发表机构
Cornell University; Paderborn University; College of William & Mary; Kennesaw State University; University of Minnesota Twin Cities; York University（康奈尔大学; 帕德博恩大学; 威廉玛丽学院; 肯尼索州立大学; 明尼苏达大学双城分校; 约克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究等定向A型链复形箭图表示，证明其轨道与2×n网格图混合二聚体覆盖一一对应，利用相关矩阵公式计数轨道并讨论维数向量均匀时的生成函数。
AI 中文摘要
箭图表示由一组向量空间以及这些空间之间作为线性映射的箭头构成。本研究探讨等定向A型中同时为链复形的箭图表示，即连续箭头复合为零的情形。我们证明，这类表示在基变换作用下的轨道与2×n网格图的混合二聚体覆盖一一对应。后者可赋予偏序，构成分配格，且我们证明链复形轨道上的退化序是该偏序的加细。此外，我们利用Claussen与Ovenhouse近期的矩阵公式对这些轨道进行计数，这也相当于计算高度受限A型根上的Kostant分拆函数。当维数向量均匀时，我们讨论其与光在玻璃板间反射的路径的对应关系，并给出显式生成函数。
英文摘要
A quiver representation consists of a collection of vector spaces along with a set of arrows, which are linear maps between these spaces. In this work, we study quiver representations in equioriented type $A$ which are also chain complexes; that is, in which consecutive arrows compose to zero. We show that orbits of these representations under a change of basis action are in bijection with mixed dimer covers of a $2 \times n$ grid graph. The latter object can be endowed with a partial order which is a distributive lattice, and we show that the degeneration order on the orbits of chain complexes is a coarsening of this partial order. In addition, we use recent matrix formulae of Claussen and Ovenhouse to enumerate these orbits. This also computes the Kostant partition function applied to height-restricted, type $A$ roots. When the dimension vector is uniform, we discuss a correspondence with paths of a beam of light bouncing between glass plates and give an explicit generating function.
Comments22 pages, comments very welcome!
