Enumeration of Graded (3 + 1)-Avoiding Posets

Abstract

The notion of (3+1)-avoidance appears in many places in enumerative combinatorics, but the natural goal of enumerating all (3+1)-avoiding posets remains open. In this paper, we enumerate \emphgraded (3+1)-avoiding posets. Our proof consists of a number of structural theorems followed by some generating function magic.

Keywords

• posets
• (3 + 1)-avoiding
• generating functions
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]