论文标题
泡泡晶格I：结构
Bubble Lattices I: Structure
论文作者
论文摘要
C. Greene引入了洗牌晶格作为DNA突变的理想化模型，并发现了这种结构的显着组合和枚举特性。我们尝试从晶格理论的角度来解释这些属性。为此，我们介绍并研究了泡沫晶格的散装晶格的订单扩展。我们在本地和全球（使用反转集的概念）（通过某些变换单词的某些转换）中表征了气泡晶格。然后，我们证明气泡晶格是极端的，可通过间隔加倍构建。最后，我们证明我们的泡泡晶格是对肖克顿，康比和第二作者较早研究的Hochschild晶格的概括。
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.
