A new proof of an identity concerning $5$-core partitions

Authors

  • Russelle Guadalupe University of the Philippines Diliman

DOI:

https://doi.org/10.53733/724

Keywords:

$5$-core partitions, dissection formulas, Ramanujan's parameter

Abstract

Let $a_5(n)$ be the number of partitions of $n$ that are $5$-cores. We provide a new elementary proof of an identity involving $a_5(n)$ due to Baruah and Berndt by employing $2$-dissection formulas and identities involving the Ramanujan's parameter $k(q)$ due to Cooper, Chern, and Tang.

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Author Biography

Russelle Guadalupe, University of the Philippines Diliman

Russelle Guadalupe
Institute of Mathematics
University of the Philippines
Diliman, Quezon City 1101
Philippines

rguadalupe@math.upd.edu.ph

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Published

27-05-2026

How to Cite

Guadalupe, R. (2026). A new proof of an identity concerning $5$-core partitions. New Zealand Journal of Mathematics, 57, 25–29. https://doi.org/10.53733/724

Issue

Vol. 57 (2026)

Section

Articles