Overpartition Pairs
نویسنده
چکیده
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.
منابع مشابه
Rank and Congruences for Overpartition Pairs
The rank of an overpartition pair is a generalization of Dyson’s rank of a partition. The purpose of this paper is to investigate the role that this statistic plays in the congruence properties of pp(n), the number of overpartition pairs of n. Some generating functions and identities involving this rank are also presented.
متن کاملOverpartition Pairs and Two Classes of Basic Hypergeometric Series
We study the combinatorics of two classes of basic hypergeometric series. We first show that these series are the generating functions for certain overpartition pairs defined by frequency conditions on the parts. We then show that when specialized these series are also the generating functions for overpartition pairs with bounded successive ranks, overpartition pairs with conditions on their Du...
متن کاملSome Arithmetic Properties of Overpartition K -tuples
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...
متن کاملArithmetic 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...
متن کاملArithmetic Properties of Overpartition Pairs into Odd Parts
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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