You're confusing string literals (code) and strings (values).

In the source, "$2$1" is a string literal. It results in a string made up of the values of $1 and $2. 

my $p = "$2$1";       # my $p = $2.$1;
                      # Doesn't change the value of $2 or $1.

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In the source, "$ARGV[0]" is a string literal. It results in a string made up of the value of $ARGV[0]. 

my $p = "$ARGV[0]";   # my $p = "".$ARGV[0];
                      # Doesn't change the value of $ARGV[0].

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If you want process the value of a variable for $1 and $2 and replace them, you are trying to implement a templating system. There's a one that matches your specs called String::Interpolate. 

use String::Interpolate qw( interpolate);

my $t = '$1$2';
  or 
my $t = $ARGV[0];

my $p = interpolate($t);

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In reply to Re: Interpolation of capture buffers not working when regex stored in variable by ikegami
in thread Interpolation of capture buffers not working when regex stored in variable by jacklh

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