Combinations of Ranks and Cranks of Partitions Moduli 6, 9 and 12 and Their Comparison with the Partition Function

Let L \(\epsilon\) {6, 9, 12}. We determine the generating functions of certain combinations of three ranks and three cranks modulo L in terms of eta quotients. Then, using the periodicity of signs of these eta quotients, we compare their values with the values of \( \frac{p(n}{L/3} \)

Authors and Affiliations

1. Department of Mathematics and Computer Science, University of Lethbridge, AB T1K 3M4, Lethbridge, Canada

   Zafer Selcuk Aygin

2. Division of Mathematical Sciences School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore

   Song Heng Chan

Corresponding author

Correspondence to Zafer Selcuk Aygin .

Editors and Affiliations

1. Department of Mathematics, University of Florida, Gainesville, FL, USA

   Krishnaswami Alladi

2. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, USA

   Bruce C. Berndt

3. Research Institute for Symbolic Computation, Johannes Kepler University Linz, Linz, Austria

   Peter Paule

4. Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN, USA

   James A. Sellers

5. Department of Mathematics, Pennsylvania State University, University Park, PA, USA

   Ae Ja Yee

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