TY  - JOUR
TT  - The part-frequency matrices of a partition
AU  - Keith, William J.
PY  - 2016
DA  - August
DO  - 10.13069/jacodesmath.41075
JF  - Journal of Algebra Combinatorics Discrete Structures and Applications
PB  - iPeak Academy
WT  - DergiPark
SN  - 2148-838X
SP  - 177
EP  - 186
VL  - 3
IS  - 3
N2  - A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, whichis elementary to describe and is naturally motivated by Glaisher’s bijection. We prove results thatsuggest surprising usefulness for such a simple tool, including the existence of a related statistic thatrealizes every possible Ramanujan-type congruence for the partition function. To further exhibit itsresearch utility, we give an easy generalization of a theorem of Andrews, Dixit and Yee [1] on the mocktheta functions. Throughout, we state a number of observations and questions that can motivate anarray of investigations.
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UR  - https://doi.org/10.13069/jacodesmath.41075
L1  - https://dergipark.org.tr/en/download/article-file/226203
ER  -