This book presents a printed testimony for the fact that George Andrews, one of the world’s leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80. To honor George Andrews on this occasion, the conference “Combinatory Analysis 2018” was organized at the Pennsylvania State University from June 21 to 24, 2018. This volume comprises the original articles from the Special Issue “Combinatory Analysis 2018 – In Honor of George Andrews’ 80th Birthday” resulting from the conference and published in Annals of Combinatorics. In addition to the 37 articles of the Andrews 80 Special Issue, the book includes two new papers. These research contributions explore new grounds and present new achievements, research trends, and problems in the area. The volume is complemented by three special personal contributions: “The Worlds of George Andrews, a daughter’s take” by Amy Alznauer, “My association and collaboration with George Andrews” by Krishna Alladi, and “Ramanujan, his Lost Notebook, its importance” by Bruce Berndt. Another aspect which gives this Andrews volume a truly unique character is the “Photos” collection. In addition to pictures taken at “Combinatory Analysis 2018”, the editors selected a variety of photos, many of them not available elsewhere: “Andrews in Austria”, “Andrews in China”, “Andrews in Florida”, “Andrews in Illinois”, and “Andrews in India”. This volume will be of interest to researchers, PhD students, and interested practitioners working in the area of Combinatory Analysis, q-Series, and related fields.

This book presents a printed testimony for the fact that George Andrews, one of the world's leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80. To honor George Andrews on this occasion, the conference "Combinatory Analysis 2018" was organized at the Pennsylvania State University from June 21 to 24, 2018. This volume comprises the original articles from the Special Issue "Combinatory Analysis 2018 - In Honor of George Andrews' 80th Birthday" resulting from the conference and published in Annals of Combinatorics. In addition to the 37 articles of the Andrews 80 Special Issue, the book includes two new papers. These research contributions explore new grounds and present new achievements, research trends, and problems in the area. The volume is complemented by three special personal contributions: "The Worlds of George Andrews, a daughter's take" by Amy Alznauer, "My association and collaboration with George Andrews" by Krishna Alladi, and "Ramanujan, his Lost Notebook, its importance" by Bruce Berndt. Another aspect which gives this Andrews volume a truly unique character is the "Photos" collection. In addition to pictures taken at "Combinatory Analysis 2018", the editors selected a variety of photos, many of them not available elsewhere: "Andrews in Austria", "Andrews in China", "Andrews in Florida", "Andrews in Illinois", and "Andrews in India". This volume will be of interest to researchers, PhD students, and interested practitioners working in the area of Combinatory Analysis, q-Series, and related fields.

George Andrews is one of the most influential figures in number theory and combinatorics. In the theory of partitions and q-hypergeometric series and in the study of Ramanujan's work, he is the unquestioned leader. To suitably honor him during his 70th birthday year, an International Conference on Combinatory Analysis was held at The Pennsylvania State University during December 5-7, 2008. Three issues of the Ramanujan Journal comprising Volume 23 were published in 2010 as the refereed proceedings of that conference. The Ramanujan Journal was proud to bring out that volume honoring one of its Founding Editors. In view of the great interest that the mathematical community has in the influential work of Andrews, it was decided to republish Volume 23 of The Ramanujan Journal in this book form, so that the refereed proceedings are more readily available for those who do not subscribe to the journal but wish to possess this volume. As a fitting tribute to George Andrews, many speakers from the conference contributed research papers to this volume which deals with a broad range of areas that signify the research interests of George Andrews. In reproducing Volume 23 of The Ramanujan Journal in this book form, we have included two papers—one by Hei-Chi Chan and Shaun Cooper, and another by Ole Warnaar—which were intended for Volume 23 of The Ramanujan Journal, but appeared in other issues. The enormous productivity of George Andrews remains unabated in spite of the passage of time. His immensely fertile mind continues to pour forth seminal ideas year after year. He has two research papers in this volume. May his eternal youthfulness and his magnificent research output continue to inspire and influence researchers in the years ahead.

