Well, this is a hack, but...

#! /usr/bin/perl
 
### make some files
my @dirs = qw(pAuLs PaULs pauls);
mkdir($_,0755) for @dirs;
 
my $name="PauLS";
 
### all the work
$name=~s/(\w)/[\l$1\u$1]/g;
my @list = map{ chomp; $_ } `ls -d $name`;
 
### show what we got
print "[".join("][",@list)."]\n";
 
### remove the dirs
rmdir($_) for @dirs;
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Well, you had to fork, and you get a list back rather than a single file, but, it is case insensitive. I think your better off doing the opendir and living with it (as that is what the ls probably did anyway).

my @a=qw(random brilliant braindead); print $a[rand(@a)];