Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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FURTHER RESULTS ON BIASES IN INTEGER PARTITIONS

  • Chern, Shane (Department of Mathematics Penn State University)
  • Received : 2021.02.10
  • Accepted : 2021.06.04
  • Published : 2022.01.31
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Abstract

Let pa,b,m(n) be the number of integer partitions of n with more parts congruent to a modulo m than parts congruent to b modulo m. We prove that pa,b,m(n) ≥ pb,a,m(n) whenever 1 ≤ a < b ≤ m. We also propose some conjectures concerning series with nonnegative coefficients in their expansions.

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References

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