• Title/Summary/Keyword: Regular overpartition

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THE UNIMODALITY OF THE r3-CRANK OF 3-REGULAR OVERPARTITIONS

  • Robert XiaoJian Hao;Erin YiYing Shen
    • Bulletin of the Korean Mathematical Society
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    • v.61 no.3
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    • pp.621-635
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    • 2024
  • An 𝑙-regular overpartition of n is an overpartition of n with no parts divisible by 𝑙. Recently, the authors introduced a partition statistic called r𝑙-crank of 𝑙-regular overpartitions. Let Mr𝑙(m, n) denote the number of 𝑙-regular overpartitions of n with r𝑙-crank m. In this paper, we investigate the monotonicity property and the unimodality of Mr3(m, n). We prove that Mr3(m, n) ≥ Mr3(m, n - 1) for any integers m and n ≥ 6 and the sequence {Mr3(m, n)}|m|≤n is unimodal for all n ≥ 14.

DIVISIBILITY AND ARITHMETIC PROPERTIES OF CERTAIN ℓ-REGULAR OVERPARTITION PAIRS

  • ANUSREE ANAND;S.N. FATHIMA;M.A. SRIRAJ;P. SIVA KOTA REDDY
    • Journal of applied mathematics & informatics
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    • v.42 no.4
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    • pp.969-983
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    • 2024
  • For an integer ℓ ≥ 1, let ${\bar{B}}_{\ell}(n)$ denotes the number of ℓ-regular over partition pairs of n. For certain conditions of ℓ, we study the divisibility of ${\bar{B}}_{\ell}(n)$ and arithmetic properties for ${\bar{B}}_{\ell}(n)$. We further obtain infinite family of congruences modulo 2t satisfied by ${\bar{B}}_3(n)$ employing a result of Ono and Taguchi (2005) on nilpotency of Hecke operators.