolon. That being said, I think you are confusing Perl's built-in grep function with the unix grep utility. This is a common problem for new-comers. Simply adding the semicolon will not completely fix that line. You need to describe more fully what you are trying to achieve.