Enumerating Chains in Partially Ordered Sets

We study the enumerative properties of partially ordered sets, or posets. Specifically, we study flag f-vectors of posets, which are vectors of positive integers that encode information about the relationships between elements of posets. We seek to identify necessary and sufficient conditions on entries of flag f-vectors which will allow us to determine if an arbitrary vector is a flag f-vector of a poset. We study several cases of posets to reveal how different aspects of a poset\u27s structure manifest themselves in their corresponding flag f-vectors