Graph-theoretic modeling of linked partition ideals yields q-difference systems whose solution via q-multi-summations produces proofs of Andrews-Gordon identities.
Andrews-Gordon Type Series for Kanade-Russell Conjectures
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abstract
We construct Andrews-Gordon type evidently positive series as generating functions of partitions satisfying certain difference conditions in six conjectures by Kanade and Russell. We construct generating functions for missing partition enumerants, naturally without claiming new partition identities. Thus, we obtain $q$-series conjectures as companions to Kanade and Russell's combinatorial conjectures.
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math.CO 1years
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.