所有模的超分秩之间的不等式
Inequalities between overpartition ranks for all moduli
摘要：
在本文中，我们给出了一个完整的描述之间可能发生的不平等的过度划分的行列。如果$ \overline{N}(a,c,n) $表示$ n $的满分个数，其秩与$ a $模$ c,$全等，我们证明了对于任何$ c\ge7 $和$ 0\le a<b\le\left\lfloor\frac{c}{2}\right\rfloor $，我们都有足够大的$n$的$ \overline{N}(a,c,n)>\overline{N}(b,c,n) $。秩差$ \overline{N}(a,c,n)-\overline{N}(b,c,n) $的符号取决于在小模数的情况下$ n $模$ c $的剩余类，例如$ c=6, $，这是由于Ji，Zhang和Zhao（2018）和Ciolan（2020）的工作而已知的。我们表明，同样的行为适用于$ c\in\{2,3, 4,5\}. $
英文摘要：
In this paper we give a full description of the inequalities that can occur between overpartition ranks. If $ \overline{N}(a,c,n) $ denotes the number of overpartitions of $ n $ with rank congruent to $ a $ modulo $ c,$ we prove that for any $ c\ge7 $ and $ 0\le a<b\le\left\lfloor\frac{c}{2}\right\rfloor $ we have $ \overline{N}(a,c,n)>\overline{N}(b,c,n) $ for $n$ large enough. That the sign of the rank differences $ \overline{N}(a,c,n)-\overline{N}(b,c,n) $ depends on the residue class of $ n $ modulo $ c $ in the case of small moduli, such as $ c=6, $ is known due to the work of Ji, Zhang and Zhao (2018) and Ciolan (2020). We show that the same behavior holds for $ c\in\{2,3, 4,5\}. $
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