论文标题
第一个较高的stasheff-tamari订单是较高的布鲁哈特订单的商
The first higher Stasheff-Tamari orders are quotients of the higher Bruhat orders
论文作者
论文摘要
我们证明了Dimakis和Müller-Hoissen较高的Tamari命令与第一个较高的Stasheff-tamari订单相吻合。为此，我们表明，较高的塔玛里订单可以被视为从较高的bruhat订单到第一个较高的stasheff--tamari订单的订单保留地图的图像。该地图是通过将循环界限的第一座横截面的第一个横截面定义的。我们提供了一个新的证据，表明该地图是汇总的，并进一步证明了地图已满，这需要上述猜想。我们解释了额定订单的图表如何汇总且完全对应于Posets的商。我们的结果将第一个较高的Stasheff-tamari命令与有关塔玛里较高订单在可集成系统中的作用的文献联系起来。
We prove the conjecture that the higher Tamari orders of Dimakis and Müller-Hoissen coincide with the first higher Stasheff--Tamari orders. To this end, we show that the higher Tamari orders may be conceived as the image of an order-preserving map from the higher Bruhat orders to the first higher Stasheff--Tamari orders. This map is defined by taking the first cross-section of a cubillage of a cyclic zonotope. We provide a new proof that this map is surjective and show further that the map is full, which entails the aforementioned conjecture. We explain how order-preserving maps which are surjective and full correspond to quotients of posets. Our results connect the first higher Stasheff--Tamari orders with the literature on the role of the higher Tamari orders in integrable systems.
