Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 60: Issue 2-3
Equalities for the 𝑟3-Crank of 3-Regular Overpartitions
Authors:
Robert X. J. Hao College of Science and Mathematics, Nanjing Institute of Technology, Nanjing 211167, P. R. China

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and
Erin Y. Y. Shen School of Mathematics, Hohai University, Nanjing 210098, P. R. China

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Pages:
123–132
Online Publication Date:
24 Oct 2023
Publication Date:
24 Oct 2023
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2023.01542
Keywords:
Regular overpartition; crank; combinatorial interpretation; equality
Restricted access

Lovejoy introduced the partition function Al¯n as the number of 𝑙-regular overpartitions of 𝑛. Andrews defined (𝑘, 𝑖)-singular overpartitions counted by the partition function C¯k,in, and pointed out that C¯3,1n=A3¯n. Meanwhile, Andrews derived an interesting divisibility property that C¯3,19n+3≡C¯3,19n+6≡0 (mod 3). Recently, we constructed the partition statistic 𝑟𝑙-crank of 𝑙-regular overpartitions and give combinatorial interpretations for some congruences of Al¯n as well as the congruences of Andrews. In this paper, we aim to prove some equalities for the 𝑟3-crank of 3-regular overpartitions.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
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ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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