Enumeration of Graded (3+1)-Avoiding Posets

摘要

The notion of (3+1)-avoidance has shown up in many places in enumerativecombinatorics. The natural goal of enumeration of all (3+1)-avoiding posetsremains open. In this paper, we enumerate graded (3+1)-avoiding posets for bothreasonable definitions of the word "graded." Our proof consists of a number ofstructural theorems followed by some generating function magic. We also provideasymptotics for the growth rate of the number of graded (3 + 1)-avoidingposets.