Abstract
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.
Original language | English |
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Pages (from-to) | 76-85 |
Number of pages | 10 |
Journal | Advances in Applied Mathematics |
Volume | 110 |
DOIs | |
State | Published - Sep 2019 |
Bibliographical note
Funding Information:We thank the referee for giving us more pointers to the reference [10] . This work was supported by a grant from the Simons Foundation (# 429370 , Richard Ehrenborg).
Publisher Copyright:
© 2019 Elsevier Inc.
Keywords
- Euler characteristic with compact support
- Incidence Hopf algebra
- Noncrossing hypertree
- Ordered partition
- Permutahedron
ASJC Scopus subject areas
- Applied Mathematics