Coxeter-biCatalan combinatorics

Emily Barnard (1) , Nathan Reading (1)

1 Department of mathematics [North Carolina]

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.

Nous considérons des problèmes énumératifs liés à la combinatoire de Coxeter-Catalan et conjecturons que tous les problèmes ont la même solution, que nous appelons le nombre $W$ -biCatalan. Nous prouvons la conjecture dans de nombreux cas.

Mots clés: alternating arc diagram; doubled root poset; twin nonnesting partitions; twin sortable element

Domaines: Mathématique discrète [cs.DM]

Emily Barnard, Nathan Reading. Coxeter-biCatalan combinatorics. 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), Jul 2015, Daejeon, South Korea. pp.157-168, ⟨10.46298/dmtcs.2519⟩. ⟨hal-01337831⟩