论文标题
整数和拉姆齐定理的乘法表示
Multiplicative representations of integers and Ramsey's theorem
论文作者
论文摘要
令$ \ Mathcal {b} =（b_1，\ ldots，b_h）$为$ h $ - 集合的正整数。令$ g _ {\ mathcal {b}}（n）$计数$ n = b_1 \ cdots b_h $中的$ n $的表示形式，其中$ b_i \ in b_i $ in b_i $ in b_i $ for ALL $ i \ in \ in \ in \ {1，\ ldots，h \ \} $。事实证明，$ \ liminf_ {n \ rightarrow \ infty} g _ {\ Mathcal {b}}}（n）\ geq 2 $含义$ \ limsup_ {
Let $\mathcal{B} = (B_1,\ldots, B_h)$ be an $h$-tuple of sets of positive integers. Let $g_{\mathcal{B} }(n)$ count the number of representations of $n$ in the form $n = b_1\cdots b_h$, where $b_i \in B_i$ for all $i \in \{1,\ldots, h\}$. It is proved that $\liminf_{n\rightarrow \infty} g_{\mathcal{B} }(n) \geq 2$ implies $\limsup_{n\rightarrow \infty} g_{\mathcal{B} }(n) = \infty$.
