论文标题
理性的非交叉Coxeter-Catalan组合学
Rational Noncrossing Coxeter-Catalan Combinatorics
论文作者
论文摘要
我们解决了Coxeter-Catalan组合学中的两个开放问题。首先，我们使用杰出子词的组合介绍了任何有限的Coxeter组的一个理性非交叉对象。其次，我们给出了这些非交叉加泰罗尼亚对象的类型均匀证据，该对象使用相关的Hecke代数的特征理论和Lusztig的Exotic Fourier变换来计算合理的Coxeter-catalan数字。我们解决了合理的非交叉停车对象的相同问题。
We solve two open problems in Coxeter-Catalan combinatorics. First, we introduce a family of rational noncrossing objects for any finite Coxeter group, using the combinatorics of distinguished subwords. Second, we give a type-uniform proof that these noncrossing Catalan objects are counted by the rational Coxeter-Catalan number, using the character theory of the associated Hecke algebra and the properties of Lusztig's exotic Fourier transform. We solve the same problems for rational noncrossing parking objects.
