Identities for 3-core and 5-core partitions

Yoon Kyung Park

doi:10.4134/JKMS.2014.51.2.225

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J. Korean Math. Soc. 2014; 51(2): 225-238

Printed March 1, 2014

https://doi.org/10.4134/JKMS.2014.51.2.225

Identities for 3-core and 5-core partitions

Yoon Kyung Park

Korea Institute for Advanced Study

Abstract

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Abstract

We apply modular function theory to find the relation among $t$-core partitions. By using the generators of function field corresponding to a certain modular group, we reprove the identities in \cite{BaruahBerndt} because their relations are linear for $t=3$ or $5$.

Keywords: $t$-cores, modular functions

MSC numbers: 05A17, 11F03, 11F30