Webdeveloped a new aspect of the theory of partitions - overpartitions. A hint of such a subject can also been seen in Hardy and Ramanujan [13, p.304]. An overpartition of nis a non-increasing sequence of positive integers whose sum is nin which the rst occurrence of a part may be overlined. If p(n) denotes the number of overpartitions of nthen X1 ... WebAbstract. Recently, Shen studied the arithmetic properties of ℓ-regular overpartition func-tion Aℓ(n), which counts the number of overpartitions of ninto parts not divisible by ℓ. In this note, we will present some new congruences modulo 5 when ℓis a power of 5. Keywords. Congruence, overpartition, regular partition. 2010MSC.
Singular overpartitions International Journal of Number Theory
WebAbstract The objective in this paper is to present a general theorem for overpartitions analogous to Rogers–Ramanujan type theorems for ordinary partitions with restricted successive ranks. Dedicated to the memory of Paul Bateman and Heini Halberstam Keywords: Overpartitions Rogers–Ramanujan identities successive ranks Frobenius … Webℓ-regular overpartitons has received a great deal of attention. For a positive integer l 2, a partition is called ℓ-regular if none of its parts is divisible by ℓ. An overpartition of n is a … diameter of the sun vs earth
Some Congruences for Overpartitions with Restriction
Web17 de jan. de 2024 · The connection between \(\ell \)-regular overpartitions and Andrews’ singular overpartitions is that \(\overline{C}_{3,1}(n)=\overline{A}_{3}(n)\) for all \(n\ge … Web1 de dez. de 2016 · partitions; congruences (k, ℓ)-regular bipartitions modular forms MSC classification Primary: 05A17: Partitions of integers Secondary: 11P83: Partitions; congruences and congruential restrictions Type Research Article Information Bulletin of the Australian Mathematical Society , Volume 95 , Issue 3 , June 2024 , pp. 353 - 364 Web21 de ago. de 2015 · In this paper, we call the overpartitions enumerated by the function (Formula presented.)l-regular overpartitions. For (Formula presented.) and (Formula … diameter of the world