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      Proofs and Reductions of Kanade and Russell's partition identities

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          Abstract

          We prove seven of the Rogers-Ramanujan type identities modulo \(12\) that were conjectured by Kanade and Russell. Included among these seven are the two original modulo \(12\) identities, in which the products have asymmetric congruence conditions, as well as the three symmetric identities related to the principally specialized characters of certain level \(2\) modules of \(A_9^{(2)}\). We also give reductions of four other conjectures in terms of single-sum basic hypergeometric series.

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          Further Identities of the Rogers-Ramanujan Type

          L. Slater (1952)
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            The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities

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              A Combinatorial Generalization of the Rogers-Ramanujan Identities

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                Author and article information

                Journal
                17 September 2018
                Article
                1809.06089
                1c8a1f3b-4651-4feb-ad69-ec3e0dfb886d

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math.NT math.CO

                Combinatorics,Number theory
                Combinatorics, Number theory

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