论文标题
对称组的抛物线商的连续Lehmer代码
A Consecutive Lehmer Code for Parabolic Quotients of the Symmetric Group
论文作者
论文摘要
在本文中，我们为抛物线排列定义了一个编码，该编码区分了抛物线$ 231 $ - 避免排列。我们证明，这些代码上的分类顺序实现了抛物线塔玛利晶格，并得出了直接而简单的证据，即抛物线塔玛里tamari lattice与某些$ν$ -tamari lattice是同构，并具有明确的差异。此外，我们证明了此两次射击与首次在（Ceballos，Fang andMühle，2020）中证明晶格同构时所使用的地图$θ$密切相关，并在其中解决了一个空旷的问题。
In this article we define an encoding for parabolic permutations that distinguishes between parabolic $231$-avoiding permutations. We prove that the componentwise order on these codes realizes the parabolic Tamari lattice, and conclude a direct and simple proof that the parabolic Tamari lattice is isomorphic to a certain $ν$-Tamari lattice, with an explicit bijection. Furthermore, we prove that this bijection is closely related to the map $Θ$ used when the lattice isomorphism was first proved in (Ceballos, Fang and Mühle, 2020), settling an open problem therein.
