MATEMATIČKI VESNIK Vol. 69, No. 3, pp. 192–206 (2017) 

Arithmetic properties of 3regular bipartitions with designated summandsM. S. Mahadeva Naika and S. Shivaprasada NayakaM.S.M.N: Department of Mathematics, Bangalore University, Central College Campus, Bangalore560 001, Karnataka, India Email: msmnaika@rediffmail.com and S.S.N: Department of Mathematics, Bangalore University, Central College Campus, Bangalore560 001, Karnataka, India Email: shivprasadnayaks@gmail.comAbstract: Recently Andrews, Lewis and Lovejoy introduced the partition functions $PD\left(n\right)$ defined by the number of partitions of $n$ with designated summands and they found several modulo 3 and 4. In this paper, we find several congruences modulo 3 and 4 for $PB{D}_{3}\left(n\right)$, which represent the number of 3regular bipartitions of $n$ with designated summands. For example, for each $n\ge 1$ and $\alpha \ge 0$ $PB{D}_{3}(4\xb7{3}^{\alpha +2}n+10\xb7{3}^{\alpha +1})\equiv 0\phantom{\rule{4.44443pt}{0ex}}(mod\phantom{\rule{0.277778em}{0ex}}3)$. Keywords: Partitions; designated summands; congruences. Classification (MSC2000): 05A17; 11P83 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 20 Jun 2017. This page was last modified: 7 Jul 2017.
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