English

Enumeration of Graded (3+1)-Avoiding Posets

Combinatorics 2015-10-15 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1106.5480,
  title  = {Enumeration of Graded (3+1)-Avoiding Posets},
  author = {Joel Brewster Lewis and Yan X Zhang},
  journal= {arXiv preprint arXiv:1106.5480},
  year   = {2015}
}

Comments

28 pages, 10 figures. Many changes and corrections thanks to referee comments. Final version

R2 v1 2026-06-21T18:28:15.913Z