  The notion of (3+1)-avoidance has shown up in many places in enumerative
combinatorics. The natural goal of enumeration of 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 magic. We also provide
asymptotics for the growth rate of the number of graded (3 + 1)-avoiding
posets.
