On the number of l-regular overpartitions

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Web1 de jan. de 2024 · Given a positive integer, let count the number of overpartitions of in which there are exactly overlined parts and nonoverlined parts, the difference between …

Arithmetic properties of l-regular overpartitions International ...

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 WebThe column "row_num" doesn't exist because the logical order of processing requires the dbms to apply the WHERE clause before it evaluates the SELECT clause. The … high blood pressure and taking aleve

Infinite families of congruences for k-regular overpartitions ...

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 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 … WebExample: 5 = 1 + 4, 5 = 2 + 3, since L C M ( 1, 4) < L C M ( 2, 3) = 6, the largest LCM of the partitions of 5 is 6. The definition of "partition" is the standard definition of it. In order to … high blood pressure and the pact act

Congruences for ℓ-regular overpartition for ℓ ∈ {5, 6, 8 ...

Web9 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 … Web( 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 ) how far is maysel wv from charleston wvWebWe consider new properties of the combinatorial objects known as overpartitions (which are natural generalizations of integer partitions). In particular, we establish an infinite set … high blood pressure and taking phentermine

"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. " - On the number of l-regular overpartitions

On the number of l-regular overpartitions

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 … 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

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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. Web2 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 …

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 … 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.

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 … 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 ...

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 ...

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 … how far is mayport florida from orlandoWebThe 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 far is mcadenville from meWebThe 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 how far is mazeppa mn from rochester mnWebAbstract. 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 … how far is mazomanie from madisonWeb24 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 … how far is maywood il from chicago ilhttp://lovejoy.perso.math.cnrs.fr/overpartitions.pdf how far is mayville wi from fond du lac wiWebnumber 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 high blood pressure and thyroid disease