Using periodicity to obtain partition congruences

Al-Saedi, Ali H.

doi:10.1016/j.jnt.2017.02.011

Cited by 5 publications

(3 citation statements)

References 17 publications

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“…In particular, about its mathematical properties. In 1920, Ramanujan [2] discovered remarkable arithmetic patterns for the partition function 𝑝(𝑛) 𝑝(𝑙𝑛 + 𝑡) ≡ 0 (𝑚𝑜𝑑 𝑙), where (𝑙, 𝑡) = (5,4), (7,5), (11,6). Following Ramanujan's discovery of these beautiful identities, the study of partitions has progressed far beyond 𝑝(𝑛).…”

Section: Introduction 11 Partitions and Overpartitionsmentioning

confidence: 99%

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A Note on Overpartition Triples

Al-Saedi,

Sharqi

2023

Iraqi Journal of Science

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Let n be a positive integer and denotes the number of overpartition triples. In this note, we prove two identities modulo 16 and 32 for . We provide a new method to reprove a result of Lin Wang for completely determining and modulo 16. Also, we find and prove an infinite family of congruences modulo 32 for . The new method relies on expanding the fourth power of the overpartition infinite product together with the help of Gauss' identity.

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Section: Introduction 11 Partitions and Overpartitionsmentioning

confidence: 99%

“…Several other generalizations, such as plane partitions and plane overpartitions have been introduced and investigated. For example, see [11], [12], [13] and [14].…”

Section: Introduction 11 Partitions and Overpartitionsmentioning

confidence: 99%

A Note on Overpartition Triples

Al-Saedi,

Sharqi

2023

Iraqi Journal of Science

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“…The concept of plane overpartitions was introduced as a natural extension of the overpartitions and plane partitions [3]. In [4], the author defined the concept of k-rowed plane overpartitions, which is plane overpartitions with the number of rows at most k, as a restricted variant of plane overpartitions for a fixed number k of rows. The k-rowed plane overpartitions generating function is represented by…”

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confidence: 99%

2-Rowed Plane Overpartitions Modulo 8 and 16

Al-Saedi

2022

Iraqi Journal of Science

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In a recent study, a special type of plane overpartitions known as k-rowed plane overpartitions has been studied. The function denotes the number of plane overpartitions of n with a number of rows at most k. In this paper, we prove two identities modulo 8 and 16 for the plane overpartitions with at most two rows. We completely specify the modulo 8. Our technique is based on expanding each term of the infinite product of the generating function of the modulus 8 and 16 and in which the proofs of the key results are dominated by an intriguing relationship between the overpartitions and the sum of divisors, which reveals a considerable link among these functions modulo powers of 2.

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Congruences for restricted plane overpartitions modulo 4 and 8

Al-Saedi

2018

Ramanujan J

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In 2009, Corteel, Savelief and Vuletić generalized the concept of overpartitions to a new object called plane overpartitions. In recent work, the author considered a restricted form of plane overpartitions called k-rowed plane overpartions and proved a method to obtain congruences for these and other types of combinatorial generating functions. In this paper, we prove several restricted and unrestricted plane overpartition congruences modulo 4 and 8 using other techniques.2010 Mathematics Subject Classification. 11P83.

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Using periodicity to obtain partition congruences

Cited by 5 publications

References 17 publications

A Note on Overpartition Triples

A Note on Overpartition Triples

2-Rowed Plane Overpartitions Modulo 8 and 16

Congruences for restricted plane overpartitions modulo 4 and 8

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