On inequalities and linear relations for 7-core partitions

Byungchan Kim

doi:10.1016/j.disc.2009.09.024

On inequalities and linear relations for 7-core partitions

Byungchan Kim

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Recently, Ramanujan's modular equations have been applied by N.D. Baruah and B.C. Berndt to obtain a linear relation for 5-core partitions and by A. Berkovich and H. Yesilyurt to obtain inequalities for 7-core partitions. In this paper, we generalize their results by using the theory of modular forms. In particular, we prove conjectures of Berkovich and Yesilyurt.

Original language	English
Pages (from-to)	861-868
Number of pages	8
Journal	Discrete Mathematics
Volume	310
Issue number	4
DOIs	https://doi.org/10.1016/j.disc.2009.09.024
State	Published - 28 Feb 2010

Keywords

7-core partition
Deligne's bound
Modular forms

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10.1016/j.disc.2009.09.024

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abstract = "Recently, Ramanujan's modular equations have been applied by N.D. Baruah and B.C. Berndt to obtain a linear relation for 5-core partitions and by A. Berkovich and H. Yesilyurt to obtain inequalities for 7-core partitions. In this paper, we generalize their results by using the theory of modular forms. In particular, we prove conjectures of Berkovich and Yesilyurt.",

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N2 - Recently, Ramanujan's modular equations have been applied by N.D. Baruah and B.C. Berndt to obtain a linear relation for 5-core partitions and by A. Berkovich and H. Yesilyurt to obtain inequalities for 7-core partitions. In this paper, we generalize their results by using the theory of modular forms. In particular, we prove conjectures of Berkovich and Yesilyurt.

AB - Recently, Ramanujan's modular equations have been applied by N.D. Baruah and B.C. Berndt to obtain a linear relation for 5-core partitions and by A. Berkovich and H. Yesilyurt to obtain inequalities for 7-core partitions. In this paper, we generalize their results by using the theory of modular forms. In particular, we prove conjectures of Berkovich and Yesilyurt.

KW - 7-core partition

KW - Deligne's bound

KW - Modular forms

UR - https://www.scopus.com/pages/publications/71649115001

U2 - 10.1016/j.disc.2009.09.024

DO - 10.1016/j.disc.2009.09.024

M3 - Article

AN - SCOPUS:71649115001

SN - 0012-365X

VL - 310

SP - 861

EP - 868

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 4

ER -

On inequalities and linear relations for 7-core partitions

Abstract

Keywords

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