Proofs and reductions of various conjectured partition identities of Kanade and Russell

2018/09/17 by Bringmann, Kathrin, Jennings-Shaffer, Chris, Mahlburg, Karl
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1809.06089

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 A₉⁽²⁾. We also give reductions of four other conjectures in terms of single-sum basic hypergeometric series.

Related

• Proofs of Modulo 11 and 13 Cylindric Kanade-Russell Conjectures for A₂ Rogers-Ramanujan Type Identities
• Proofs of some partition identities conjectured by Kanade and Russell
• Further q-reflections on the modulo 9 Kanade-Russell (conjectural) identities
• Level 2 standard modules for A⁽²⁾₉ and partition conditions of Kanade-Russell
• Some New Congruences and Partition-Theoretic Interpretations for the Coefficients of Some Rogers-Ramanujan Type Identities