Rad HAZU, Matematičke znanosti, Vol. 29 (2025), 97-115.

THE POD FUNCTION AND ITS CONNECTION WITH OTHER PARTITION FUNCTIONS

Hemjyoti Nath

Department of Mathematical Sciences, Tezpur University, Napaam, Tezpur, Assam, India
e-mail: msm22017@tezu.ac.in

Abstract.   The number of partitions of n wherein odd parts are distinct and even parts are unrestricted, is often denoted by pod(n). In this paper, we provide linear recurrence relations for pod(n) and the connections of pod(n) with other partition functions.

2020 Mathematics Subject Classification.   11P81, 11P83.

Key words and phrases.   Integer partitions, recurrence relations.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857mwo1vcreny

References:

  1. G. E. Andrews, Integer partitions with even parts below odd parts and the mock theta functions, Ann. Comb. 22 (2018), 433-445.
    MathSciNet     CrossRef

  2. C. Ballantine and A. Welch, Ped and pod partitions: combinatorial proofs of recurrence relations, Discrete Math. 346 (2023), no. 3, Paper No. 113259, 20 pp.
    MathSciNet     CrossRef

  3. C. Ballantine and M. Merca, 4-regular partitions and the pod function, Quaest. Math. 46 (2023), 2027-2051.
    MathSciNet     CrossRef

  4. N. D. Baruah, Divisibility of sums of partition numbers by multiples of 2 and 3, Bull. Aust. Math. Soc. 110 (2024), 271-279.
    MathSciNet     CrossRef

  5. B. C. Berndt, Number Theory in the Spirit of Ramanujan, American Mathematical Society, Providence, 2006.
    MathSciNet     CrossRef

  6. H.-C. Chan, Ramanujan's cubic continued fraction and an analog of his "most beautiful identity", Int. J. Number Theory 6 (2010), 673-680.
    MathSciNet     CrossRef

  7. M. D. Hirschhorn, The power of q. A personal journey, Developments in Mathematics 49, Springer, Cham, 2017.
    MathSciNet     CrossRef

  8. M. D. Hirschhorn, Partition in 3 colours, Ramanujan J. 45 (2018), 399-411.
    MathSciNet     CrossRef

  9. M. D. Hirschhorn and J. A. Sellers, Arithmetic properties of partitions with odd parts distinct, Ramanujan J. 22 (2010), 273-284.
    MathSciNet     CrossRef

  10. M. Merca, A further look at cubic partitions, Ramanujan J. 59 (2022), 253-277.
    MathSciNet     CrossRef

  11. S. Radu and J. A. Sellers, Congruence properties modulo 5 and 7 for the pod function, Int. J. Number Theory 7 (2011), 2249-2259.
    MathSciNet     CrossRef

Rad HAZU Home Page