  Partially ordered patterns (POPs) generalize the notion of classical patterns
studied in the literature in the context of permutations, words, compositions
and partitions. In this paper, we give a number of general, and specific
enumerative results for POPs in permutations defined by bipartite graphs,
substantially extending the list of known results in this direction. In
particular, we completely characterize the Wilf-equivalence for patterns
defined by the N-shape posets.
