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Algorithmic Algebraic Combinatorics and Gröbner Bases
This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries. There is special emphasis on algorithmic aspects and the use of the theory of Gröbner bases.
Investigations in Algebraic Theory of Combinatorial Objects
X Köchendorffer, L.A. Kalu:lnin and their students in the 50s and 60s. Nowadays the most deeply developed is the theory of binary invariant relations and their combinatorial approximations. These combinatorial approximations arose repeatedly during this century under various names (Hecke algebras, centralizer rings, association schemes, coherent configurations, cellular rings, etc.-see the first paper of the collection for details) andin various branches of mathematics, both pure and applied. One of these approximations, the theory of cellular rings (cellular algebras), was developed at the end of the 60s by B. Yu. Weisfeiler and A.A. Leman in the course of the first serious attempt to study the complexity of the graph isomorphism problem, one of the central problems in the modern theory of combinatorial algorithms. At roughly the same time G.M. Adelson-Velskir, V.L. Arlazarov, I.A. Faradtev and their colleagues had developed a rather efficient tool for the constructive enumeration of combinatorial objects based on the branch and bound method. By means of this tool a number of "sports-like" results were obtained. Some of these results are still unsurpassed.
Lie Groups and Lie Algebras
This collection contains papers conceptually related to the classical ideas of Sophus Lie (i.e., to Lie groups and Lie algebras). Obviously, it is impos sible to embrace all such topics in a book of reasonable size. The contents of this one reflect the scientific interests of those authors whose activities, to some extent at least, are associated with the International Sophus Lie Center. We have divided the book into five parts in accordance with the basic topics of the papers (although it can be easily seen that some of them may be attributed to several parts simultaneously). The first part (quantum mathematics) combines the papers related to the methods generated by the concepts of quantiz...
Topics in Number Theory
From July 31 through August 3,1997, the Pennsylvania State University hosted the Topics in Number Theory Conference. The conference was organized by Ken Ono and myself. By writing the preface, I am afforded the opportunity to express my gratitude to Ken for beng the inspiring and driving force behind the whole conference. Without his energy, enthusiasm and skill the entire event would never have occurred. We are extremely grateful to the sponsors of the conference: The National Sci ence Foundation, The Penn State Conference Center and the Penn State Depart ment of Mathematics. The object in this conference was to provide a variety of presentations giving a current picture of recent, signific...
Cellular Automata, Dynamical Systems and Neural Networks
This book contains the courses given at the Third School on Statistical Physics and Cooperative Systems held at Santiago, Chile, from 14th to 18th December 1992. The main idea of this periodic school was to bring together scientists work with recent trends in Statistical Physics. More precisely ing on subjects related related with non linear phenomena, dynamical systems, ergodic theory, cellular au tomata, symbolic dynamics, large deviation theory and neural networks. Scientists working in these subjects come from several areas: mathematics, biology, physics, computer science, electrical engineering and artificial intelligence. Recently, a very important cross-fertilization has taken place with regard to the aforesaid scientific and technological disciplines, so as to give a new approach to the research whose common core remains in statistical physics. Each contribution is devoted to one or more of the previous subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The expository text of Fran
Meromorphic Functions and Projective Curves
This book contains an exposition of the theory of meromorphic functions and linear series on a compact Riemann surface. Thus the main subject matter consists of holomorphic maps from a compact Riemann surface to complex projective space. Our emphasis is on families of meromorphic functions and holomorphic curves. Our approach is more geometric than algebraic along the lines of [Griffiths-Harrisl]. AIso, we have relied on the books [Namba] and [Arbarello-Cornalba-Griffiths-Harris] to agreat exten- nearly every result in Chapters 1 through 4 can be found in the union of these two books. Our primary motivation was to understand the totality of meromorphic functions on an algebraic curve. Though...
Algebraic Structures and Operators Calculus
Introduction I. General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 II. Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 III. Lie algebras: some basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter 1 Operator calculus and Appell systems I. Boson calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 II. Holomorphic canonical c...
Topics in Algebraic Graph Theory
The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmonic analysis, and are increasingly being used in such areas as computer networks where symmetry is an important feature. Other books cover portions of this material, but this book is unusual in covering both of these aspects and there are no other books with such a wide scope. Peter J. Cameron, internationally recognized for his substantial contributions to the area, served as academic consultant ...
Handbook of Graph Theory
In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition-over 400 pages longer than its prede
