In a series of papers the first author and Ono connected the rank, a partition statistic
introduced by Dyson, to weak Maass forms, a new class of functions related to modular …

Abstract In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures on the rank of a
partition by establishing formulae for the generating functions for rank differences in …

Let p¯(n) denote the number of overpartitions of n. In this paper, we show that p¯(5 n)≡(− 1)
np¯(4⋅ 5 n)(mod 5) for n≥ 0 and p¯(n)≡(− 1) np¯(4 n)(mod 8) for n≥ 0 by using the …

We extend partition-theoretic work of Andrews, Bressoud, and Burge to overpartitions,
defining the notions of successive ranks, generalized Durfee squares, and generalized …

We construct Young wall models for the crystal bases of level 1 irreducible highest weight
representations and Fock space representations of quantum affine algebras in types E 6 (1) …

We study the geometry and topology of Hilbert schemes of points on the orbifold surface,
respectively the singular quotient surface, where is a finite subgroup of type A or D. We give …

In this paper, we construct Young wall models for the level 1 highest weight and Fock space
crystals of quantum affine algebras in types E 6 (2) and F 4 (1). Our starting point in each …

Let p (n) denote the integer partition function. Good conjectured that Δ rp (n) alternates in
sign up to a certain value n= n (r), and then it stays positive. Gupta showed that for any given …

Let ̄ p (n) p¯(n) denote the number of overpartitions of n n. Recently, Fortin–Jacob–Mathieu
and Hirschhorn–Sellers independently obtained 2-, 3-and 4-dissections of the generating …

Thermal properties of nuclear surface are investigated in a semi-infinite medium. Explicit
analytical expressions are given for the temperature dependence of surface thickness …