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On the crank function of cubic partition pairs
Citation
Kim, B., & Toh, P. C. (2018). On the crank function of cubic partition pairs. Annals of Combinatorics, 22, 803-818. https://doi.org/10.1007/s00026-018-0407-z
Abstract
We study a crank function M(m, n) for cubic partition pairs. We show that the function M(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.
Date Issued
2018
Publisher
Springer
Journal
Annals of Combinatorics
Project
RI 3/12 TPC
Grant ID
NRF-2013R1A1A2061326
MOE2014-T2-1-051
Funding Agency
Ministry of Education, Republic of Korea
Ministry of Education, Singapore
National Institute of Education, Singapore