how do I get all combinations of a set of constants?

<?php // RAY_combinations_all_ordered_subsets.php
error_reporting(E_ALL);
echo "<pre>";


// PROBLEM: FIND ALL ORDERED SUBSETS OF A CHARACTER SET
// EXAMPLE: IN "ABC" IT MUST FIND "A", "AB", "BA", ETC.


// FUNCTION TO GENERATE THE COMBINATIONS OF CHARACTERS IN A STRING.
// OUTPUT IS AN ARRAY OF COUNT = strlen() FACTORIAL
// ADAPTED FROM http://cogo.wordpress.com/2008/01/08/string-permutation-in-php/
function string_combinations($str)
{
    if (strlen($str) < 2) return array($str);

    $combos = array();
    $endpop = substr($str, 1);

    // RECURSE
    foreach (string_combinations($endpop) as $permutation)
    {
        $length = strlen($permutation);
        for ($i = 0; $i <= $length; $i++)
        {
            $combos[] = substr($permutation, 0, $i) . $str[0] . substr($permutation, $i);
        }
    }
    return $combos;
}


// GENERATE THE COMBINATIONS OF ELEMENTS IN A ONE-DIMENSIONAL ARRAY
function array_combinations($arr)
{
    $return = array();

    // GET THE NUMERIC KEY RANGE OF THE INPUT ARRAY
    $str = implode('', range(0, count($arr)-1));

    // GET THE KEY COMBINATIONS
    $combos = string_combinations($str);

    // ITERATE OVER THE COMBINATIONS
    foreach ($combos as $combo)
    {
        $out = array();
        while (strlen($combo))
        {
           $key   = substr($combo,0,1);
           $combo = substr($combo,1);
           $out[] = $arr[$key];
        }
        $ndx = implode(NULL, $out);
        $return[$ndx] = $out;
    }
    return $return;
}


// DEMONSTRATE THE CODE
$abc = 'ABCDEF';
$abc = str_split($abc);
$cnt = count($abc) - 1;

// GET ALL LARGEST COMBINATIONS IN ARRAY FORMAT
$out = array_combinations($abc);
$out = array_keys($out);

// REDUCE THE STRING LENGTHS TO FIND SMALLER COMBINATIONS
while ($cnt)
{
    foreach ($out as $key)
    {
        $key = substr($key, 0, $cnt);
        $key = str_split($key);
        sort($key);
        $key = implode(NULL, $key);
        $new[$key] = $key;
    }
    $cnt--;
}

// WITH EACH OF THE REDUCED STRINGS, ADD ALL COMBINATIONS
foreach ($new as $abc)
{
    $arr = array_combinations(str_split($abc));
    $out = array_merge($out, array_keys($arr));
}

// SHOW THE WORK PRODUCT
sort($out);
echo "FOUND " . number_format(count($out)) . " COMBINATIONS";
echo PHP_EOL;
print_r($out);

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