On the number of l-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 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.
On the number of l-regular overpartitions
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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 ... http://lovejoy.perso.math.cnrs.fr/overpartitions.pdf
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 … 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 )
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 … 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 …
Web19 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 …
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 hendricks family distilleryWeb1 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 … laptop cabinet with chargingWebAbstract. 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 … hendricks family foundation wiWeb2 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 … hendricks family dentistry va beachWebSince 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: hendricks family dentistry reviewshendricks family foundationWebAbstract 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 hendricks family distillery omro wi