A proof of conjectured partition identities of Nandi

TL;DR

This paper extends the theory of linked partition ideals with automata and uses it to prove three new Rogers-Ramanujan type identities related to affine Lie algebra modules.

Contribution

It introduces a novel automata-based approach to linked partition ideals and proves identities conjectured by Nandi using vertex operator methods.

Findings

Proved three Rogers-Ramanujan type identities of modulo 14.

Extended linked partition ideals theory with finite automata.

Connected identities to affine Lie algebra modules.

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 $A^{(2)}_{2}$.