Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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INFINITE FAMILIES OF CONGRUENCES MODULO 2 FOR 2-CORE AND 13-CORE PARTITIONS

  • Ankita Jindal (Indian Statistical Institute) ;
  • Nabin Kumar Meher (Department of Mathematics Indian Institute of Information Technology Raichur, Government of Engineering College Yermarus Campus)
  • Received : 2023.01.16
  • Accepted : 2023.06.13
  • Published : 2023.09.01
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Abstract

A partition of n is called a t-core partition if none of its hook number is divisible by t. In 2019, Hirschhorn and Sellers [5] obtained a parity result for 3-core partition function a3(n). Motivated by this result, both the authors [8] recently proved that for a non-negative integer α, a3αm(n) is almost always divisible by an arbitrary power of 2 and 3 and at(n) is almost always divisible by an arbitrary power of pji, where j is a fixed positive integer and t = pa11pa22···pamm with primes pi ≥ 5. In this article, by using Hecke eigenform theory, we obtain infinite families of congruences and multiplicative identities for a2(n) and a13(n) modulo 2 which generalizes some results of Das [2].

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Acknowledgement

We thank the anonymous referee for going through the paper carefully and giving his/her useful comments which improves the readability of the manuscript. The second author is thankful to BITS Pilani Hyderabad Campus for providing the nice research facilities during the initial part of this project, where both the authors met and started working on this project.

References

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