On identities of the Rogers-Ramanujan type
By Andrew V. Sills. 2006
160 citations recorded by the source corpus.
A generalized Bailey pair, which contains several special cases considered by Bailey (Proc. London Math. Soc. (2), 50, 421–435 (1949)), is derived and used to find a number of new Rogers-Ramanujan type identities. Consideration of associated q-difference equations points to a connection with a mild extension of Gordon’s combinatorial generalization of the Rogers-Ramanujan identities (Amer. J. Math., 83, 393–399 (1961)). This, in turn, allows the formulation of natural combinatorial interpretations of many of the identities in Slater’s list (Proc. London Math. Soc. (2) 54, 147–167 (1952)), as well as the new identities presented here. A list of 26 new double sum–product Rogers-Ramanujan type identities are included as an Appendix.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/c6e8f40cd091573dcc2149f8f8e51d402bee6115
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In Algebra and Number Theory
- Anne Schilling
- George E. Andrews
- Andrew V. Sills
- V. Spiridonov
- Kathrin Bringmann
- Eric T. Mortenson
- Frank G. Garvan
- Ken Ichi Ono
In Discrete Mathematics and Combinatorics
- Anne Schilling
- George E. Andrews
- V. Spiridonov
- Kathrin Bringmann
- Eric T. Mortenson
- Frank G. Garvan
- Alexander Berkovich
- Karl Mahlburg
Citations in the corpus
- A Survey of Multipartitions Congruences and Identities (2008, background): “8 Interpretations of Multiple q-Series Identities There are numerous theorems identifying multiple q-series including [1], [2], [4], [5], [24].”
- Crystal structure on rigged configurations (2005, methodology): “The Andrews–Bailey construction [1, 4] relie s on an iterative transformation property of theq-binomial coefficient, which is one of the simplest unrestri cted configuration sums, and can be used to prove infinite families of Rogers–Ramanujan type identities.”
- Rogers-Ramanujan-Slater Type Identities (2008, background): “Bailey studied Rogers’s work and as a result was able to simplify and extend it in [12, 13].”