ON THE EXISTENCE OF GRAHAM PARTITIONS WITH CONGRUENCE CONDITIONS

Byungchan Kim; Ji Young Kim; Chong Gyu Lee; Sang June Lee; Poo Sung Park

doi:10.4134/BKMS.b200730

ON THE EXISTENCE OF GRAHAM PARTITIONS WITH CONGRUENCE CONDITIONS

Byungchan Kim, Ji Young Kim, Chong Gyu Lee, Sang June Lee, Poo Sung Park

School of Natural Sciences

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

1 Scopus citations

Abstract

In 1963, Graham introduced a problem to find integer partitions such that the reciprocal sum of their parts is 1. Inspired by Graham’s work and classical partition identities, we show that there is an integer partition of a sufficiently large integer n such that the reciprocal sum of the parts is 1, while the parts satisfy certain congruence conditions.

Original language	English
Pages (from-to)	15-25
Number of pages	11
Journal	Bulletin of the Korean Mathematical Society
Volume	59
Issue number	1
DOIs	https://doi.org/10.4134/BKMS.b200730
State	Published - Jan 2022

Keywords

Graham partition
Rogers–Ramanujan identity
Sum of reciprocals

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abstract = "In 1963, Graham introduced a problem to find integer partitions such that the reciprocal sum of their parts is 1. Inspired by Graham{\textquoteright}s work and classical partition identities, we show that there is an integer partition of a sufficiently large integer n such that the reciprocal sum of the parts is 1, while the parts satisfy certain congruence conditions.",

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AB - In 1963, Graham introduced a problem to find integer partitions such that the reciprocal sum of their parts is 1. Inspired by Graham’s work and classical partition identities, we show that there is an integer partition of a sufficiently large integer n such that the reciprocal sum of the parts is 1, while the parts satisfy certain congruence conditions.

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ON THE EXISTENCE OF GRAHAM PARTITIONS WITH CONGRUENCE CONDITIONS

Abstract

Keywords

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