The antipode of the noncrossing partition lattice

被引：2
|
作者：
Ehrenberg, Richard [1 ]
Happ, Alex [2 ]
机构：
[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA
[2] Christian Bros Univ, Dept Math, Memphis, TN 38104 USA
来源：
ADVANCES IN APPLIED MATHEMATICS | 2019年 / 110卷
关键词：
Incidence Hopf algebra; Noncrossing hypertree; Ordered partition; Permutahedron; Euler characteristic with compact support;
D O I：
10.1016/j.aam.2019.03.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove the cancellation-free formula for the antipode of the noncrossing partition lattice in the reduced incidence Hopf algebra of posets due to Einziger. The proof is based on a map from chains in the noncrossing partition lattice to noncrossing hypertrees and expressing the alternating sum over these fibers as an Euler characteristic. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：76 / 85
页数：10
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