Enumeration of graded (3+1)-avoiding posets

The notion of (3+1)-avoidance has shown up in many places in enumerative combinatorics, but the natural goal of enumerating all (3+1)-avoiding posets remains open. In this paper, we enumerate graded (3+1)-avoiding posets for both reasonable definitions of the word “graded.” Our proof consists of a number of structural theorems followed by some generating function computations. We also provide asymptotics for the growth rate of the number of graded (3+1)-avoiding posets.