  A K-theoretic analogue of RSK insertion and Knuth equivalence relations was
first introduced in 2006 by Buch, Kresch, Shimozono, Tamvakis, and Yong. The
resulting K-Knuth equivalence relations on words and increasing tableaux on [n]
has prompted investigation into the equivalence classes of tableaux arising
from these relations. Of particular interest are the tableaux that are unique
in their class, which we refer to as unique rectification targets (URTs). In
this paper we give several new families of URTs and a bound on the length of
intermediate words connecting two K-Knuth equivalent words. In addition, we
describe an algorithm to determine if two words are K-Knuth equivalent and to
compute all K-Knuth equivalence classes of tableaux on [n].
