A proof of conjectured partition identities of Nandi

Abstract

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 for modulus 14 that were posed by Nandi through a vertex operator theoretic construction of the level 4 standard modules of the affine Lie algebra $A^{(2)}_{2}$.