On support $\tau$-tilting graphs of gentle algebras
Changjian Fu, Shengfei Geng, Pin Liu, Yu Zhou

TL;DR
This paper studies the combinatorial structure of support τ-tilting graphs for gentle algebras, proving their connectivity and a property related to cluster algebra exchange graphs, thus advancing understanding of their algebraic and combinatorial features.
Contribution
It establishes the connectivity and reachable-in-face property of support τ-tilting graphs for gentle algebras, confirming a conjecture related to cluster algebra exchange graphs.
Findings
Support τ-tilting graph of gentle algebra is connected.
Support τ-tilting graph has the reachable-in-face property.
Confirmed a conjecture by Fomin and Zelevinsky for this class of algebras.
Abstract
Let be a finite-dimensional gentle algebra over an algebraically closed field. We investigate the combinatorial properties of support -tilting graph of . In particular, it is proved that the support -tilting graph of is connected and has the so-called reachable-in-face property. This property was conjectured by Fomin and Zelevinsky for exchange graphs of cluster algebras which was recently confirmed by Cao and Li.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Quantum many-body systems
