Geoffrey B. Campbell

Vector Partitions, Visible Points and Ramanujan Functions (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book 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.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 564
• Erscheinungstermin: 29. Mai 2024
• Englisch
• ISBN-13: 9781040026441
• Artikelnr.: 70545542

Autorenporträt

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.

Inhaltsangabe

Section I. Background and History. 1. History timeline partitions. Section
II. Integer Partition Theory. 3. Integer partition generating functions. 4.
Continued fraction partition identities. 5. Partition congruences. 6.
Ferrers diagrams. 7.Durfee Squares. 8. Gaussian polynomials. 9. Plane
Partitions from MacMahon to Andrews. 10. Asymptotics for Partition
Functions. 11. Rogers-Ramanujan identities in Statistical Mechanics.
Section III. Vector Partition Theory. 12. Vector partitions and their
generating function identities. 13. Integer Partitions generalized to
Vector Partitions. 14. Weighted Vector Partitions as hybrid n-space
variations. 15. Functional Equations for n-space Vector Partitions. 16.
Binary Partitions and their Vector Generalizations. 17. n-ary Partitions
and their Vector Generalizations. 18. Some Binary and n-ary Partition
Analytic Formulas. Section IV. 19. Features of the Visible Lattice Points.
20. Visible Point Vector Identities in the first Hyperquadrant. 21. Visible
Point Vector Identities in Hyperpyramid lattices. 22. Polylogarithms, and
Parametric Euler Sum identities. 23. Visible Point Vector identities from
particular Euler sum values. 24. Visible Point Vector Identities in Skewed
Hyperpyramid lattices. 25. Harmonic Sums applied to VPV Identities. 26. The
Ramanujan trigonometric function and visible point identities. 27. Other
non-weighted n-space Vector Partition Theorems. 28. VPV Identity cases
related to some exponential relations. Section V. Models, Interpretations
and some Useful Tools. 29. 2D and 3D Stepping Stones, Forests, Orchards and
Light Diffusions. 30. Euler Products over Primes and new VPV Formulas. 31.
Determinants, Bell Polynomial Expansions for Vector Partitions. 32.
Glossary.