论文标题
扎根树上的行李箱
Rowmotion on rooted trees
论文作者
论文摘要
生根树是一个poset，其Hasse图是具有独特最小元素的图理论树。我们研究了T.最近的伊丽莎白，罗比，普兰特和萨根（T.）的抗小节和较低阶理想的行模，考虑了围栏上的行模，这些围栏是posets，其hasse图是一条路径（但允许任何数量的最小元素）。他们表明，在这种情况下，可以用圆柱体的瓷砖来描述轨道。他们还定义了一个称为同音法的新概念，这意味着统计量在相同大小的所有轨道上都具有恒定值。这是一个弱研究的同性恋概念，这是一个弱的概念，该概念需要在所有轨道上的统计量平均值恒定值。围栏上的行动通常对于某些统计数据而言，但不是同源性。我们介绍了一个在植根树上的划线模型。我们使用它来研究各种特定类型的树木，并表明它们在某些统计数据中表现出同音法，尽管不是同源性。
A rooted tree T is a poset whose Hasse diagram is a graph-theoretic tree having a unique minimal element. We study rowmotion on antichains and lower order ideals of T. Recently Elizalde, Roby, Plante and Sagan considered rowmotion on fences which are posets whose Hasse diagram is a path (but permitting any number of minimal elements). They showed that in this case, the orbits could be described in terms of tilings of a cylinder. They also defined a new notion called homometry which means that a statistic takes a constant value on all orbits of the same size. This is a weaker condition than the well-studied concept of homomesy which requires a constant value for the average of the statistic over all orbits. Rowmotion on fences is often homometric for certain statistics, but not homomesic. We introduce a tiling model for rowmotion on rooted trees. We use it to study various specific types of trees and show that they exhibit homometry, although not homomesy, for certain statistics.
