The antipode of the noncrossing partition lattice

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2 Scopus citations


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 languageEnglish
Pages (from-to)76-85
Number of pages10
JournalAdvances in Applied Mathematics
StatePublished - 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.


  • Euler characteristic with compact support
  • Incidence Hopf algebra
  • Noncrossing hypertree
  • Ordered partition
  • Permutahedron

ASJC Scopus subject areas

  • Applied Mathematics


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