PreprintarXiv licencearXiv
On dimension of posets excluding a standard example
Abstract
We prove that for every integer d ≥ 3, there exists α<1 such that the maximum dimension of an n-element poset containing no standard example of order d as an induced subposet is 𝒪d(nα). For d=3, we obtain an upper bound 𝒪(n2/3log n), while we also construct a family of S3-free posets with dimension Ω(n1/3/log n). The proofs were found by OpenAI's ChatGPT-6 Astra.
Related
BibTeX
@misc{hodor2026dimension,
title = {{On dimension of posets excluding a standard example}},
author = {Jędrzej Hodor and Piotr Micek and William T. Trotter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24774},
eprint = {2610.24774},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24774},
}
RIS
TY - UNPB
TI - On dimension of posets excluding a standard example
AU - Jędrzej Hodor
AU - Piotr Micek
AU - William T. Trotter
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24774
UR - https://arxiv.org/abs/2610.24774
AB - We prove that for every integer d ≥ 3, there exists α<1 such that the maximum dimension of an n-element poset containing no standard example of order d as an induced subposet is 𝒪_d(n^α). For d=3, we obtain an upper bound 𝒪(n^2/3log n), while we also construct a family of S_3-free posets with dimension Ω(n^1/3/log n). The proofs were found by OpenAI's ChatGPT-6 Astra.
ER -