论文标题
Hochschild格子和洗牌格
Hochschild lattices and shuffle lattices
论文作者
论文摘要
Saneblidze S. saneblidze在研究与自由环纤维相关的Hochschild络合物的研究中定义了FreeHedron，这是一种通过HyperCube的截断过程构建的某些多层人士。最近由F. apkoton猜想，并由C. Combe证明，FreeHedron的$ 1 $ skeleton的一定取向带有晶格结构。由此产生的晶格被称为Hochschild晶格，是一致的统一和极端。这些属性允许定义三个相关结构：Galois图，规范联接复合物和核心标签顺序。在本文中，我们研究和表征这些结构。我们表现出从Hochschild晶格的核心标签顺序到C. Greene的特定洗牌晶格的同构。我们还发现了Hochschild晶格的核心标签顺序，其不可减数的Poset和FreeHedron之间的枚举联系。这些连接很好地平行了围绕塔马里质量鲜明的晶格，非交叉分区晶格和Associahedra的情况。
In his study of a Hochschild complex arising in connection with the free loop fibration, S. Saneblidze defined the freehedron, a certain polytope constructed via a truncation process from the hypercube. It was recently conjectured by F. Chapoton and proven by C. Combe that a certain orientation of the $1$-skeleton of the freehedron carries a lattice structure. The resulting lattice was dubbed the Hochschild lattice and is congruence uniform and extremal. These properties allow for the definition of three associated structures: the Galois graph, the canonical join complex and the core label order. In this article, we study and characterize these structures. We exhibit an isomorphism from the core label order of the Hochschild lattice to a particular shuffle lattice of C. Greene. We also uncover an enumerative connection between the core label order of the Hochschild lattice, a certain order extension of its poset of irreducibles and the freehedron. These connections nicely parallel the situation surrounding the better-known Tamari lattices, noncrossing partition lattices and associahedra.
