  We prove a conjecture of Guo and Poznanovi\'{c} concerning chains in certain
01-fillings of moon polyominoes. A key ingredient of our proof is a
correspondence between words $w$ and pairs $(\mathcal{W}(w), \mathcal{M}(w))$
of increasing tableaux such that $\mathcal{M}(w)$ determines the lengths of the
longest strictly increasing and strictly decreasing sequences in every
subinterval of $w$. We define this correspondence by using Thomas and Yong's
K-infusion operator and then use it to obtain the bijections that prove the
conjecture of Guo and Poznanovi\'{c}. In constructing our bijections we
introduce new variants of the RSK correspondence and Knuth equivalence.
