On the Crank Function of Cubic Partition Pairs

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 patte...

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Bibliographic Details
Published inAnnals of combinatorics Vol. 22; no. 4; pp. 803 - 818
Main Authors Kim, Byungchan, Toh, Pee Choon
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2018
Springer Nature B.V
Subjects
Combinatorics
Mathematics
Mathematics and Statistics
Partitions (mathematics)
Partitions
Partition crank
11P83
Cubic partitions
Congruences
Modular forms
05A17
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Summary: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.
ISSN:0218-0006
0219-3094
DOI:10.1007/s00026-018-0407-z