The antipode of the noncrossing partition lattice

Richard Ehrenborg; Alex Happ

doi:10.1016/j.aam.2019.03.007

The antipode of the noncrossing partition lattice

Richard Ehrenborg, Alex Happ

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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
Pages (from-to)	76-85
Number of pages	10
Journal	Advances in Applied Mathematics
Volume	110
DOIs	https://doi.org/10.1016/j.aam.2019.03.007
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

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10.1016/j.aam.2019.03.007

Cite this

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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.",

keywords = "Euler characteristic with compact support, Incidence Hopf algebra, Noncrossing hypertree, Ordered partition, Permutahedron",

author = "Richard Ehrenborg and Alex Happ",

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AU - Happ, Alex

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N2 - 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.

AB - 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.

KW - Euler characteristic with compact support

KW - Incidence Hopf algebra

KW - Noncrossing hypertree

KW - Ordered partition

KW - Permutahedron

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JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

ER -

The antipode of the noncrossing partition lattice

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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