Permutations Avoiding Certain Partially-Ordered Patterns

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