The Schwartzian Transform is indeed most appropriate in this case. However your sort code is a little buggy. OP may have better luck with:

print join "\n", map {"$_->[0]"} sort {$a->[1] <=> $b->[1]} map {[$_, 
+-M]} @DirList;

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Note that the replies to What is "Schwarzian Transform" (aka Schwartzian) contain many useful comments and references pertaining to the Schwartzian Transform too.

DWIM is Perl's answer to Gödel

In reply to Re^3: sorting a directories content by GrandFather
in thread sorting a directories content by Anonymous Monk

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