A Conjecture of Han on 3-Cores and Modular Forms

Amanda Clemm
Additional contact information
Amanda Clemm: Department of Mathematics, Emory University, Emory, Atlanta, GA 30322, USA

Mathematics, 2014, vol. 2, issue 4, 1-8

Abstract: In his study of Nekrasov–Okounkov type formulas on “partition theoretic” expressions for families of infinite products, Han discovered seemingly unrelated q -series that are supported on precisely the same terms as these infinite products. In collaboration with Ono, Han proved one instance of this occurrence that exhibited a relation between the numbers a(n) that are given in terms of hook lengths of partitions, with the numbers b(n) that equal the number of 3-core partitions of n . Recently Han revisited the q-series with coefficients a(n) and b(n) , and numerically found a third q -series whose coefficients appear to be supported on the same terms. Here we prove Han’s conjecture about this third series by proving a general theorem about this phenomenon.

Keywords: hook length; partition; modular form (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/2/4/232/pdf (application/pdf)
https://www.mdpi.com/2227-7390/2/4/232/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:2:y:2014:i:4:p:232-239:d:43746

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().