Maximal green sequences for arbitrary triangulations of marked surfaces (Extended Abstract)

Matthew R. Mills (1)

1 University of Nebraska–Lincoln

In general, the existence of a maximal green sequence is not mutation invariant. In this paper we show that it is in fact mutation invariant for cluster quivers associated to most marked surfaces. We develop a procedure to find maximal green sequences for cluster quivers associated to an arbitrary triangulation of closed higher genus marked surfaces with at least two punctures. As a corollary, it follows that any triangulation of a marked surface with at least one boundary component has a maximal green sequence.

Mots clés: Combinatorics

Domaines: Combinatoire [math.CO]

Matthew R. Mills. Maximal green sequences for arbitrary triangulations of marked surfaces (Extended Abstract). 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6383⟩. ⟨hal-02166351⟩