A Hopf algebra of subword complexes (Extended abstract)

Nantel Bergeron (1) , Cesar Ceballos (2)

1 Department of Mathematics and Statistics [Toronto]
2 Faculty of Mathematics [Vienna]

We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf algebra induces a natural non-trivial sub-Hopf algebra on c-clusters in the theory of cluster algebras.

Domaines: Combinatoire [math.CO]

Nantel Bergeron, Cesar Ceballos. A Hopf algebra of subword complexes (Extended abstract). 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6359⟩. ⟨hal-02173743⟩