Enumeration of Graded (3+1)-Avoiding Posets

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.

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

References in corpus (3)

• (2+2)-free posets, ascent sequences and pattern avoiding permutations
• A generalization of the Birthday problem and the chromatic polynomial
• Counting (3+1) - Avoiding permutations

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• The Newton polytope and Lorentzian property of chromatic symmetric functions
• Bijective proof of a conjecture on unit interval posets
• Structure and enumeration of (3+1)-free posets (extended abstract)