论文标题
所有模量的过度分区排名之间的不平等
Inequalities between overpartition ranks for all moduli
论文作者
论文摘要
在本文中，我们全面描述了过度分区等级之间可能发生的不平等现象。如果$ \ OVILLINE {n}（a，c，n）$表示$ n $的过度分支的数量，等级与$ a $ a $ modulo $ c，$，我们证明，对于任何$ c \ ge7 $和$ c \ ge7 $和$ 0 \ le a <b \ le a <b \ le \ le \ le \ weft \ weft \ lfloor \ lfloor \ frac \ frac $ c} $ \ + edline {n}（a，c，n）> \ edimelline {n}（b，c，n）$ for $ n $足够大。等级差异的符号$ \叠加{n}（a，c，n） - \ operline {n}（b，b，c，n）$取决于$ n $ modulo $ c $ $ c = 6的残基类别，例如$ c = 6，例如$ C = 6，$是由于JI，Zhang和Zhang and Zhang and Zhao（Zhao（2018）和Ciolan（2020）而闻名。我们表明，$ c \ in \ {2,3，4,5 \}的同一行为也具有相同的行为。 $
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\}. $
