论文标题
单色产品和总和$ 2 $ - 颜色的$ \ mathbb {n} $
Monochromatic products and sums in $2$-colorings of $\mathbb{N}$
论文作者
论文摘要
我们表明，任何$ 2 $ - 颜色的$ \ mathbb {n} $包含$ \ \ {x，y，xy，x+y \}的形式的许多单色集，$和更一般的单色单色集的表单$ \ \ \ \ for { $ k \ in \ mathbb {n}。$沿途，我们证明了一个单色sums定理的单色产品，该产品扩展了Hindman的定理和此结果的多彩变体，以任何“平衡”着色。
We show that any $2$-coloring of $\mathbb{N}$ contains infinitely many monochromatic sets of the form $\{x,y,xy,x+y\},$ and more generally monochromatic sets of the form $\{x_i,\prod x_i,\sum x_i: i\leq k\}$ for any $k\in\mathbb{N}.$ Along the way we prove a monochromatic products of sums theorem that extends Hindman's theorem and a colorful variant of this result that holds in any 'balanced' coloring.
