Structure and Enumeration of (3+1)-Free Posets

@article{GuayPaquet2012StructureAE,
  title={Structure and Enumeration of (3+1)-Free Posets},
  author={Mathieu Guay-Paquet and Alejandro H. Morales and Eric Rowland},
  journal={Annals of Combinatorics},
  year={2012},
  volume={18},
  pages={645-674}
}
A poset is (3+1)-free if it does not contain the disjoint union of chains of lengths 3 and 1 as an induced subposet. These posets play a central role in the (3+1)-free conjecture of Stanley and Stembridge. Lewis and Zhang have enumerated (3+1)-free posets in the graded case by decomposing them into bipartite graphs, but until now the general enumeration problem has remained open. We give a finer decomposition into bipartite graphs which applies to all (3+1)-free posets and obtain generating… CONTINUE READING

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