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Author: Hélène Barcelo
Publisher: Springer
ISBN: 3030051412
Category : Mathematics
Languages : en
Pages : 362
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Book Description
This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.
Author: Hélène Barcelo
Publisher: Springer
ISBN: 3030051412
Category : Mathematics
Languages : en
Pages : 362
Get Book
Book Description
This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.
Author: Hélène Barcelo
Publisher:
ISBN: 9783030051426
Category : Combinatorial analysis
Languages : en
Pages : 362
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Book Description
This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools.
Author: Chris Godsil
Publisher: CRC Press
ISBN: 9780412041310
Category : Mathematics
Languages : en
Pages : 382
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Book Description
This book presents an introduction to some of the interactions between algebra and combinatorics. It focuses on the characteristic and matchings polynomials of a graph and introduces the theory of polynomial spaces. The book is intended for beginning graduate students in mathematics.
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: Shum Kar Ping
Publisher: World Scientific
ISBN: 9811215480
Category : Mathematics
Languages : en
Pages : 500
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Book Description
This volume composed of twenty four research articles which are selected from the keynote speakers and invited lectures presented in the 3rd International Congress in Algebra and Combinatorics (ICAC2017) held on 25-28 August 2017 in Hong Kong and one additional invited article. This congress was specially dedicated to Professor Leonid Bokut on the occasion of his 80th birthday.
Author: Christopher Francisco
Publisher: Walter de Gruyter
ISBN: 3110250403
Category : Mathematics
Languages : en
Pages : 377
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Book Description
This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological articles the editors have included in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian such as in the papers by Roberts, Yao, Hummel and Leuschke.
Author: Bruno Benedetti
Publisher: Springer
ISBN: 3319201557
Category : Mathematics
Languages : en
Pages : 227
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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: Louis J. Billera
Publisher: Cambridge University Press
ISBN: 9780521179799
Category : Mathematics
Languages : en
Pages : 0
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Book Description
During 1996-97 MSRI held a full academic-year program on combinatorics, with special emphasis on its connections to other branches of mathematics, such as algebraic geometry, topology, commutative algebra, representation theory, and convex geometry. The rich combinatorial problems arising from the study of various algebraic structures are the subject of this book, which features work done or presented at the program's seminars. The text contains contributions on matroid bundles, combinatorial representation theory, lattice points in polyhedra, bilinear forms, combinatorial differential topology and geometry, Macdonald polynomials and geometry, enumeration of matchings, the generalized Baues problem, and Littlewood-Richardson semigroups. These expository articles, written by some of the most respected researchers in the field, present the state of the art to graduate students and researchers in combinatorics as well as in algebra, geometry, and topology.
Author: Andrew Beveridge
Publisher: Springer
ISBN: 3319242989
Category : Mathematics
Languages : en
Pages : 778
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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: Mahir Can
Publisher: Springer
ISBN: 149390938X
Category : Mathematics
Languages : en
Pages : 360
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Book Description
This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: structure and representation theory of reductive algebraic monoids monoid schemes and applications of monoids monoids related to Lie theory equivariant embeddings of algebraic groups constructions and properties of monoids from algebraic combinatorics endomorphism monoids induced from vector bundles Hodge–Newton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semi groups are strongly π-regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics and the theory of algebraic group embeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings and algebraic combinatorics merged under the umbrella of algebraic monoids.
