Séminaire Lotharingien de Combinatoire, 93B.54 (2025), 12 pp.
Jonah Berggren
Turbulence Polyhedra
Abstract.
A framing on a DAG (directed acyclic graph) gives a notion of compatibility on its routes which induces a regular unimodular triangulation on the underlying flow polytope. We define framed turbulence charts and their turbulence polyhedra, generalizing DAGs by removing the assumptions of directedness and acyclicity. We obtain presentations for turbulence polyhedra using special walks called "trails" on the underlying turbulence chart and we obtain subdivisions (and in many cases triangulations) of the turbulence polyhedra induced by a notion of compatibility on its trails. As a special case, we obtain presentations and subdivisions for flow polyhedra of framed directed graphs (without assuming acyclicity). As a motivating special case, we define and study the turbulence polyhedron of the fringed quiver of a gentle algebra, providing new insights into g-vector fans of gentle algebras.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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