极小偏序集上的双有理行运动和Coxeter运动
Birational rowmotion and coxeter-motion on minuscule posets
摘要：
双有理行运动是有限偏序集上所有正实值函数集合上的离散动力系统，它是组合行运动在阶理想上的双有理提升。已知极小偏序集的组合行运动具有与Coxeter数相等的阶，并且对于精化的阶理想基数统计量表现出文件同调现象。在本文中，我们推广这些结果的双有理数设置。此外，作为两链乘积上双有理提升的推广，我们在极小偏序集上引入了双有理Coxeter-运动，并证明了它具有周期性和齐次性。
英文摘要：
Birational rowmotion is a discrete dynamical system on the set of all positive real-valued functions on a finite poset, which is a birational lift of combinatorial rowmotion on order ideals. It is known that combinatorial rowmotion for a minuscule poset has order equal to the Coxeter number, and exhibits the file homomesy phenomenon for refined order ideal cardinality statistic. In this paper we generalize these results to the birational setting. Moreover, as a generalization of birational promotion on a product of two chains, we introduce birational Coxeter-motion on minuscule posets, and prove that it enjoys periodicity and file homomesy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
