  As suggested by Currie, we apply the probabilistic method to problems
regarding pattern avoidance. Using techniques from analytic combinatorics, we
calculate asymptotic pattern occurrence statistics and use them in conjunction
with the probabilistic method to establish new results about the Ramsey theory
of unavoidable patterns in the full word case (both nonabelian sense and
abelian sense) and in the partial word case.
  Keywords: Combinatorics on words; Partial words; Unavoidable patterns;
Abelian patterns; Probabilistic method; Analytic combinatorics; Ramsey theory.
