On cobweb posets and their combinatorially admissible sequences

In computer science a directed acyclic graph, also called DAG, is a directed graph with no directed cycles. Utility of DAG‘s is widely known and appreciated. Some algorithms for example, search algorithms become simpler when applied to DAGs. DAGs considered as a generalization of trees have a lot of applications in computer science, bioinformatics, physics and many natural activities of humanity and nature. For example in information categorization systems, such as folders in a computer or in Serializability Theory of Transaction Processing Systems and many others. Here we introduce specific DAGs as generalization of trees being inspired by algorithm of the Fibonacci tree growth.