论文标题
泡泡晶格II：组合学
Bubble Lattices II: Combinatorics
论文作者
论文摘要
我们介绍了两个简单络合物，即非交叉匹配络合物和非交叉两分络合物。这两个复合物与我们先前文章“泡泡晶格I：结构”中引入的气泡晶格密切相关（Arxiv：2202.02874）。我们从列举和几何观点研究了这些复合物。特别是，我们证明这些复合物是可壳的，并为某些精制的面部数字提供了明确的公式。最后，我们猜想了这些精制的面部数字与所谓的shuffle晶格的M-Triangle的有趣联系。
We introduce two simplicial complexes, the noncrossing matching complex and the noncrossing bipartite complex. Both complexes are intimately related to the bubble lattice introduced in our earlier article "Bubble Lattices I: Structure" (arXiv:2202.02874). We study these complexes from both an enumerative and a geometric point of view. In particular, we prove that these complexes are shellable and give explicit formulas for certain refined face numbers. Lastly, we conjecture an intriguing connection of these refined face numbers to the so-called M-triangle of the shuffle lattice.
