Graph-theoretic modeling of linked partition ideals yields q-difference systems whose solution via q-multi-summations produces proofs of Andrews-Gordon identities.
Proofs and reductions of various conjectured partition identities of Kanade and Russell
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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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2019 1verdicts
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Linked partition ideals, directed graphs and $q$-multi-summations
Graph-theoretic modeling of linked partition ideals yields q-difference systems whose solution via q-multi-summations produces proofs of Andrews-Gordon identities.