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On the number of l-regular overpartitions

WebThe combinatorial interpretation of the coefficient ofqnin (2.1) is: “the number of overpartitions of nin which overlined parts are ℓ-regular, nonoverlined parts that are multiples of ℓare distinct, and other nonover- lined parts are unrestricted.” 98 A. M. ALANAZI, B. M. ALENAZI, W. J. KEITH, AND A. O. MUNAGI 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 …

Scilit Article - On the number of l-regular overpartitions

WebAbstract Let b ℓ (n) denote the number of ℓ-regular partitions of n, where ℓ is prime and 3 ≤ ℓ ≤ 23. In this paper we prove results on the distribution of b ℓ (n) modulo m for any odd integer m > 1 with 3 ∤ m if ℓ ≠ 3. Keywords: Partitions modular forms AMSC: 11P83 Web24 de abr. de 2024 · Abstract. For any given positive integers m and n, let pm ( n) denote the number of overpartitions of n with no parts divisible by 4 m and only the parts congruent to m modulo 2 m overlined. In this paper, we prove Ramanujan-type congruences modulo 2 for pm ( n) by applying q -series and Ramanujan’s theta-function identities. how does mobile check deposit fraud work https://itsbobago.com

On the number of l-regular overpartitions Semantic Scholar

Web1 de abr. de 2009 · For any given positive integersmand n, let pm (n) denote the number of overpartitions of n with no parts divisible by 4mand only the parts congruent tommodulo 2moverlined. In this paper, we prove… Expand Some Congruences for Overpartitions with Restriction H. Srivastava, N. Saikia Mathematics 2024 Webdivisible by ℓ. Let bℓ(n) denote the number of ℓ-regular partitions of n. We know that its generating function is X n≥0 bℓ(n)qn = (qℓ;qℓ)∞ (q;q)∞. On the other hand, an overpartition of n is a partition of n in which the first occurrence of each part can be overlined. Let p(n) be the number of overpartitions of n. We also WebWe consider new properties of the combinatorial objects known as overpartitions (which are natural generalizations of integer partitions). In particular, we establish an infinite set … photo of indian culture

Refinements of the results on partitions and overpartitions with ...

Category:On some new congruences for ℓ-regular overpartitions - Journal

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On the number of l-regular overpartitions

OVERPARTITIONS - American Mathematical Society

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 ... 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 …

On the number of l-regular overpartitions

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WebAbstract In a very recent work, G. E. Andrews defined the combinatorial objects which he called singular overpartitions with the goal of presenting a general theorem for overpartitions which is analogous to theorems of Rogers–Ramanujan type for ordinary partitions with restricted successive ranks. http://lovejoy.perso.math.cnrs.fr/overpartitions.pdf

Web1 de jan. de 2024 · An overpartition of is a partition of where the first occurrence of a number may be overlined. For example, there are four overpartitions of , namely, . Let be the number of overpartitions of in which the difference between largest and smallest parts is at most , and if the difference is exactly , then the largest part cannot be overlined. 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.

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. Web20 de abr. de 2024 · An l -regular overpartition of

WebSince the overlined parts form a partition into distinct parts and the non-overlined parts form an ordinary partition, we have the generating function X1 n=0 p(n)qn= Y1 n=1 1+qn 1¡qn = 1+2q+4q2+8q3+14q4+:::(1.1) For example, the 14 overpartitions of 4 are 4;4;3+1;3+1;3+1;3+1;2+2;2+2;2+1+1; 2+1+1;2+1+1;2+1+1;1+1+1+1;1+1+1+1:

Web20 de abr. de 2024 · Andrews defined singular overpartitions counted by the partition function [Formula: see text]. It denotes the number of overpartitions of [Formula: see … how does moby dick startWeb24 de mai. de 2024 · Recently, Andrews introduced the partition function (Formula presented.) as the number of overpartitions of n in which no part is divisible by k and … how does mint track expensesWeb2 de mar. de 2024 · In this paper, we study various arithmetic properties of the function \(\overline{po}_\ell (n)\), which denotes the number of \(\ell\)-regular overpartitions of n … how does mob psycho 100 endWebIn a recent work, Andrews introduced the new combinatorial objects called singular overpartitions. He proved that these singular overpartitions can be enumerated by the partition function C ¯ k, i ( n) which denotes the number of overpartitions of n in which no part is divisible by k and only parts ≡ ± i ( mod k) may be overlined. how does mobility cars workWeb1 de jun. de 2024 · ℓ(n) denote the number of overpartitions of a non-negative integer n with no part divisible by ℓ, where ℓ is a positive integer. In this paper, we prove infinite … how does mobility prevent pressure injuriesWebThe objective in this paper is to present a general theorem for overpartitions analogous to Rogers–Ramanujan type theorems for ordinary partitions with restricted successive … how does mobility scheme workWebLet A ¯ l (n) be the number of overpartitions of n into parts not divisible by l. In this paper, we call the overpartitions enumerated by the function A ¯ l ( n ) l -regular overpartitions. For … how does mobility affect wound healing