English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Inequalities between overpartition ranks for all moduli

MPS-Authors
/persons/resource/persons235089

Ciolan,  Alexandru
Max Planck Institute for Mathematics, Max Planck Society;

Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Supplementary Material (public)
There is no public supplementary material available
Citation

Ciolan, A. (2022). Inequalities between overpartition ranks for all moduli. Ramanujan Journal, 58(2), 463-489. doi:10.1007/s11139-021-00436-5.


Cite as: https://hdl.handle.net/21.11116/0000-0008-B509-2
Abstract
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\}. $