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arXiv · 1303.3652

Structure and enumeration of (3+1)-free posets

Mathieu Guay-Paquet·Alejandro H. Morales·Eric Rowland
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Abstract

A poset is (3+1)-free if it does not contain the disjoint union of chains of length 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 functions which count (3+1)-free posets with labelled or unlabelled vertices. Using this decomposition, we obtain a decomposition of the automorphism group and asymptotics for the number of (3+1)-free posets.

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Mathieu Guay-Paquet, Alejandro H. Morales, Eric Rowland. 2013-03-15. Structure and enumeration of (3+1)-free posets. https://doi.org/10.1007/s00026-014-0249-2

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