On the number of l-regular overpartitions
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 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 …
On the number of l-regular overpartitions
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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 … 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 …
WebFor any positive integer ℓ, a partition is called ℓ-regular if none of its parts are divisible by ℓ. Let bℓ(n) denote the number of ℓ-regular partitions of n. We know that its generating … WebLet A ¯ l (n) be the number of overpartitions of n into parts not divisible by l. In this paper, we call the overpartitions enumerated by the function A ¯ l ( n ) l -regular overpartitions. For …
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 … 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.
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 …
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 ) do you refrigerate german chocolate cakeWeb14 de dez. de 2024 · Arabian Journal of Mathematics - In this paper, we study various arithmetic properties of the function $$\overline{p}_{2,\,\, k}(n)$$ , which denotes the number of ... emergency vet in hickoryhttp://lovejoy.perso.math.cnrs.fr/overpartitions.pdf do you refrigerate irish cream after openingWeb15 de abr. de 2024 · Specialties: Your nearby Five Guys at 45 River Road in Edgewater is ready to offer you a classic take on burgers, hot dogs, fries, milkshakes and more. … do you refrigerate ketchupemergency vet in flower mound txWeb9 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 … emergency vet in hickory ncWeb8 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 ... emergency vet in lake havasu city