Communications of the Korean Mathematical Society (대한수학회논문집)

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ON PARTITION CONGRUENCES FOR OVERCUBIC PARTITION PAIRS

  • Kim, Byung-Chan (School of Liberal Arts Seoul National University of Science and Technology)
  • Received : 2011.04.26
  • Published : 2012.07.31
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Abstract

In this note, we investigate partition congruences for a certain type of partition function, which is named as the overcubic partition pairs in light of the literature. Let $\bar{cp}(n)$ be the number of overcubic partition pairs. Then we will prove the following congruences: $$\bar{cp}(8n+7){\equiv}0(mod\;64)\;and\;\bar{cp}(9m+3){\equiv}0(mod\;3)$$.

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References

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  1. Congruences modulo 27 for cubic partition pairs vol.171, 2017, https://doi.org/10.1016/j.jnt.2016.07.012
  2. New congruences for overcubic partition pairs vol.10, pp.4, 2017, https://doi.org/10.1515/tmj-2017-0050