New congruences modulo 5 and 9 for partitions with odd parts distinct

Fang, Houqing; Xue, Fanggang; Yao, Olivia X. M.

doi:10.2989/16073606.2019.1653394

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2021

2024

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Cited by 7 publications

(2 citation statements)

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“…Much work has been done in studying arithmetic properties of PED and POD partitions. Among the may articles on the subject see, for example, [8,10,13,15,23,25,29] for congruences for PED partitions and [16,18,22,27,31] for congruences for POD partitions. Hence, this would be a natural topic of further study.…”

Section: Discussionmentioning

confidence: 99%

PED and POD partitions: Combinatorial proofs of recurrence relations

Ballantine

Welch

2023

Discrete Mathematics

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Section: Discussionmentioning

confidence: 99%

PED and POD partitions: Combinatorial proofs of recurrence relations

Ballantine

Welch

2023

Discrete Mathematics

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“…The pod(n) function has been studied widely. It appears, for example, in the works of K. Alladi [1,2], G. E. Andrews [3,4], G. E. Andrews and M. Merca [8], C. Ballantine, M. Merca, D. Passary, A. J. Yee [11], A. Berkovich and F. Garvan [12], S.-P. Cui, W. X. Gu, Z. S. Ma [18], H. Fang, F. Xue, O. X. M. Yao [20], M. D. Hirschhorn and J. A.…”

Section: Introductionmentioning

confidence: 99%

$4$-Regular partitions and the pod function

Ballantine¹,

Merca²

2021

Preprint

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The partition function pod(n) enumerates the partitions of n wherein odd parts are distinct and even parts are unrestricted. Recently, a number of properties for pod(n) have been established. In this paper, for k ∈ {0, 2} we consider the partitions of n into distinct parts not congruent to k modulo 4 and the 4-regular partitions of n in order to obtain new properties for pod(n). In this context, we derive two new infinite families of linear inequalities involving the function pod(n) and obtain new identities of Watson type.

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A further look at cubic partitions

Merca

2021

Ramanujan J

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New congruences modulo 5 and 9 for partitions with odd parts distinct

Cited by 7 publications

References 20 publications

PED and POD partitions: Combinatorial proofs of recurrence relations

PED and POD partitions: Combinatorial proofs of recurrence relations

$4$-Regular partitions and the pod function

A further look at cubic partitions

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