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Séminaire Lotharingien de Combinatoire, B81c (2020), 28 pp.

# Adam Walsh and S. Ole Warnaar

# Modular Nekrasov-Okounkov Formulas

**Abstract.**
Using Littlewood's map, which decomposes a partition into its *r*-core
and *r*-quotient, Han and Ji have shown that many well-known hook-length
formulas admit modular analogues.
In this paper we present a variant of the Han-Ji `multiplication theorem'
based on a new analogue of Littlewood's decomposition.
We discuss several applications to hook-length formulas, one of which
leads us to conjecture a modular analogue of the *q*,*t*-Nekrasov-Okounkov
formula.

Received: February 17, 2019.
Accepted: February 13, 2020.

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