Enumeration formulو for pattern restricted Stirling permutations

We classify k -Stirling permutations avoiding a set of ordered patterns of length three according to Wilf-equivalence. Moreover, we derive enumeration formulو for all of the classes using a variety of techniques such as the kernel method, a bijection related to a classical result of Simion and Schmidt, and also structural decompositions of k -Stirling permutations via the so-called component block decomposition, or via bijections with families of trees.