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PreprintCC BY 4.0arXiv

Generalised flip order on the faces of nestohedra

  • Pierre-Louis Curien
  • Bérénice Delcroix-Oger
  • Jovana Obradović
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Abstract

Tamari lattices and weak Bruhat order are classical posets on the vertices of associahedra and permutohedra. These posets are particular instances of the \emph{flip order} on the vertices of graph associahedra. We present here a generalisation of the flip order to all the faces of nestohedra, encoded in terms of hypergraphs. For right-filled hypergraphs, we characterise our order in terms of generalised inversions. As an application, we describe shuffle products on faces of suitable nestohedra as sums over intervals in this order.

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Cite

BibTeXRIS
BibTeX
@misc{curien2026generalised,
  title = {{Generalised flip order on the faces of nestohedra}},
  author = {Pierre-Louis Curien and Bérénice Delcroix-Oger and Jovana Obradović},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2607.20132},
  eprint = {2607.20132},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.20132},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Generalised flip order on the faces of nestohedra
AU  - Pierre-Louis Curien
AU  - Bérénice Delcroix-Oger
AU  - Jovana Obradović
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2607.20132
UR  - https://arxiv.org/abs/2607.20132
AB  - Tamari lattices and weak Bruhat order are classical posets on the vertices of associahedra and permutohedra. These posets are particular instances of the \emph{flip order} on the vertices of graph associahedra. We present here a generalisation of the flip order to all the faces of nestohedra, encoded in terms of hypergraphs. For right-filled hypergraphs, we characterise our order in terms of generalised inversions. As an application, we describe shuffle products on faces of suitable nestohedra as sums over intervals in this order.
ER  -