Combinatorial Reciprocity Theorems An Invitation To Enumerative Geometric Combinatorics PDF Download
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| Author | : Matthias Beck |
| Publisher | : |
| Total Pages | : |
| Release | : 2018 |
| Genre | : MATHEMATICS |
| ISBN | : 9781470449964 |
Download Combinatorial Reciprocity Theorems Book in PDF, ePub and Kindle
Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics. Written in a fri.
| Author | : R. P. Stanley |
| Publisher | : |
| Total Pages | : 103 |
| Release | : 1974 |
| Genre | : |
| ISBN | : |
Download Combinatorial Reciprocity Theorems Book in PDF, ePub and Kindle
| Author | : Matthias Beck |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 308 |
| Release | : 2018-12-12 |
| Genre | : Combinatorial analysis |
| ISBN | : 147042200X |
Download Combinatorial Reciprocity Theorems: An Invitation to Enumerative Geometric Combinatorics Book in PDF, ePub and Kindle
Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics. Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature. Topics include concise introductions to partially ordered sets, polyhedral geometry, and rational generating functions, followed by highly original chapters on subdivisions, geometric realizations of partially ordered sets, and hyperplane arrangements.
| Author | : Bruce E. Sagan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 304 |
| Release | : 2020-10-16 |
| Genre | : Education |
| ISBN | : 1470460327 |
Download Combinatorics: The Art of Counting Book in PDF, ePub and Kindle
This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.
| Author | : Hibi Takayuki |
| Publisher | : World Scientific |
| Total Pages | : 476 |
| Release | : 2019-05-30 |
| Genre | : Mathematics |
| ISBN | : 9811200491 |
Download Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes Book in PDF, ePub and Kindle
This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.
| Author | : Rolf Schneider |
| Publisher | : Springer Nature |
| Total Pages | : 352 |
| Release | : 2022-09-21 |
| Genre | : Mathematics |
| ISBN | : 3031151275 |
Download Convex Cones Book in PDF, ePub and Kindle
This book provides the foundations for geometric applications of convex cones and presents selected examples from a wide range of topics, including polytope theory, stochastic geometry, and Brunn–Minkowski theory. Giving an introduction to convex cones, it describes their most important geometric functionals, such as conic intrinsic volumes and Grassmann angles, and develops general versions of the relevant formulas, namely the Steiner formula and kinematic formula. In recent years questions related to convex cones have arisen in applied mathematics, involving, for example, properties of random cones and their non-trivial intersections. The prerequisites for this work, such as integral geometric formulas and results on conic intrinsic volumes, were previously scattered throughout the literature, but no coherent presentation was available. The present book closes this gap. It includes several pearls from the theory of convex cones, which should be better known.
| Author | : Christos A. Athanasiadis |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 342 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821840800 |
Download Algebraic and Geometric Combinatorics Book in PDF, ePub and Kindle
This volume contains original research and survey articles stemming from the Euroconference ``Algebraic and Geometric Combinatorics''. The papers discuss a wide range of problems that illustrate interactions of combinatorics with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and partially ordered sets. Among the topics covered are combinatorics of polytopes, lattice polytopes, triangulations and subdivisions, Cohen-Macaulay cell complexes, monomial ideals, geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig combinatorics, and graph colorings. This book is aimed at researchers and graduate students interested in various aspects of modern combinatorial theories.
| Author | : Jaime Gutierrez |
| Publisher | : Springer |
| Total Pages | : 222 |
| Release | : 2015-01-20 |
| Genre | : Computers |
| ISBN | : 3319150812 |
Download Computer Algebra and Polynomials Book in PDF, ePub and Kindle
Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.
| Author | : Ezra Miller |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 705 |
| Release | : 2007 |
| Genre | : Combinatorial analysis |
| ISBN | : 0821837362 |
Download Geometric Combinatorics Book in PDF, ePub and Kindle
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.
| Author | : Charalambos A. Charalambides |
| Publisher | : CRC Press |
| Total Pages | : 632 |
| Release | : 2018-10-08 |
| Genre | : Business & Economics |
| ISBN | : 1482296314 |
Download Enumerative Combinatorics Book in PDF, ePub and Kindle
Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem. Extensively classroom tested, this text was designed for introductory- and intermediate-level courses in enumerative combinatorics, but the far-reaching applications of the subject also make the book useful to those in operational research, the physical and social science, and anyone who uses combinatorial methods. Remarks, discussions, tables, and numerous examples support the text, and a wealth of exercises-with hints and answers provided in an appendix--further illustrate the subject's concepts, theorems, and applications.
