On the number of l-regular overpartitions

Author: zoyj

August undefined, 2024

WebLet A¯k(n) be the number of overpartitions of n into parts not divisible by k. In this paper, we find infinite families of congruences modulo 4, 8 and 16 for A¯2k(n) ... On the … Webnumber of overpartitions of nin which no part is divisible by kand only parts ≡ ±i (mod k) may be overlined. In recent times, divisibilityof C3ℓ,ℓ(n), C4ℓ,ℓ(n) and C6ℓ,ℓ(n) by 2 and 3 are studied for certain values of ℓ. In this article, we study divisibility of C3ℓ,ℓ(n), C4ℓ,ℓ(n) and C6ℓ,ℓ(n) by primes p

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

Web24 de jul. de 2024 · Analogously, for a positive integer \ell >1, an overpartition is called \ell -regular if none of its parts is divisible by \ell . The number of the \ell -regular … 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 … gap insurance is it necessary

ARITHMETIC PROPERTIES OF $(k,\ell )$ -REGULAR BIPARTITIONS

Web8 de jul. de 2003 · between overpartitions of nand Frobenius partitions counted by p Q;O(n) in which the number of overlined parts in is equal to the number of non-overlined parts in the bottom row of . In addition to providing a useful representation of overpartitions, the bijection implies q-series identities like Corollary 1.2. (1.4) Xn k=0 ( 1=a;q) kckakq k ... 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 … 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 … gap insurance ohio

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

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. WebIt denotes the number of overpartitions of n in which no part is divisible by k and only parts ≡ ± i (mod k) may be overlined. He proved that C ¯ 3, 1 (9 n + 3) and C ¯ 3, 1 (9 n + 6) are divisible by 3. In this paper, we aim to introduce a crank of l-regular overpartitions for l … gap insurance kia motors financeWeb19 de set. de 2024 · Let {\overline {A}}_ {\ell } (n) be the number of overpartitions of n into parts not divisible by \ell . In this paper, we prove that {\overline {A}}_ {\ell } (n) is almost … gap insurance in michigan

"WebAndrews defined singular overpartitions counted by the partition function [Formula: see text]. It denotes the number of overpartitions of [Formula: see text] in which no part is … " - On the number of l-regular overpartitions

On the number of l-regular overpartitions

Some Congruences for Overpartitions with Restriction

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 … 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.

Did you know?

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 … Web24 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 …

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

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 WebIn 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.

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

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. black louis vuitton bag replicahttp://lovejoy.perso.math.cnrs.fr/overpartitions.pdf black louis vuitton bag with cheetah printWeb9 de set. de 2024 · 4 Citations Metrics Abstract Let A̅ ℓ ( n) denote the number of overpartitions of a non-negative integer n with no part divisible by ℓ, where ℓ is a … black louis vuitton handbags crossbodyWebAbstract. 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. gap insurance new carWeb17 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 … gap insurance on a paid off carWebSince 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: gap insurance numberWeb8 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 … gap insurance new york