3 papers
math.QA2021
Multi-grounded partitions and character formulas
Jehanne Dousse, Isaac Konan
We introduce a new generalisation of partitions, multi-grounded partitions, related to ground state paths indexed by dominant weights of Lie algebras. We use these to express chara…
math.CO2019
Generalisations of Capparelli's and Primc's identities, I: coloured Frobenius partitions and combinatorial proofs
Jehanne Dousse, Isaac Konan
In these two companion papers, we give infinite families of partition identities which generalise Primc's and Capparelli's identities, and study their consequences on the theory of…
math.QA2019
Generalisations of Capparelli's and Primc's identities, II: perfect crystals and explicit character formulas
Jehanne Dousse, Isaac Konan
In the first paper of this series, we gave infinite families of coloured partition identities which generalise Primc's and Capparelli's classical identities. In this second paper,…