气泡格 I：结构
Bubble Lattices I: Structure
AI总结：
本文从格论视角解释洗牌格的组合性质，引入其序扩张气泡格，给出局部与全局刻画，证明其极值性、可由区间加倍构造，并推广了 Hochschild 格。
摘要：
C. Greene 引入洗牌格作为 DNA 突变的理想化模型，并发现了该结构显著的组合与计数性质。我们尝试从格论视角解释这些性质。为此，我们引入并研究洗牌格的一个序扩张，即气泡格。我们既局部地（通过洗牌词的某些变换）也全局地（利用反演集的概念）刻画气泡格。随后我们证明气泡格是极值的，并且可通过区间加倍来构造。最后，我们证明该气泡格是 Chapoton、Combe 和第二作者早先研究的 Hochschild 格的推广。
英文摘要：
C. Greene introduced the shuffle lattice as an idealized model for DNA mutation and discovered remarkable combinatorial and enumerative properties of this structure. We attempt an explanation of these properties from a lattice-theoretic point of view. To that end, we introduce and study an order extension of the shuffle lattice, the bubble lattice. We characterize the bubble lattice both locally (via certain transformations of shuffle words) and globally (using a notion of inversion set). We then prove that the bubble lattice is extremal and constructable by interval doublings. Lastly, we prove that our bubble lattice is a generalization of the Hochschild lattice studied earlier by Chapoton, Combe and the second author.
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。
