Geodesic
Coxeter-biCatalan combinatorics
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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We consider several counting problems related to Coxeter-Catalan combinatorics and conjecture that the problems all have the same answer, which we call the $W$ -biCatalan number. We prove the conjecture in many cases. 
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     author = {Barnard, Emily and Reading, Nathan},
     title = {Coxeter-biCatalan combinatorics},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2519},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2519/}
}
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Barnard, Emily; Reading, Nathan. Coxeter-biCatalan combinatorics. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2519. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2519/

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