Geodesic
Extending the weak order on Coxeter groups
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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We introduce a new family of complete lattices, arising from a digraph together with a valuation on its vertices and generalizing a previous construction of the author. We then apply this to the study of two long-standing conjectures of Dyer, and we provide a description of the Tamari lattice with this theory. 
@article{DMTCS_2020_special_379_a91,
     author = {Viard, Francois},
     title = {Extending the weak order on {Coxeter} groups},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6409},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6409/}
}
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%T Extending the weak order on Coxeter groups
%J Discrete mathematics & theoretical computer science
%D 2020
%V DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
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Viard, Francois. Extending the weak order on Coxeter groups. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6409. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6409/

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