A Conjecture of Han on 3-Cores and Modular Forms

Mathematics

Amanda Clemm¹ 

[1] Department of Mathematics, Emory University, Emory, Atlanta, GA 30322, USA; E-Mail

关键词: hook length;    partition;    modular form;   

DOI  :  10.3390/math2040232

来源: mdpi

【 摘 要 】

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 , 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.

【 授权许可】

CC BY   
© 2014 by the author; licensee MDPI, Basel, Switzerland.