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Breaking the Infinite Barrier in the 1/3--2/3 Conjecture
Abstract
The balance constant is a poset parameter measuring how well random linear extensions can be split according to their relative order on two elements. We give an ε-improvement for the balance constant over the bound by Brightwell, Felsner and Trotter (1995), for some small ε>0. This is the first general result towards the 1/3--2/3 conjecture in over 30 years.
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BibTeX
@misc{aires2026breaking,
title = {{Breaking the Infinite Barrier in the $\frac13$--$\frac23$ Conjecture}},
author = {Max Aires and Swee Hong Chan and Igor Pak and Greta Panova},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.30888},
eprint = {2609.30888},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30888},
}
RIS
TY - UNPB
TI - Breaking the Infinite Barrier in the 1/3--2/3 Conjecture
AU - Max Aires
AU - Swee Hong Chan
AU - Igor Pak
AU - Greta Panova
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2609.30888
UR - https://arxiv.org/abs/2609.30888
AB - The balance constant is a poset parameter measuring how well random linear extensions can be split according to their relative order on two elements. We give an ε-improvement for the balance constant over the bound by Brightwell, Felsner and Trotter (1995), for some small ε>0. This is the first general result towards the 1/3--2/3 conjecture in over 30 years.
ER -