Preface

In March 2008, an International Conference on Partitions, q-Series, and Modular Forms was held at the University of Florida. This conference was one of the highlights of the year-long Program in Algebra, Number Theory, and Combinatorics (ANTC) held in the Mathematics Department. The University of Florida Mathematics Department has been the venue of several conferences covering the theory of partitions and q-hypergeometric series. But what made this 2008 conference so special was that its outstanding success led to the start of year-long programs in ANTC in our department, with the 2007–2008 program being the first. The 2008 conference received generous support from the National Science Foundation, the Department of Mathematics, the College of Liberal Arts and Sciences, and the Office of Research and Graduate Programs of the University of Florida and for this we are most grateful. The organizers of this conference were Krishnaswami Alladi, Alexander Berkovich, and Frank Garvan of the University of Florida, and George Andrews of The Pennsylvania State University who is Distinguished Visiting Professor in Florida each year in the Spring Term. This volume is the outgrowth of the 2008 Gainesville conference on partitions, q-series, and modular forms, and contains major surveys and research papers related to some of the talks given at the conference. The papers have been arranged in the alphabetical order of the authors names. Major MacMahon, a towering figure in the area of Combinatory Analysis, initiated several major lines of study, one of which was the subject of plane partitions. He created a calculational and analytic method for the purpose of determining the generating function for plane partitions, but it did not turn out to be what was he had intended, so he had to develop an alternative treatment in the next two decades. George Andrews and Peter Paule provide a charming account of the resurrection of MacMahon’s dream of using partition analysis to treat plane partitions and show how the computer algebra package Omega has now played a decisive role in a successful treatment of plane partitions via partition analysis. Andrews and Paule point out that many essential features of this approach were known to MacMahon and so this solution is very much along the lines of MacMahon’s original dream.