Generalizations of Nekrasov-Okounkov Identity
Amer Iqbal, Shaheen Nazir, Zahid Raza, Zain Saleem
TL;DR
This paper extends the Nekrasov-Okounkov identity by leveraging the cyclic symmetry of the topological vertex, providing new generalizations of the original partition sum formula.
Contribution
It introduces several new generalizations of the Nekrasov-Okounkov identity based on the cyclic symmetry of the topological vertex, expanding its mathematical framework.
Findings
Derived new product-sum identities for partitions
Connected topological vertex symmetry with partition functions
Enhanced understanding of Nekrasov-Okounkov identity generalizations
Abstract
Nekrasov-Okounkov identity gives a product representation of the sum over partitions of a certain function of partition hook length. In this paper we give several generalizations of the Nekrasov-Okounkov identity using the cyclic symmetry of the topological vertex.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Algebraic structures and combinatorial models