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

Producción científica: Article › revisión exhaustiva

2 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	76-85
Número de páginas	10
Publicación	Advances in Applied Mathematics
Volumen	110
DOI	https://doi.org/10.1016/j.aam.2019.03.007
Estado	Published - sept 2019

Nota bibliográfica

Publisher Copyright:
© 2019 Elsevier Inc.

Financiación

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).

Financiadores	Número del financiador
Simons Foundation	429370

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2019.03.007

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title = "The antipode of the noncrossing partition lattice",

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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year = "2019",

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doi = "10.1016/j.aam.2019.03.007",

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T1 - The antipode of the noncrossing partition lattice

AU - Ehrenborg, Richard

AU - Happ, Alex

PY - 2019/9

Y1 - 2019/9

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

UR - https://www.scopus.com/pages/publications/85067389261

UR - https://www.scopus.com/pages/publications/85067389261#tab=citedBy

U2 - 10.1016/j.aam.2019.03.007

DO - 10.1016/j.aam.2019.03.007

M3 - Article

AN - SCOPUS:85067389261

SN - 0196-8858

VL - 110

SP - 76

EP - 85

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

ER -

The antipode of the noncrossing partition lattice

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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