This paper provides an upper bound for several subsets of maximal repeats and
maximal pairs in compressed strings and also presents a formerly unknown
relationship between maximal pairs and the run-length Burrows-Wheeler
transform.
This relationship is used to obtain a different proof for the Burrows-Wheeler
conjecture which has recently been proven by Kempa and Kociumaka in "Resolution
of the Burrows-Wheeler Transform Conjecture".
More formally, this paper proves that a string S with z LZ77-factors and
without q-th powers has at most 73(log2∣S∣)(z+2)2 runs in the
run-length Burrows-Wheeler transform and the number of arcs in the compacted
directed acyclic word graph of S is bounded from above by 18q(1+logq∣S∣)(z+2)2