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On 3-Regular Partitions in 3-Colors

Author

Listed:
  • D. S. Gireesh

    (M. S. Ramaiah University of Applied Sciences, Peenya, Bengaluru)

  • M. S. Mahadeva Naika

    (Bangalore University, Central College Campus, Bengaluru)

Abstract

We consider p{3,3}(n), the number of 3-regular partitions in 3-colors. We find the generating functions for p{3,3}(n) and deduce congruences modulo large powers of 3. We also find the generating functions and congruences for linear combination of p3(n) (the number of partitions of n in 3-colors) by finding the relation connecting p3(n) and p{3,3}(n). As an application, we find finite discrete convolution of p{3,1}(n) and p{3,2}(n).

Suggested Citation

  • D. S. Gireesh & M. S. Mahadeva Naika, 2019. "On 3-Regular Partitions in 3-Colors," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(1), pages 137-148, March.
    • Handle: RePEc:spr:indpam:v:50:y:2019:i:1:d:10.1007_s13226-019-0312-0
    DOI: 10.1007/s13226-019-0312-0
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