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

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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

Publisher Copyright:
© 2019 Elsevier Inc.

Funding

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).

Funders	Funder number
Simons Foundation	429370

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.",

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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.

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KW - Incidence Hopf algebra

KW - Noncrossing hypertree

KW - Ordered partition

KW - Permutahedron

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JO - Advances in Applied Mathematics

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ER -

The antipode of the noncrossing partition lattice

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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