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
