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.
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页码：76 / 85
页数：10
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