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PreprintCC BY 4.0arXiv

Invariance of rowmotion for variants of the Tamari lattice

  • Ben Adenbaum
  • Emily Barnard
  • Cesar Ceballos
  • Clément Chenevière
  • Colin Defant
  • Sam Hopkins
  • Matthias Müller
  • Martin Rubey
  • Jessica Striker
Open at sourcePDFDOICite

Abstract

We show that the rowmotion operator from dynamical algebraic combinatorics behaves the same on all alt ν-Tamari lattices for a fixed lattice path ν. We use this invariance of rowmotion to establish cyclic sieving and homomesy results for rational Tamari lattices. We also conjecture that this invariance extends to the more general cross Tamari lattices.

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Cite

BibTeXRIS
BibTeX
@misc{adenbaum2026invariance,
  title = {{Invariance of rowmotion for variants of the Tamari lattice}},
  author = {Ben Adenbaum and Emily Barnard and Cesar Ceballos and Clément Chenevière and Colin Defant and Sam Hopkins and Matthias Müller and Martin Rubey and Jessica Striker},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12983},
  eprint = {2609.12983},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12983},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Invariance of rowmotion for variants of the Tamari lattice
AU  - Ben Adenbaum
AU  - Emily Barnard
AU  - Cesar Ceballos
AU  - Clément Chenevière
AU  - Colin Defant
AU  - Sam Hopkins
AU  - Matthias Müller
AU  - Martin Rubey
AU  - Jessica Striker
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12983
UR  - https://arxiv.org/abs/2609.12983
AB  - We show that the rowmotion operator from dynamical algebraic combinatorics behaves the same on all alt ν-Tamari lattices for a fixed lattice path ν. We use this invariance of rowmotion to establish cyclic sieving and homomesy results for rational Tamari lattices. We also conjecture that this invariance extends to the more general cross Tamari lattices.
ER  -