Year: 2026
Type: preprint
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 $\varepsilon$-improvement for the balance constant over the bound by Brightwell, Felsner and Trotter (1995), for some small $\varepsilon>0$. This is the first general result towards the $\frac{1}{3}$--$\frac{2}{3}$ conjecture in over 30 years.
Source: arXiv (Cornell University)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214603325