带标记曲面的非交叉划分
组合数学
2026-05-22 v6
摘要
我们定义了无穿孔（内部标记点）的带标记曲面的非交叉划分。我们证明了非交叉划分上的自然偏序是一个分次格，并从拓扑上描述了其秩函数。该格中的下区间同构于其他曲面的非交叉划分格的乘积。类似地，我们定义了具有双点的对称带标记曲面的非交叉划分，并证明了若干类似结果。对称性与双点的结合起到了人们可能预期由穿孔所起的作用。
引用
@article{arxiv.2212.13799,
title = {Noncrossing partitions of a marked surface},
author = {Nathan Reading},
journal= {arXiv preprint arXiv:2212.13799},
year = {2026}
}
备注
39 pages, 13 figures. Version 3: Removed the assertion that the noncrossing partitions of a symmetric marked surface with double points form a lattice and provided a counterexample. Version 4: Minor changes, additions, and corrections in connection with the release of arXiv:2312.17331. Version 5: accepted SIAM J. Discrete Math. Version 6: final pre-publication version