  $V$-order is a global order on strings related to Unique Maximal
Factorization Families (UMFFs), which are themselves generalizations of Lyndon
words. $V$-order has recently been proposed as an alternative to
lexicographical order in the computation of suffix arrays and in the
suffix-sorting induced by the Burrows-Wheeler transform. Efficient $V$-ordering
of strings thus becomes a matter of considerable interest. In this paper we
present new and surprising results on $V$-order in strings, then go on to
explore the algorithmic consequences.
