标题： 所有 Shi 区域与核心分拆之间的双射 显示英文标题

标题： A Bijection Between All Shi Regions and Core Partitions

摘要： 我们扩展了Fishel-Vazirani在$m$-Shi安排的主区域上的双射。 我们的映射将类型$A_{n}$的$m$-Shi安排的所有最小房间与某一类（等价类的）$n$-核心分拆进行双射。 作为我们证明的一个步骤，我们给出了$S_{n}$轨道中某些$m$-最小房间的分类，这些房间本身也是$m$-最小的。 显示英文摘要

摘要： We extend the bijection of Fishel-Vazirani on dominant regions of the $m$-Shi arrangement. Our map puts the set of all minimal chambers of the $m$-Shi arrangement of Type $A_{n}$ in bijection with a certain set of (equivalence classes of) $n$-core partitions. As a step to our proof, we give a potentially interesting classification of the alcoves in the $S_{n}$-orbit of an $m$-minimal alcove which are themselves $m$-minimal.