A regex to find if a letter occurs exactly $n times.

Is this what you were looking for as a first step?

#!/usr/bin/perl

# http://perlmonks.org/?node_id=1201500

use strict;
use warnings;

my @words = glob '{i,x}' x 6;

print "@words\n";

my $n = 1; # number of times a letter occurs in a word

my @oneletter = grep
  /^(?|
  (?=.*?(.)(?!.*\1))
  (?:
  (?:(?!\1).)*
  \1
  ){$n}
  (?:(?!\1).)*
  |
  (?=.*(.))
  (?:
  (?:(?!\1).)*
  \1
  ){$n}
  (?:(?!\1).)*
  )$
  /x, @words;

print "\n@oneletter\n\n", scalar @oneletter, "\n";
[download]

Update: fails for some test cases

Can you share some interesting test cases?

-QM
--
Quantum Mechanics: The dreams stuff is made of

Too much cheating?

#!/usr/bin/perl

# http://perlmonks.org/?node_id=1201500

use strict;
use warnings;

my $file = '/usr/share/dict/words';

open my $fh, '<', $file or die "$! opening $file";
chomp( my @words = grep /^[a-z]{5,}$/, <$fh>);

my @good = grep frequencysequence($_), @words;

print "@good\n\n" . @good . "\n";

sub frequencysequence
  {
  for my $n ( 1 .. ((-1 + sqrt 1 + 8 * length) / 2) =~ s/^(\d+)\..*/$1
+ + 1/er )
    {
    "@_\n@_" =~ /
      (.).*
      \n
      (?: (?:(?!\1).)* \1 ){$n}
      (?:(?!\1).)*
      $ /x or return 0;
    }
  return 1;
  }
[download]

On my system outputs:

acacia allele assays banana baobab bedded bonobo bowwow cocoon deadhea
+ded deemed doodad eddied eerier effete fesses heeded horror hubbub in
+ning lessee lollop mammal manana messes needed papaya peeped peeper p
+epped pepper pippin powwow reefer revere rococo salsas seeded senses 
+sereneness settee sleeveless tattoo teeter teethe wedded weeded xxvii
+i xxxvii

49
[download]

Nice solution of the "variable length lookbehind" not allowed problem!

But why \n instead of $ ? *

edit

I suppose it's necessary because the following assertion wouldn't be executed?

update

*) well, I just noticed the "@_\n@_" part where you are doubling the input, which explains the "\n" and some other confusion about pos.

I agree, "too much cheating!" ;-p

Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)
Je suis Charlie!}

...sum the count of matches...

There's always the brute force method of generating every possible regex, assuming arithmetic sequence starting at 1. For a max frequency of 6, this covers 21 letter words. It makes me wonder what the breaking point is of my machine.

Note that in (3), only lengths that are triangular will do.

I'll have to find some time to chase this -- perhaps tomorrow.

I just remembered that Perl supports recursive regexes and relative back-references, so you might not be limited to a hard limit.

Unfortunately I don't have the time to play with it.

FWIW if using s///g was allowed you just needed a pattern which repeatedly deleted one character of each group, iff exactly one of them is unique.

Your criterion was met, if the string is empty afterwards.

Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)
Je suis Charlie!}