Arithmetic Properties of 9-Regular Partitions with Distinct Odd Parts

Hemanthkumar, B.; Bharadwaj, H. S. Sumanth; Naika, M. S. Mahadeva

doi:10.1007/s40306-018-0274-z

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Cited by 6 publications

(2 citation statements)

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“…. The generating function of pod ℓ (n) is as follows (see [8]). ∞ n=0 pod ℓ (n)q n = (q 2 ; q 2 ) ∞ (q ℓ ; q ℓ ) ∞ (q 4ℓ ; q 4ℓ ) ∞ (q; q) ∞ (q 4 ; q 4 ) ∞ (q 2ℓ ; q…”

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confidence: 99%

Distribution of ℓ-regular partitions with distinct odd parts

Chiranjit

2023

Preprint

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Let $pod_{\ell}(n)$ be the number of $\ell$-regular partitions of $n$ with distinct odd parts. In this article, we prove that for any positive integer $k$, the set of non-negative integers $n$ for which $pod_{\ell}(n)\equiv 0 \pmod{p^{k}}$ has density one. We also exhibit several multiplicative identities for $pod_{3}(n)$, $pod_{5}(n)$ and $pod_{7}(n)$ using the Hecke eigenforms, and some results of Ono, Robins, and Wahl. 2010 Mathematics Subject Classification. Primary: 05A17, 11P83, 11F11, 11F20

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confidence: 99%

Distribution of ℓ-regular partitions with distinct odd parts

Chiranjit

2023

Preprint

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“…In this article, we consider ℓ-regular partitions of n with distinct odd parts and even parts are unrestricted, and denote by pod ℓ (n). The generating function of pod ℓ (n) is as follows (see [9]).…”

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confidence: 99%