论文标题
Hochschild Lattices的几何和组合探索
A geometric and combinatorial exploration of Hochschild lattices
论文作者
论文摘要
Hochschild Lattices是Caploton最近引入的Dexter Meet-semilattices的特定间隔。这些晶格的自然几何实现会导致Saneblidze引入的某些细胞复合物，称为Hochschild多面体。我们获得了Hochschild Lattices的几种几何特性，即我们给出立方实现，确定这些晶格是可壳的，并表明它们是通过间隔加倍来构造的。我们还证明了几种组合特性是其$ K $链的枚举并计算其学位多项式。
Hochschild lattices are specific intervals in the dexter meet-semilattices recently introduced by Chapoton. A natural geometric realization of these lattices leads to some cell complexes introduced by Saneblidze, called the Hochschild polytopes. We obtain several geometrical properties of the Hochschild lattices, namely we give cubic realizations, establish that these lattices are EL-shellable, and show that they are constructible by interval doubling. We also prove several combinatorial properties as the enumeration of their $k$-chains and compute their degree polynomials.
