论文标题
关于最小部分和整数分区部分的猜想
On Conjectures Concerning the Smallest Part and Missing Parts of Integer Partitions
论文作者
论文摘要
对于正整数$ s $和$ l \ geq 3 $，Berkovich和UNCU（Ann。Comb。$ 23 $（$ 2019 $）$ 263 $ - $ 284 $），猜想了两套密切相关的分区的大小之间的不平等，其部分在间隔$ \ \ f {s，\ ldots，\ ldots，ldots，l+s，l+s \ s中。通过指定不允许的零件以及最小零件，将进一步的限制放在集合上。作者证明了他们对$ s = 1 $和$ s = 2 $的猜想。在本文中，我们通过证明更强的定理证明了一般$ s $的猜想。我们还证明了同一论文中发现的其他相关猜想。
For positive integers $s$ and $L \geq 3$, Berkovich and Uncu (Ann. Comb. $23$ ($2019$) $263$--$284$) conjectured an inequality between the sizes of two closely related sets of partitions whose parts lie in the interval $\{s, \ldots, L+s\}$. Further restrictions are placed on the sets by specifying impermissible parts as well as a minimum part. The authors proved their conjecture for the cases $s=1$ and $s=2$. In the present article, we prove the conjecture for general $s$ by proving a stronger theorem. We also prove other related conjectures found in the same paper.
