版本更新 · v2arXiv:2609.30888
Breaking the Infinite Barrier in the $\frac{1}{3}$--$\frac{2}{3}$ Conjecture
Max Aires, Swee Hong Chan, Igor Pak, Greta Panova
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.
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math.CO · cs.DM