Congruences for 7 and 49-regular partitions modulo powers of 7

Adiga, Chandrashekara; Dasappa, Ranganatha

doi:10.1007/s11139-017-9936-z

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Introduction and Notations1

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2018

2023

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Cited by 5 publications

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“…In this sequel, we establish infinite families of congruences for B k,ℓ (n) modulo certain positive integers, for specific values of k, ℓ. We next study the distribution of B k,ℓ (n) for (k, ℓ) ∈ { (3,5), (2,6), (2,4), (4,6)}. Moreover, we prove several infinite families of congruences modulo 2 and 3 for B k,ℓ (n).…”

Section: Introduction and Notationsmentioning

confidence: 99%

WITHDRAWN: On New Congruences and Density Results for(k, 𝓁)-regular Bipartitions Modulo m

Vidya

2023

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Let Bk,𝓁(n) denote the number of (k, 𝓁)-regular bipartitions. Recently, Dou discovered an infinite family of congruences modulo 11 for B3,11(n). She also presented several conjectures on Bk,𝓁(n). In this article, we establish infinite families of congruences for Bk,𝓁(n) modulo certain positive integers, for specific values of k, 𝓁. We next study the distribution of Bk,𝓁(n) for (k, 𝓁) ∈ {(3, 5),(2, 6),(2, 4),(4, 6)}. Moreover, we prove several infinite families of congruences modulo 2 and 3 for Bk,𝓁(n). We use arithmetic properties of modular forms and Hecke eigenforms to prove our results.

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