Campbell G.B. Vector Partitions, Visible Points and Ramanujan Functions

Chapman and Hall/CRC, 2024. — 567 p.Vector Partitions, Visible Points, and Ramanujan Functions offer 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 the 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 book intends 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 identitiesServes as a reference for graduate students and researchers in physics, applied mathematics, number theory, and computational mathematics and offers a variety of practical examples as well as sets of exercises suitable for students and researchers.Geoffrey B. Campbell completed his Ph.D. at the 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 Ph.D. 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; and as Analyst Researcher for a Royal Commission. Geoffrey specializes in complex data, and machine learning including data analytics. He is also a published poet in Australian anthologies and literary magazines.