can you post your code so we can see/adjust what you're doing?

from scratch, here's a (untested) solution. Basically, instead of the concat building of a $row string, you map to loop over the cols, and also use join. But first hash everything up.

my %all = ( p => {}, v => {} );
my %s;
foreach my $row ( @results ){
  $all{p}->{ $row->{p_id} } = 1;
  $all{v}->{ $row->{v_id} } = 1;
  $s{ $row->{v_id} }->{ $row->{p_id} } = $row->{s_id};
}
my @p = sort keys %{$all{p}};
my @v = sort keys %{$all{v}};
print join("|", "      ", map { sprintf(" p_%-2d ",$_) } @p ), "\n";
print "-"x(7*(@p+1)) . "\n";
foreach my $v ( @v ){
# note hash slice
  print
    join( "|",                    # delim
      sprintf(" v_%-2d ",$v),     # first column
      map {
        defined($_) ? sprintf(" s_%-2d ",$_) : "      "   # format acc
+ordingly
      } @{$s{$v}}{ @p }           # all the s values for the 'p' colum
+ns; done via a hash slice
    ),
    "\n";
}
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