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A proof of conjectured partition identities of Nandi

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arxiv 1910.12461 v2 pith:YVJK3UCD submitted 2019-10-28 math.CO math.NTmath.QAmath.RT

Motoki Takigiku , Shunsuke Tsuchioka This is my paper · ORCID
classification math.COmath.NTmath.QAmath.RT
keywords identitiesnandipartitiontheoryaffinealgebraandrewsapply
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abstract

We generalize the theory of linked partition ideals due to Andrews using finite automata in formal language theory and apply it to prove three Rogers--Ramanujan type identities of modulo 14 that were posed by Nandi through vertex operator theoretic construction of the level 4 standard modules of the affine Lie algebra $A^{(2)}_{2}$.

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  1. Leading Terms of Relations on a Level 5 Module over the Twisted Affine Lie Algebra $A_2^{(2)}$

    math.CO 2025-11 conditional novelty 5.0 of 10

    The partial partition conditions for level 5 A2^(2) L(5Λ0) match the specialized character through q^41, miss one partition each at q^42 and q^48, and differ from the Borcea-dual A1^(1) level 2 identity.

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