Antichain Toggling and Rowmotion
Antichain Toggling and Rowmotion
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反链切换和 Rowmotion
DOI：
10.37236/7454
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
M. Joseph
中科院分区：
文献类型：
--
作者：
M. Joseph
本文分析了偏序集的反链集上的肘节群。由简单对合生成的切换群首先由卡梅隆和Fon-Der-Flaass为偏序集的序理想引入。最近Striker激发了对一般子集族（包括反链）上的切换群的研究。本文通过研究反链的切换群与序理想之间的关系，构建两个群之间的显式同构（对于有限偏序集）来扩展这项工作。我们还专注于在动力代数组合学中已经得到很好研究的偏序集的反链上的行运动作用，将其描述为反链切换的组合。我们还描述了一个分段线性模拟切换到斯坦利的链多面体。我们研究的连接与分段线性切换爱因斯坦和Propp介绍了顺序多面体，并证明了几乎所有的反链切换扩展到分段线性设置的结果。
In this paper, we analyze the toggle group on the set of antichains of a poset. Toggle groups, generated by simple involutions, were first introduced by Cameron and Fon-Der-Flaass for order ideals of posets. Recently Striker has motivated the study of toggle groups on general families of subsets, including antichains. This paper expands on this work by examining the relationship between the toggle groups of antichains and order ideals, constructing an explicit isomorphism between the two groups (for a finite poset). We also focus on the rowmotion action on antichains of a poset that has been well-studied in dynamical algebraic combinatorics, describing it as the composition of antichain toggles. We also describe a piecewise-linear analogue of toggling to the Stanley’s chain polytope. We examine the connections with the piecewise-linear toggling Einstein and Propp introduced for order polytopes and prove that almost all of our results for antichain toggles extend to the piecewise-linear setting.