On the number of l-regular overpartitions
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. 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 …
On the number of l-regular overpartitions
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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 … 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 …
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 … 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
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 ... 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
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 …
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 how to spell torchesWeb24 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 … rdw-cv co toWeb1 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 rdw-cv counthttp://lovejoy.perso.math.cnrs.fr/overpartitions.pdf how to spell torah in hebrewWebAbstract 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. how to spell totalitarianismWeb1 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 … rdw-cv high meaning mayo clinicWebAbstract 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 … how to spell touchay