





















Abstract:In the study of flow polytopes, a directed acyclic graph (DAG) with a choice of framing gives a regular unimodular triangulation on its space of unit nonnegative flows. In representation theory, a gentle algebra has recently been equipped with a space of unit flows admitting triangulation and subdivision results capturing its tau-tilting theory. These theories from different areas of mathematics overlap: flows on gently framed DAGs are the same as flows on paired representation-finite gentle algebras. In this article we develop the common generalization of these two theories by defining (framed) turbulence charts, which may be thought of as analogs of (framed) DAGs without the conditions of (D)irectedness and (A)cyclicity. The space of unit flows on a turbulence chart is its turbulence polyhedron. We give presentation, subdivision, and triangulation results on turbulence polyhedra which restrict to known results in the settings of framed DAGs and gentle algebras.
| Comments: | 48 pages, 26 figures, comments welcome |
| Subjects: | Combinatorics (math.CO); Representation Theory (math.RT) |
| MSC classes: | 05C21 (primary) 05E10, 52B11 (secondary) |
| Cite as: | arXiv:2605.24327 [math.CO] |
| (or arXiv:2605.24327v1 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24327 arXiv-issued DOI via DataCite (pending registration) |
From: Jonah Berggren [view email]
[v1]
Sat, 23 May 2026 01:16:37 UTC (1,077 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。