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PreprintarXiv licencearXiv

Positivity for graph Laurent phenomenon algebras

  • Ross Glew
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Abstract

Laurent phenomenon algebras were introduced by Lam and Pylyavskyy as a generalisation of cluster algebras. For a family associated with directed graphs, they showed that every cluster variable is a Laurent polynomial in the variables of any cluster and conjectured that these expansions have nonnegative coefficients. We prove this conjecture for all directed graphs without loops or multiple edges with respect to an arbitrary seed cluster.

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Cite

BibTeXRIS
BibTeX
@misc{glew2026positivity,
  title = {{Positivity for graph Laurent phenomenon algebras}},
  author = {Ross Glew},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08914},
  eprint = {2610.08914},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08914},
}
RIS
TY  - UNPB
TI  - Positivity for graph Laurent phenomenon algebras
AU  - Ross Glew
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08914
UR  - https://arxiv.org/abs/2610.08914
AB  - Laurent phenomenon algebras were introduced by Lam and Pylyavskyy as a generalisation of cluster algebras. For a family associated with directed graphs, they showed that every cluster variable is a Laurent polynomial in the variables of any cluster and conjectured that these expansions have nonnegative coefficients. We prove this conjecture for all directed graphs without loops or multiple edges with respect to an arbitrary seed cluster.
ER  -