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Cataland: Why the Fuss?
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) Cet article a éte moissonné depuis la source Episciences

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The main objects of noncrossing Catalan combinatorics associated to a finite Coxeter system are noncross- ing partitions, sortable elements, and cluster complexes. The first and the third of these have known Fuss–Catalan generalizations. We provide new viewpoints for these, introduce a corresponding generalization of sortable elements as elements in the positive Artin monoid, and show how this perspective ties together all three generalizations. 
@article{DMTCS_2020_special_379_a33,
     author = {Stump, Christian and Thomas, Hugh and Williams, Nathan},
     title = {Cataland: {Why} the {Fuss?}},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2020},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     doi = {10.46298/dmtcs.6351},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6351/}
}
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%V DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
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Stump, Christian; Thomas, Hugh; Williams, Nathan. Cataland: Why the Fuss?. 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.6351

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