Geodesic
Enumeration of Graded (3 + 1)-Avoiding Posets
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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The notion of (3+1)-avoidance appears in many places in enumerative combinatorics, but the natural goal of enumerating all (3+1)-avoiding posets remains open. In this paper, we enumerate \emphgraded (3+1)-avoiding posets. Our proof consists of a number of structural theorems followed by some generating function magic. 
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     author = {Lewis Brewster, Joel and Zhang, Yan X},
     title = {Enumeration of {Graded} (3 + {1)-Avoiding} {Posets}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3019},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3019/}
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Lewis Brewster, Joel; Zhang, Yan X. Enumeration of Graded (3 + 1)-Avoiding Posets. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3019. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3019/

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