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.
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