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Author: Daniel Krob
Publisher: Springer Science & Business Media
ISBN: 3662041669
Category : Mathematics
Languages : en
Pages : 815
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Book Description
This book contains the extended abstracts presented at the 12th International Conference on Power Series and Algebraic Combinatorics (FPSAC '00) that took place at Moscow State University, June 26-30, 2000. These proceedings cover the most recent trends in algebraic and bijective combinatorics, including classical combinatorics, combinatorial computer algebra, combinatorial identities, combinatorics of classical groups, Lie algebra and quantum groups, enumeration, symmetric functions, young tableaux etc...
Author: Daniel Krob
Publisher: Springer Science & Business Media
ISBN: 3662041669
Category : Mathematics
Languages : en
Pages : 815
Get Book Here
Book Description
This book contains the extended abstracts presented at the 12th International Conference on Power Series and Algebraic Combinatorics (FPSAC '00) that took place at Moscow State University, June 26-30, 2000. These proceedings cover the most recent trends in algebraic and bijective combinatorics, including classical combinatorics, combinatorial computer algebra, combinatorial identities, combinatorics of classical groups, Lie algebra and quantum groups, enumeration, symmetric functions, young tableaux etc...
Author: Bruno Benedetti
Publisher: Springer
ISBN: 3319201557
Category : Mathematics
Languages : en
Pages : 222
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Book Description
Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects. This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.
Author: Alex Martsinkovsky
Publisher: American Mathematical Soc.
ISBN: 1470419556
Category : Mathematics
Languages : en
Pages : 258
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Book Description
This volume contains selected expository lectures delivered at the Maurice Auslander Distinguished Lectures and International Conference, held May 1–6, 2014, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Several significant developments of the last decade in representation theory of finite-dimensional algebras are related to combinatorics. Three of the five lectures in this volume deal, respectively, with the Catalan combinatorics, the combinatorics of Gelfand-Zetlin polytopes, and the combinatorics of tilting modules. The remaining papers present history and recent advances in the study of left orders in left Artinian rings and a survey on invariant theory of Artin-Schelter regular algebras.
Author: Marcelo Aguiar
Publisher: American Mathematical Soc.
ISBN: 1470437112
Category : Mathematics
Languages : en
Pages : 639
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Book Description
This monograph studies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. It provides a careful, organized and unified treatment of several recent developments in the field, and brings forth many new ideas and results. It has two parts, each divided into eight chapters, and five appendices with background material. Part I gives a detailed discussion on faces, flats, chambers, cones, gallery intervals, lunes and other geometric notions associated with arrangements. The Tits monoid plays a central role. Another important object is the category of lunes which generalizes the classical associative operad. Also discussed are the descent and lune identities, distance functions on chambers, and the combinatorics of the braid arrangement and related examples. Part II studies the structure and representation theory of the Tits algebra of an arrangement. It gives a detailed analysis of idempotents and Peirce decompositions, and connects them to the classical theory of Eulerian idempotents. It introduces the space of Lie elements of an arrangement which generalizes the classical Lie operad. This space is the last nonzero power of the radical of the Tits algebra. It is also the socle of the left ideal of chambers and of the right ideal of Zie elements. Zie elements generalize the classical Lie idempotents. They include Dynkin elements associated to generic half-spaces which generalize the classical Dynkin idempotent. Another important object is the lune-incidence algebra which marks the beginning of noncommutative Möbius theory. These ideas are also brought upon the study of the Solomon descent algebra. The monograph is written with clarity and in sufficient detail to make it accessible to graduate students. It can also serve as a useful reference to experts.
Author: Stephen Melczer
Publisher: Springer Nature
ISBN: 3030670805
Category : Mathematics
Languages : en
Pages : 418
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Book Description
This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.
Author: Patricia Hersh
Publisher: American Mathematical Soc.
ISBN: 1470427249
Category : Biography & Autobiography
Languages : en
Pages : 369
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Book Description
Richard Stanley's work in combinatorics revolutionized and reshaped the subject. His lectures, papers, and books inspired a generation of researchers. In this volume, these researchers explain how Stanley's vision and insights influenced and guided their own perspectives on the subject. As a valuable bonus, this book contains a collection of Stanley's short comments on each of his papers. This book may serve as an introduction to several different threads of ongoing research in combinatorics as well as giving historical perspective.
Author: Thomas Lam
Publisher: Springer
ISBN: 1493906828
Category : Mathematics
Languages : en
Pages : 226
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Book Description
This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.
Author: Andrew Beveridge
Publisher: Springer
ISBN: 3319242989
Category : Mathematics
Languages : en
Pages : 775
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Book Description
This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when combinatorics was the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The three-part structure of the volume reflects the three workshops held during Fall 2014. In the first part, topics on extremal and probabilistic combinatorics are presented; part two focuses on additive and analytic combinatorics; and part three presents topics in geometric and enumerative combinatorics. This book will be of use to those who research combinatorics directly or apply combinatorial methods to other fields.
Author: Michael Joswig
Publisher: American Mathematical Society
ISBN: 1470467410
Category : Mathematics
Languages : en
Pages : 398
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Book Description
The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $texttt{polymake}$.
Author: Octavian Iordache
Publisher: Springer
ISBN: 3319525514
Category : Technology & Engineering
Languages : en
Pages : 197
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Book Description
This book presents a domain of extreme industrial and scientific interest: the study of smart systems and structures. It presents polytope projects as comprehensive physical and cognitive architectures that support the investigation, fabrication and implementation of smart systems and structures. These systems feature multifunctional components that can perform sensing, control, and actuation. In light of the fact that devices, tools, methodologies and organizations based on electronics and information technology for automation, specific to the third industrial revolution, are increasingly reaching their limits, it is essential that smart systems be implemented in industry. Polytope projects facilitate the utilization of smart systems and structures as key elements of the fourth industrial revolution. The book begins by presenting polytope projects as a reference architecture for cyber-physical systems and smart systems, before addressing industrial process synthesis in Chapter 2. Flow-sheet trees, cyclic separations and smart configurations for multi-component separations are discussed here. In turn, Chapter 3 highlights periodic features for drug delivery systems and networks of chemical reactions, while Chapter 4 applies conditioned random walks to polymers and smart materials structures. Chapter 5 examines self-assembly and self-reconfiguration at different scales from molecular to micro systems. Smart devices and technologies are the focus of chapter 6. Modular micro reactor systems and timed automata are examined in selected case studies. Chapter 7 focuses on inferential engineering designs, concept-knowledge, relational concept analysis and model driven architecture, while Chapter 8 puts the spotlight on smart manufacturing, industry 4.0, reference architectures and models for new product development and testing. Lastly, Chapter 9 highlights the polytope projects methodology and the prospects for smart systems and structures. Focusing on process engineering and mathematical modeling for the fourth industrial revolution, the book offers a unique resource for engineers, scientists and entrepreneurs working in chemical, biochemical, pharmaceutical, materials science or systems chemistry, students in various domains of production and engineering, and applied mathematicians.
