用随机3CNF公式证明随机三角群的不可序性
Non-orderability of random triangular groups by using random 3CNF formulas
摘要：
我们证明了在三角二项模型$Γ(n, p)$中随机组$Γ$是a.a.s.对于$p\in(cn^{-2}, n^{-3/2-\varepsilon})$不可左序，其中$c, \varepsilon$是满足$\varepsilon>0$，${c>(1/8)\log_{4/3}{2}\approx 0.3012}$的任何常数。我们还证明了，如果对任何固定的$\varepsilon>0$，有$p\geq (1+\varepsilon)(\log n)n^{-2}$，则随机的$Γ\in Γ(n,p)$有a.a.s.没有非平凡的左可序子。我们通过构造3CNF公式，编码左序性的必要条件，然后证明它们的不可满足性a.a.s.
英文摘要：
We show that a random group $Γ$ in the triangular binomial model $Γ(n, p)$ is a.a.s. not left-orderable for $p\in(cn^{-2}, n^{-3/2-\varepsilon})$, where $c, \varepsilon$ are any constants satisfying $\varepsilon>0$, ${c>(1/8)\log_{4/3}{2}\approx 0.3012}$. We also prove that if $p\geq (1+\varepsilon)(\log n)n^{-2}$ for any fixed $\varepsilon>0$, then a random $Γ\in Γ(n,p)$ has a.a.s. no non-trivial left-orderable quotients. We proceed by constructing 3CNF formulas, which encode necessary conditions for left-orderability and then proving their unsatisfiability a.a.s.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
