发表机构
Vrije Universiteit Brussel; imec-SMIT（布鲁塞尔自由大学; imec-SMIT）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从多项式族构造显式非对角 Ramsey 图，通过插值和标量限制得到指数界，并给出确定性多项式时间算法。
AI 中文摘要
我们从入射点-超平面旗的多项式族构造显式非对角 Ramsey 图。通用插值将有序团配置的精确维数转化为其系数-标签关联上的界。在临界维数，一个多项式将禁止对图像与其对角线分离；删除相应边保留三角秩证书。标量限制实现有理端点而无舍入损失。所得固定-$s$ 指数具有前导尺度 $s/(2\log_2s)$，短 Frobenius 关系给出显式例子 $R(16,t)\ge\Omega(t^{2.0539221767\ldots})$。有限纤维构造给出范围 $s^2(\log s)^2=o(\log t)$。对于固定参数，代数预处理终止，域初始化、顶点解码和邻接判定在扩展度上取确定性多项式时间。我们还保留一个无消去变体，并为具有显著边的通用禁止配置表述过滤论证。
英文摘要
We construct explicit off-diagonal Ramsey graphs from polynomial families of incident point--hyperplane flags. Universal interpolation translates the exact dimension of ordered clique configurations into a bound on their coefficient--label incidence. At the critical dimension, a polynomial separates the forbidden-pair image from its diagonal; deleting the corresponding edges preserves a triangular rank certificate. Restriction of scalars realizes the rational endpoint without rounding loss. The resulting fixed-$s$ exponent has leading scale $s/(2\log_2s)$, and short Frobenius relations give the explicit example $R(16,t)\geΩ(t^{2.0539221767\ldots})$. A finite-fiber construction gives the range $s^2(\log s)^2=o(\log t)$. For fixed parameters, algebraic preprocessing terminates and field initialization, vertex decoding and adjacency take deterministic time polynomial in the extension degree. We also retain an elimination-free variant and formulate the filtering argument for general forbidden configurations with a distinguished edge.
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