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The theory of partitions
1. The elementary theory of partitions 2. Infinite series generating functions 3. Restricted partitions and permutations 4. Compositions and Simon Newcomb's problem 5. The Hardy-Ramanujan-RademacherExpand
The lost notebook and other unpublished papers
The so-called "Lost Notebook" of S.R. Ramanujan was brought to light in 1976 as part of the Watson bequest, by G.E. Andrews with whose introduction this collection of unpublished manuscripts opens. AExpand
Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
AbstractThe eight-vertex model is equivalent to a “solid-on-solid” (SOS) model, in which an integer heightli is associated with each sitei of the square lattice. The Boltzmann weights of the modelExpand
Ramanujan's Lost Notebook: Part I
In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, AndrewsExpand
Dyson's crank of a partition
holds. He was thus led to conjecture the existence of some other partition statistic (which he called the crank); this unknown statistic should provide a combinatorial interpretation of ^-p(lln + 6)Expand
q-series : their development and application in analysis, number theory, combinatorics, physics, and computer algebra
Found opportunities Classical special functions and L. J. Rogers W. N. Bailey's extension of Roger's work Constant terms Integrals Partitions and $q$-series Partitions and constant terms The hardExpand
ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS
88. Teo Mora Solving Polynomial Equation Systems, I 89. Klaus Bichteler Stochastic Integration with Jumps 90. M. Lothaire Algebraic Combinatorics on Words 91. A. A. Ivanov & S. V. Shpectorov GeometryExpand
The number of smallest parts in the partitions of n
Abstract We denote by spt(n) the total number of appearances of the smallest part in each integer partition of n. We shall relate spt(n) to the Atkin-Garvan moments of ranks, and we shall prove thatExpand
Problems and Prospects for Basic Hypergeometric Functions
Publisher Summary This chapter discusses certain problems and prospects for basic hypergeometric functions. It also focuses on finite linear homogeneous ordinary q-difference equations withExpand
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