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2009 Congruences for Han's generating function
Dan Collins, Sally Wolfe
Involve 2(2): 225-236 (2009). DOI: 10.2140/involve.2009.2.225

Abstract

For an integer t1 and a partition λ, we let t(λ) be the multiset of hook lengths of λ which are divisible by t. Then, define ateven(n) and atodd(n) to be the number of partitions of n such that |t(λ)| is even or odd, respectively. In a recent paper, Han generalized the Nekrasov–Okounkov formula to obtain a generating function for at(n)=ateven(n)atodd(n). We use this generating function to prove congruences for the coefficients at(n).

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Dan Collins. Sally Wolfe. "Congruences for Han's generating function." Involve 2 (2) 225 - 236, 2009. https://doi.org/10.2140/involve.2009.2.225

Information

Received: 29 September 2008; Accepted: 17 January 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1167.05007
MathSciNet: MR2501339
Digital Object Identifier: 10.2140/involve.2009.2.225

Subjects:
Primary: 05A17, 11P83

Rights: Copyright © 2009 Mathematical Sciences Publishers

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