


























In this article, we investigate polynomial generalizations of the van der Waerden theorem with a focus on largeness properties of recurrence patterns. We prove an $IP_r^\star$-strengthened version of the polynomial van der Waerden theorem, where the recurrence set is guaranteed to be large in a precise combinatorial sense. As applications, we obtain new monochromatic polynomial configurations in both additive and multiplicative settings, including refined results over sum subsystems of IP-sets. Additionally, we prove exponential monochromatic patterns are abundant.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。