Stella Cohen, Michael Dougherty, Andrew D. Harsh, Spencer Park Martin
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引用次数: 0
摘要
非交叉分割网格以其多种多样的组合外观和性质而闻名。例如，该网格是秩对称的，并由加泰罗尼亚数枚举。在这篇文章中，我们介绍了一大系列具有上述两种性质的新非交叉分割网格，每个网格的参数都是平面上 n 个点的配置。
Noncrossing Partition Lattices from Planar Configurations
The lattice of noncrossing partitions is well-known for its wide variety of combinatorial appearances and properties. For example, the lattice is rank-symmetric and enumerated by the Catalan numbers. In this article, we introduce a large family of new noncrossing partition lattices with both of these properties, each parametrized by a configuration of n points in the plane.
期刊介绍：
Discrete & Computational Geometry (DCG) is an international journal of mathematics and computer science, covering a broad range of topics in which geometry plays a fundamental role. It publishes papers on such topics as configurations and arrangements, spatial subdivision, packing, covering, and tiling, geometric complexity, polytopes, point location, geometric probability, geometric range searching, combinatorial and computational topology, probabilistic techniques in computational geometry, geometric graphs, geometry of numbers, and motion planning.
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