论文标题
Baruah和Begum的猜想在受限的太小零件功能上的功能
A conjecture of Baruah and Begum on the smallest parts function of restricted overpartitions
论文作者
论文摘要
2017年，Andrews，Dixit，Schultz和Yee介绍了$ \ Overline {\ textrm {spt}}_Ω（n）$，这表示$ n $的过度零件中最小的部分的数量始终是$ n $的，其中最小的部分始终是大量的，所有奇数零件都不是所有奇数零件。最近，Baruah和Begum建立了几个内部一致性和一致性Modulo小型$ 5 $的小型$ \ overline {\ textrm {spt}}_Ω（n）$。此外，他们猜想了一个内部一致的家族，$ 5 $的任何权力和两个一致的家族Modulo均为$ 5 $。在本文中，我们确认了由于Baruah和Begum引起的三个一致性家庭。
In 2017, Andrews, Dixit, Schultz and Yee introduced the function $\overline{\textrm{spt}}_ω(n)$, which denotes the number of smallest parts in the overpartitions of $n$ in which the smallest part is always overlined and all odd parts are less than twice the smallest part. Recently, Baruah and Begum established several internal congruences and congruences modulo small powers of $5$ for $\overline{\textrm{spt}}_ω(n)$. Moreover, they conjectured a family of internal congruences modulo any powers of $5$ and two families of congruences modulo any even powers of $5$. In this paper, we confirm three families of congruences due to Baruah and Begum.
