Hochschild格的几何和组合探索
A geometric and combinatorial exploration of Hochschild lattices
摘要：
Hochschild格是最近由Chapoton引入的Dexter交半格中的一个特殊区间。这些格的自然几何实现导致Saneblidze引入的一些胞腔复形，称为Hochschild多面体。我们得到的Hochschild格的几个几何性质，即我们给立方实现，建立这些格是EL-壳，并表明，它们是可建造的区间加倍。我们还证明了几个组合性质作为其$k$ -链的计数，并计算了它们的次数多项式。
英文摘要：
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.
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