来自平面配置的非交叉分割网格

Pub Date : 2024-07-24 DOI:10.1007/s00454-024-00682-6

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Noncrossing Partition Lattices from Planar Configurations

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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.

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