论文标题
分区的最大和最小部分与伯科维奇和UNCU的猜想之间的差距
Gap between the largest and smallest parts of partitions and Berkovich and Uncu's conjectures
论文作者
论文摘要
我们证明了Berkovich and UNCU的三个主要猜想（Ann。Comb。23（2019）263--284）关于$ n $的分区数量之间的不平等，对于足够大的$ n $，最大和最小的零件之间有界限。实际上，我们的定理比其原始猜想强。我们结果的分析版本表明，某些分区的系数$ q $ series最终是积极的。
We prove three main conjectures of Berkovich and Uncu (Ann. Comb. 23 (2019) 263--284) on the inequalities between the numbers of partitions of $n$ with bounded gap between largest and smallest parts for sufficiently large $n$. Actually our theorems are stronger than their original conjectures. The analytic version of our results shows that the coefficients of some partition $q$-series are eventually positive.
