Overpartition Theorems of the Rogers–Ramanujan Type

By Jeremy Lovejoy. 2004

68 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/8b023b855f56f95ce8893e8bbe8e88896e151ab2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

The Rogers–Ramanujan–Gordon theorem for overpartitions (2011, methodology): “As pointed out by Lovejoy, the approach of using the function Jk,i(a;x; q) does not seem to apply to the general case, since for i = 1, k, the functions Jk,i(−1; 1; q) and Jk,i(−1/q; 1; q) do not appear to be expressible as single infinite products.”
Overpartitions and real quadratic fields (2004, background): “families of overpartition theorems which are analogues of some classical and celebrated results in the theory of partitions [10, 11 ].”
AN INFINITE FAMILY OF OVERPARTITION CONGRUENCES MODULO 12 (2005, background): “The function p(n) has been considered recently by a number of mathematicians; please see [1, 2, 3, 4, 5, 6, 7, 8].”
Rank and Conjugation for a Second Frobenius Representation of an Overpartition (2005, methodology): “There is another representation of an overpartition as an F -partition, the existence of which is equivalent to the q-Gauss summation, which we may write ∑ n≥0 (−1/a,−q/b; q2)n(abcq)n (cq2, q2; q2)n = (−acq2,−bcq; q2)∞ (cq2, abcq; q2)∞ .”
Parity in partition identities (2010, background): “Extend the parity indices to overpartitions in a manner that will provide natural generalizations of the work of Corteel and Lovejoy [11], [18].”
Arithmetic Properties of Overpartitions into Odd Parts (2006, unknown): “See [4, 5] and [8, 9, 10, 11, 12].”
DYSON'S RANK, OVERPARTITIONS, AND WEAK MAASS FORMS (2007, unknown): “[3, 11, 12, 13, 21, 29, 33]), but also in mathematical physics (e.”