论文标题
流程的三角剖分，充足的框架和温和的代数
Triangulations of Flow Polytopes, Ample Framings, and Gentle Algebras
论文作者
论文摘要
已知针对定向的无环图（DAG）的非负流锥被允许通过DAG框架引起的常规单型三角剖分。这些三角形限制了流多层的三角剖分，以使强度一个流，这称为dkk三角剖分。对于一类称为“足够框架”的特殊框架，这些流锥项目的这些三角构造给了一个完整的风扇。我们表征了接收足够框架的DAG，并列举了固定dag的足够框架数量。我们建立了DKK三角剖分中的最大简单与某些柔和代数的$τ$的posets之间的联系，这使我们能够在任何DKK三角测量的双图上强加POSET结构，以备其框架。使用此连接，我们能够证明，对于完整的DAG，即，那些具有等级和超级等级的内部顶点的DAG等于两个，流层是Gorenstein，并且具有单模式Ehrhart $ H^\ ast $ h^\ ast $ polynomials。
The cone of nonnegative flows for a directed acyclic graph (DAG) is known to admit regular unimodular triangulations induced by framings of the DAG. These triangulations restrict to triangulations of the flow polytope for strength one flows, which are called DKK triangulations. For a special class of framings called ample framings, these triangulations of the flow cone project to a complete fan. We characterize the DAGs that admit ample framings, and we enumerate the number of ample framings for a fixed DAG. We establish a connection between maximal simplices in DKK triangulations and $τ$-tilting posets for certain gentle algebras, which allows us to impose a poset structure on the dual graph of any DKK triangulation for an amply framed DAG. Using this connection, we are able to prove that for full DAGs, i.e., those DAGs with inner vertices having in-degree and out-degree equal to two, the flow polytopes are Gorenstein and have unimodal Ehrhart $h^\ast$-polynomials.
