论文标题
在带有指数和排列的循环不平等及其shapiro-type类似物上
On a cyclic inequality with exponents and permutations, and its Shapiro-type analogue
论文作者
论文摘要
我们证明了循环不平等$ \ sum \ limits_ {i = 1}^{i = n} \ left（\ frac {x_i} {x__ {x_ {i+1}}} \ right）^k \ geq \ geq \ sum \ sum \ limits_在特定范围内取决于置换$σ$。我们还表明，Sahpiro型概括并非如此。
We prove that the cyclic inequality $\sum\limits_{i=1}^{i=n}\left(\frac{x_i}{x_{i+1}}\right)^k\geq\sum\limits_{i=1}^{i=n}\frac{x_i}{x_{σ(i)}}$ holds for $k$ in a specific range dependant on the permutation $σ$. We also show that the same is not true for the Sahpiro-type generalizations.
