Geodesic
ORIENTED FLIP GRAPHS, NONCROSSING TREE PARTITIONS, AND REPRESENTATION THEORY OF TILING ALGEBRAS
Glasgow mathematical journal, Tome 62 (2020) no. 1, pp. 147-182

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DOI

The purpose of this paper is to understand lattices of certain subcategories in module categories of representation-finite gentle algebras called tiling algebras, as introduced by Coelho Simões and Parsons. We present combinatorial models for torsion pairs and wide subcategories in the module category of tiling algebras. Our models use the oriented flip graphs and noncrossing tree partitions, previously introduced by the authors, and a description of the extension spaces between indecomposable modules over tiling algebras. In addition, we classify two-term simple-minded collections in bounded derived categories of tiling algebras. As a consequence, we obtain a characterization of c-matrices for any quiver mutation-equivalent to a type A Dynkin quiver. 
GARVER, ALEXANDER; MCCONVILLE, THOMAS. ORIENTED FLIP GRAPHS, NONCROSSING TREE PARTITIONS, AND REPRESENTATION THEORY OF TILING ALGEBRAS. Glasgow mathematical journal, Tome 62 (2020) no. 1, pp. 147-182. doi: 10.1017/S0017089519000028
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     title = {ORIENTED {FLIP} {GRAPHS,} {NONCROSSING} {TREE} {PARTITIONS,} {AND} {REPRESENTATION} {THEORY} {OF} {TILING} {ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {147--182},
     year = {2020},
     volume = {62},
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     doi = {10.1017/S0017089519000028},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000028/}
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