The asymptotic distribution of the number of summands in unrestricted Λ-partitions
The average order of a permutation.
The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications
The paper is devoted to the derivation of the expansion formula for the powers of the Euler Product in terms of partition hook lengths, discovered by Nekrasov and Okounkov in their study of the Seiberg-Witten Theory. We provide a refinement based on a new property of -cores, and give an elementary proof by using the Macdonald identities. We also obtain an extension by adding two more parameters, which appears to be a discrete interpolation between the Macdonald identities and the generating function...
The number-theoretic content of the Jacobi triple product identity.
The size of the largest part of random plane partitions of large integers.
The spt-crank for overpartitions
Bringmann, Lovejoy, and Osburn (2009, 2010) showed that the generating functions of the spt-overpartition functions , , , and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and Liang (2012) defined an spt-crank in terms of weighted vector partitions which combinatorially explain simple congruences modulo 5 and 7 for spt(n). Chen, Ji, and Zang (2013) were able to define this spt-crank in terms of ordinary partitions. In this...
The triple, quintuple and setuple product identities revisited.