A Conjecture of Han on 3-Cores and Modular Forms
AbstractIn 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. View Full-Text
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Clemm, A. A Conjecture of Han on 3-Cores and Modular Forms. Mathematics 2014, 2, 232-239.
Clemm A. A Conjecture of Han on 3-Cores and Modular Forms. Mathematics. 2014; 2(4):232-239.Chicago/Turabian Style
Clemm, Amanda. 2014. "A Conjecture of Han on 3-Cores and Modular Forms." Mathematics 2, no. 4: 232-239.