Even smaller universal posets

József Balogh; Ramon I. Garcia; Marcelo Sales

Even smaller universal posets

Combinatorics 2026-07-14 v1

Authors: József Balogh , Ramon I. Garcia , Marcelo Sales

Abstract

We show that for every $\eta>0$ and sufficiently large $n$ , there exists a poset of size $2^{(1+\eta)n/2}$ containing all the $n$ -element posets as induced subposets. This improves a recent result of Bastide, Groenland and Nenadov. Our proof provides a labeling scheme preserving transitivity, inspired by the Boolean lattice. Among other tools, we use the Szemer\'edi Regularity Lemma.

Cite

@article{arxiv.2607.12980,
  title  = {Even smaller universal posets},
  author = {József Balogh and Ramon I. Garcia and Marcelo Sales},
  journal= {arXiv preprint arXiv:2607.12980},
  year   = {2026}
}