Modular Nekrasov-Okounkov formulas. (English) Zbl 1441.05022
Summary: Using Littlewood’s map, which decomposes a partition into its \(r\)-core and \(r\)-quotient, G.-N. Han and K. Q. Ji [Trans. Am. Math. Soc. 363, No. 2, 1041–1060 (2011; Zbl 1227.05040)] 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.
MSC:
| 05A17 | Combinatorial aspects of partitions of integers |
| 05E10 | Combinatorial aspects of representation theory |
| 05A15 | Exact enumeration problems, generating functions |
Citations:
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