论文标题
$ p $ - 斯特里特促销和$ q $ - 分区划分：分级案例
$P$-strict promotion and $Q$-partition rowmotion: the graded case
论文作者
论文摘要
促销和行动是在动态代数组合学方面的有趣行动，近年来激发了很多工作。在本文中，我们研究了$ p $ strict的标签，这些标签是有限的，分级的poset $ p $等级$ n $的标签和最多$ q $的标签，在促销下，$ n $ n $行的Semistandard Young Tableaux带有$ n $行和条目。这些$ p $ -strict的标签是在划船下的$ q $ - 分区进行的，其中$ q $等于$ p $的产品和$ q-n-1 $元素的链条。我们研究了$ p $等于详细链的产品的情况，产生了新的同源和订单，从而在Tableaux及其他地区产生了。此外，我们将两者进行培训应用于$ p $是微小的poset的情况，而当$ p $是三个元素$ v $ poset时。最后，我们在$ p $ strict标签和$ q $ - 分区的促销中给出了共鸣结果。
Promotion and rowmotion are intriguing actions in dynamical algebraic combinatorics which have inspired much work in recent years. In this paper, we study $P$-strict labelings of a finite, graded poset $P$ of rank $n$ and labels at most $q$, which generalize semistandard Young tableaux with $n$ rows and entries at most $q$, under promotion. These $P$-strict labelings are in equivariant bijection with $Q$-partitions under rowmotion, where $Q$ equals the product of $P$ and a chain of $q-n-1$ elements. We study the case where $P$ equals the product of chains in detail, yielding new homomesy and order results in the realm of tableaux and beyond. Furthermore, we apply the bijection to the cases in which $P$ is a minuscule poset and when $P$ is the three element $V$ poset. Finally, we give resonance results for promotion on $P$-strict labelings and rowmotion on $Q$-partitions.
