  A permutation $\pi$ contains a pattern $\sigma$ if and only if there is a
subsequence in $\pi$ with its letters are in the same relative order as those
in $\sigma$. Partially ordered patterns (POPs) provide a convenient way to
denote patterns in which the relative order of some of the letters does not
matter. This paper elucidates connections between the avoidance sets of a few
POPs with other combinatorial objects, directly answering five open questions
posed by Gao and Kitaev \cite{gao-kitaev-2019}. This was done by thoroughly
analysing the avoidance sets and developing recursive algorithms to derive
these sets and their corresponding combinatorial objects in parallel, which
yielded a natural bijection. We also analysed an avoidance set whose simple
permutations are enumerated by the Fibonacci numbers and derived an algorithm
to obtain them recursively.
