Webnumber of ℓ-regular overpartitions of n. The generating function of Aℓ(n) is ∑1 n=0 Aℓ(n)qn = f2 f2 1 f2 ℓ f2ℓ = φ(qℓ) φ(q): (1.6) In this paper, we shall study the arithmetic properties of ℓ-regular overpartition pairs of n. An ℓ-regular overpartition pair of nis a pair of ℓ-regular overpartitions ( ; ) where the sum Web8 de set. de 2024 · One goal of this paper is to find a generalization of ( 1.5) for k -regular partitions. For a positive integer k\ge 2, a partition is called k -regular if none of its parts …

Congruences for $$\ell$$ ℓ -regular overpartitions into odd parts ...

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 ... Web2 de mar. de 2024 · For example, there are six 3-regular overpartitions of the integer 6 into odd parts, namely 5+1, \overline {5}+1, 5+\overline {1}, \overline {5}+\overline {1}, 1+1+1+1+1+1, \overline {1}+1+1+1+1+1. This paper is organized as follows. In Sect. 2, we recall some dissection formulas which are essential to prove our main results. impact diet whey inceleme

Singular overpartitions International Journal of Number Theory

WebLet S2(n) denote the number of overpartitions λ = λ1 +λ2 +··· of n, where the final occurrence of a number may be overlined, where parts occur at most twice, and λi −λi+2 is at least 2 if λi+2 is non-overlined and at least 1 if λi+2 is overlined. Let S3(n) denote the number of overpartitions of n into parts not divisible by 3. 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 … WebThe objective in this paper is to present a general theorem for overpartitions analogous to Rogers–Ramanujan type theorems for ordinary partitions with restricted successive … impact diet whey ingredients