Arithmetic properties of $\ell$-regular overpartition pairs
نویسندگان
چکیده
منابع مشابه
Arithmetic Properties of Overpartition Pairs
Abstract. Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in congruence properties of pp(n), the number of overpartition pairs of n. In particular, they applied the theory of Klein forms to show that there exist many Ramanujan-type congruences for pp(n). In this paper, we derive two Ramanujantype identities and some explicit congruences for pp(n). Moreo...
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In this work, we investigate various arithmetic properties of the function ppo(n), the number of overpartition pairs of n into odd parts. We obtain a number of Ramanujan type congruences modulo small powers of 2 for ppo(n). For a fixed positive integer k, we further show that ppo(n) is divisible by 2 k for almost all n. We also find several infinite families of congruences for ppo(n) modulo 3 a...
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Abstract Recently, Lovejoy introduced the construct of overpartition pairs which are a natural generalization of overpartitions. Here we generalize that idea to overpartition ktuples and prove several congruences related to them. We denote the number of overpartition k-tuples of a positive integer n by pk(n) and prove, for example, that for all n ≥ 0, pt−1(tn + r) ≡ 0 (mod t) where t is prime a...
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An overpartition pair is a combinatorial object associated with the q-Gauss identity and the 1ψ1 summation. In this paper, we prove identities for certain restricted overpartition pairs using Andrews’ theory of q-difference equations for well-poised basic hypergeometric series and the theory of Bailey chains.
متن کاملArithmetic Properties of Overcubic Partition Pairs
Let b(n) denote the number of overcubic partition pairs of n. In this paper, we establish two Ramanujan type congruences and several infinite families of congruences modulo 3 satisfied by b(n). For modulus 5, we obtain one Ramanujan type congruence and two congruence relations for b(n), from which some strange congruences are derived.
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ژورنال
عنوان ژورنال: TURKISH JOURNAL OF MATHEMATICS
سال: 2017
ISSN: 1300-0098,1303-6149
DOI: 10.3906/mat-1512-62