George Andrews is one of the most influential figures in number theory and combinatorics. In the theory of partitions and q-hypergeometric series and in the study of Ramanujan's work, he is the unquestioned leader. To suitably honor him during his 70th birthday year, an International Conference on Combinatory Analysis was held at The Pennsylvania State University during December 5-7, 2008. Three issues of the Ramanujan Journal comprising Volume 23 were published in 2010 as the refereed proceedings of that conference. The Ramanujan Journal was proud to bring out that volume honoring one of its Founding Editors. In view of the great interest that the mathematical community has in the influential work of Andrews, it was decided to republish Volume 23 of The Ramanujan Journal in this book form, so that the refereed proceedings are more readily available for those who do not subscribe to the journal but wish to possess this volume. As a fitting tribute to George Andrews, many speakers from the conference contributed research papers to this volume which deals with a broad range of areas that signify the research interests of George Andrews. In reproducing Volume 23 of The Ramanujan Journal in this book form, we have included two papers—one by Hei-Chi Chan and Shaun Cooper, and another by Ole Warnaar—which were intended for Volume 23 of The Ramanujan Journal, but appeared in other issues. The enormous productivity of George Andrews remains unabated in spite of the passage of time. His immensely fertile mind continues to pour forth seminal ideas year after year. He has two research papers in this volume. May his eternal youthfulness and his magnificent research output continue to inspire and influence researchers in the years ahead.

Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Vector Partitions, Visible Points and Ramanujan Functions offers a novel theory of Vector Partitions, though very much grounded in the long-established work of others, that could be developed as an extension to the existing theory of Integer Partitions. The book is suitable for graduate students in physics, applied mathematics, number theory and computational mathematics. It takes the reader up to research level, presenting new results alongside known classical results from integer partitions and areas of vector and multipartite partition theory. It also sets forth new directions for research for the more advanced reader. Above all, the intention of the book is to bring new inspiration to others who study mathematics and related areas. It is hoped that some new ideas will be launched to add value and insight into many of the classical and new theories surrounding partitions. The book is an appreciation of the many gifted authors of research into partitions over the past century and before, in the hope that more may come of this for future generations. Features Provides a step-by-step guide through the known literature on Integer and Vector Partitions, and a focus on the not so well-known Visible Point Vector identities Serves as a reference for graduate students and researchers in physics, applied mathematics, number theory and computational mathematics Offers a variety of practical examples as well as sets of exercises suitable for students and researchers Geoffrey B. Campbell completed his PhD at Australian National University in 1998 under the esteemed physicist Professor Rodney Baxter. His affiliation with the Australian National University Mathematical Sciences Institute has continued for over 30 years. Within that time frame, Geoffrey also served eight years as an Honorary Research Fellow at LaTrobe University Mathematics and Statistics Department in Melbourne. Currently he writes ongoing articles for the Australian Mathematical Society Gazette. Within the international scope, Geoffrey currently serves as a PhD external committee member for a mathematics graduate student at Washington State University in America. Geoffrey has built a career within Australian Commonwealth and State government departments, including as an Advisor at the Department of Prime Minister and Cabinet; as Analyst Researcher for a Royal Commission. Geoffrey specializes in complex data, machine learning including data analytics. He is also a published poet in Australian anthologies and literary magazines.

This book contains seventeen contributions made to George Andrews on the occasion of his sixtieth birthday, ranging from classical number theory (the theory of partitions) to classical and algebraic combinatorics. Most of the papers were read at the 42nd session of the Sminaire Lotharingien de Combinatoire that took place at Maratea, Basilicata, in August 1998. This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions studied with a contemporary eye, together with several papers dealing with the theory of partitions. There is also a description of a maple package to deal with general q-calculus. More subjects on algebraic combinatorics are developed, especially the theory of Kostka polynomials, the ice square model, the combinatorial theory of classical numbers, a new approach to determinant calculus.