This article is cited in 3 papers

A $\tau$-Tilting Approach to Dissections of Polygons

Vincent Pilaud^a, Pierre-Guy Plamondon^b, Salvatore Stella<sup>c

a</sup> CNRS & LIX, École Polytechnique, Palaiseau, France
^b Laboratoire de Mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, France
^c University of Haifa, Israel

Abstract: We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support $\tau$-tilting simplicial complex of an explicit finite dimensional algebra. To this end, we prove a property of some induced subcomplexes of support $\tau$-tilting simplicial complexes of finite dimensional algebras.

Keywords: dissections of polygons; accordion complexes; $\tau$-tilting theory; representations of finite dimensional algebras; $\mathbf{g}$-vectors.

MSC: 16G10; 16G20; 05E10

Received: February 26, 2018; in final form May 10, 2018; Published online May 14, 2018

Language: English

DOI: 10.3842/SIGMA.2018.045

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