## Abstract

We interpret aspects of the Schur indices, that were identified with characters of highest weight modules in Virasoro (*p, p*^{′}) = (2*,* 2*k* + 3) minimal models for *k* = 1*,* 2*, . . .* , in terms of paths that first appeared in exact solutions in statistical mechanics. From that, we propose closed-form fermionic sum expressions, that is, *q, t*-series with manifestly non-negative coefficients, for two infinite-series of Macdonald indices of (*A*_{1}*, A*_{2k} ) Argyres- Douglas theories that correspond to *t*-refinements of Virasoro (*p, p*^{′}) = (2*,* 2*k* + 3) minimal model characters, and two rank-2 Macdonald indices that correspond to *t*-refinements of \( {\mathcal{W}}_3 \) non-unitary minimal model characters. Our proposals match with computations from 4d \( \mathcal{N} \) = 2 gauge theories *via* the TQFT picture, based on the work of J Song [75].

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Foda, O., Zhu, R. Closed form fermionic expressions for the Macdonald index.
*J. High Energ. Phys.* **2020, **157 (2020). https://doi.org/10.1007/JHEP06(2020)157

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### Keywords

- Conformal and W Symmetry
- String Duality
- Supersymmetry and Duality
- Conformal Field Theory