منابع مشابه
Overpartitions with Restricted Odd Differences
We use q-difference equations to compute a two-variable q-hypergeometric generating function for overpartitions where the difference between two successive parts may be odd only if the larger part is overlined. This generating function specializes in one case to a modular form, and in another to a mixed mock modular form. We also establish a two-variable generating function for the same overpar...
متن کاملArithmetic Properties of Overpartitions into Odd Parts
In this article, we consider various arithmetic properties of the function po(n) which denotes the number of overpartitions of n using only odd parts. This function has arisen in a number of recent papers, but in contexts which are very different from overpartitions. We prove a number of arithmetic results including several Ramanujan-like congruences satisfied by po(n) and some easily-stated ch...
متن کاملRank Differences for Overpartitions
The rank of a partition is the largest part minus the number of parts. This statistic was introduced by Dyson [14], who observed empirically that it provided a combinatorial explanation for Ramanujan’s congruences p(5n + 4) ≡ 0 (mod 5) and p(7n + 5) ≡ 0 (mod 7). Here p(n) denotes the usual partition function. Specifically, Dyson conjectured that if N(s,m, n) denotes the number of partitions of ...
متن کاملM2-rank Differences for Overpartitions
Abstract. This is the third and final installment in our series of papers applying the method of Atkin and Swinnerton-Dyer to deduce formulas for rank differences. The study of rank differences was initiated by Atkin and Swinnerton-Dyer in their proof of Dyson’s conjectures concerning Ramanujan’s congruences for the partition function. Since then, other types of rank differences for statistics ...
متن کاملSingular Overpartitions
The object in this paper is to present a general theorem for overpartitions analogous to Rogers-Ramanujan type theorems for ordinary partitions with restricted successive ranks.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/5248