On the number of l-regular overpartitions
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 … 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
On the number of l-regular overpartitions
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http://lovejoy.perso.math.cnrs.fr/overpartitions.pdf 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.
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 … 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 …
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: 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 …
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
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. telephone mobile samsung a51Web1 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 … telephone mip hassi messaoudWebAbstract 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. telephone marseille numeroWebnumber 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 eskom rfq\u0027sWeb2 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 … eskom rotek logoWeb( mathematics) An overpartition of n is a non-increasing sequence of natural numbers whose sum is n in which the first occurrence of a number may be overlined. quotations Verb [ edit] overpartition ( third-person singular simple present overpartitions, present participle overpartitioning, simple past and past participle overpartitioned ) eskom nkomaziWeb1 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 telephone mitel