PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Two infinite families of congruences modulo 9 for overcubic partition pairs

Volume 147 / 2017

Bernard Lishuang Lin, Erin Yiying Shen, Andrew Yezhou Wang Colloquium Mathematicum 147 (2017), 115-123 MSC: Primary 05A17; Secondary 11P83. DOI: 10.4064/cm6843-4-2016 Published online: 9 December 2016


Let $\overline {b}(n)$ denote the number of overcubic partition pairs of $n$. Applying the theory of modular forms, Kim obtained two congruences for $\overline {b}(n)$ modulo $3$ and $64$. More congruences modulo $3$ and $5$ have been found by the first author of the present paper. In this paper, we proceed with the study of the congruence properties of $\overline {b}(n)$ and establish two infinite families of congruences modulo $9$.


  • Bernard Lishuang LinSchool of Science
    Jimei University
    361021 Xiamen, P.R. China
  • Erin Yiying ShenSchool of Sciences
    Hohai University
    210098 Nanjing, P.R. China
  • Andrew Yezhou WangSchool of Mathematical Sciences
    University of Electronic Science and Technology of China
    611731 Chengdu, P.R. China

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image