On the crank function of cubic partition pairs

Byungchan Kim; Pee Choon Toh

doi:10.1007/s00026-018-0407-z

On the crank function of cubic partition pairs

Byungchan Kim, Pee Choon Toh

School of Natural Sciences

Nanyang Technological University

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

6 Scopus citations

Abstract

We study a crank functionM(m, n) for cubic partition pairs.We show that the functionM(m, n) explains a cubic partition pair congruence and we also obtain various arithmetic properties regarding M(m, n). In particular, using the Θ-operator, we confirm a conjecture on the sign pattern of c(n), the number of cubic partition pairs of n, weighted by the parity of the crank.

Original language	English
Pages (from-to)	803-818
Number of pages	16
Journal	Annals of Combinatorics
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s00026-018-0407-z
State	Published - 1 Jan 2018

Keywords

Congruences
Cubic partitions
Modular forms
Partition crank
Partitions

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10.1007/s00026-018-0407-z

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abstract = "We study a crank functionM(m, n) for cubic partition pairs.We show that the functionM(m, n) explains a cubic partition pair congruence and we also obtain various arithmetic properties regarding M(m, n). In particular, using the Θ-operator, we confirm a conjecture on the sign pattern of c(n), the number of cubic partition pairs of n, weighted by the parity of the crank.",

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AB - We study a crank functionM(m, n) for cubic partition pairs.We show that the functionM(m, n) explains a cubic partition pair congruence and we also obtain various arithmetic properties regarding M(m, n). In particular, using the Θ-operator, we confirm a conjecture on the sign pattern of c(n), the number of cubic partition pairs of n, weighted by the parity of the crank.

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KW - Cubic partitions

KW - Modular forms

KW - Partition crank

KW - Partitions

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On the crank function of cubic partition pairs

Abstract

Keywords

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