Geodesic
Structure and enumeration of $(3+1)$-free posets (extended abstract)
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

Voir la notice de l'article provenant de la source Episciences

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 are the subject of the $(3+1)$-free conjecture of Stanley and Stembridge. Recently, Lewis and Zhang have enumerated $\textit{graded}$ $(3+1)$-free posets, but until now the general enumeration problem has remained open. We enumerate all $(3+1)$-free posets by giving a decomposition into bipartite graphs, and obtain generating functions for $(3+1)$-free posets with labelled or unlabelled vertices. 
@article{DMTCS_2013_special_264_a80,
     author = {Guay-Paquet, Mathieu and Morales, Alejandro H. and Rowland, Eric},
     title = {Structure and enumeration of $(3+1)$-free posets (extended abstract)},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.12809},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12809/}
}
TY  - JOUR
AU  - Guay-Paquet, Mathieu
AU  - Morales, Alejandro H.
AU  - Rowland, Eric
TI  - Structure and enumeration of $(3+1)$-free posets (extended abstract)
JO  - Discrete mathematics & theoretical computer science
PY  - 2013
VL  - DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12809/
DO  - 10.46298/dmtcs.12809
LA  - en
ID  - DMTCS_2013_special_264_a80
ER  - 
%0 Journal Article
%A Guay-Paquet, Mathieu
%A Morales, Alejandro H.
%A Rowland, Eric
%T Structure and enumeration of $(3+1)$-free posets (extended abstract)
%J Discrete mathematics & theoretical computer science
%D 2013
%V DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12809/
%R 10.46298/dmtcs.12809
%G en
%F DMTCS_2013_special_264_a80
Guay-Paquet, Mathieu; Morales, Alejandro H.; Rowland, Eric. Structure and enumeration of $(3+1)$-free posets (extended abstract). Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.12809. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12809/

Cité par Sources :