论文标题
较高的Stasheff-tamari命令的新解释
New interpretations of the higher Stasheff--Tamari orders
论文作者
论文摘要
1996年，爱德曼（Edelman）和雷纳（Reiner）定义了两个较高的stasheff- tasheff-tamari命令，以循环多面体的三角剖分，并猜想它们重合。我们通过在较高的Auslander代数的表示理论中自然出现这些订单来打开一个代数角度来接近这种猜想，该订单是$ a $的较高的Auslander代数，表示为$ a_ {n}^d} $。为此，我们对订单进行新的组合解释，使其可比。然后，我们将这些组合解释转换为代数框架。我们还展示了奇数循环多面体的三角形如何在$ a_ {n}^{d} $的表示理论中出现，即作为最大绿色序列的等效类。此外，我们将奇怪的维度与已知$ 2D $维三角剖分的已知描述作为一组最大尺寸的非交接$ d $ simplices。这包括对两个新属性的定义，这意味着一组$ d $ - 简化会产生$（2D+1）$ - 尺寸三角剖分。
In 1996, Edelman and Reiner defined the two higher Stasheff--Tamari orders on triangulations of cyclic polytopes and conjectured them to coincide. We open up an algebraic angle for approaching this conjecture by showing how these orders arise naturally in the representation theory of the higher Auslander algebras of type $A$, denoted $A_{n}^{d}$. For this we give new combinatorial interpretations of the orders, making them comparable. We then translate these combinatorial interpretations into the algebraic framework. We also show how triangulations of odd-dimensional cyclic polytopes arise in the representation theory of $A_{n}^{d}$, namely as equivalence classes of maximal green sequences. We furthermore give the odd-dimensional counterpart to the known description of $2d$-dimensional triangulations as sets of non-intersecting $d$-simplices of a maximal size. This consists in a definition of two new properties which imply that a set of $d$-simplices produces a $(2d+1)$-dimensional triangulation.
