Philippe Choquette

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Smooth infinite words over Σ = {1, 2} are connected to the Kolakoski word K = 221121 · · ·, defined as the fixpoint of the function ∆ that counts the length of the runs of 1’s and 2’s. In this paper we extend the notion of smooth words to arbitrary alphabets and study some of their combinatorial properties. Using the run-length encoding ∆, every word is(More)
Let W be a finite Coxeter group. Generalized associahedra are convex polytopes constructed from a permutahedron of W and an orientation of the Coxeter graph ofW . They play a fundamental role in the theory of finite type cluster algebras initiated by Fomin and Zelevinsky, and also appear in algebraic topology. In this article, we show that the isometries of(More)
We introduce hyperoctahedral species (H-species) or species of type B, which are analogous to the classical tensor species, but on which we consider the action of the groups of signed permutations. We give a bistrong monoidal functor, a functor which preserves Hopf monoids, between the monoidal categories of species and H-species. We also define bilax(More)
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