Combinatorial Reciprocity Theorems An Invitation To Enumerative Geometric Combinatorics
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Combinatorial Reciprocity Theorems
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Author : Matthias Beck
language : en
Publisher:
Release Date : 2018
Combinatorial Reciprocity Theorems written by Matthias Beck and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with MATHEMATICS categories.
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.
Combinatorial Reciprocity Theorems
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Author : R. P. Stanley
language : en
Publisher:
Release Date : 1974
Combinatorial Reciprocity Theorems written by R. P. Stanley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Combinatorial Reciprocity Theorems An Invitation To Enumerative Geometric Combinatorics
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Author : Matthias Beck
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-12-12
Combinatorial Reciprocity Theorems An Invitation To Enumerative Geometric Combinatorics written by Matthias Beck and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Combinatorial analysis categories.
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.
Combinatorics The Art Of Counting
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Author : Bruce E. Sagan
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-16
Combinatorics The Art Of Counting written by Bruce E. Sagan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-16 with Education categories.
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.
Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes
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Author : Hibi Takayuki
language : en
Publisher: World Scientific
Release Date : 2019-05-30
Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes written by Hibi Takayuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-30 with Mathematics categories.
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.
Algebraic And Geometric Combinatorics
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Author : Christos A. Athanasiadis
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Algebraic And Geometric Combinatorics written by Christos A. Athanasiadis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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.
Convex Cones
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Author : Rolf Schneider
language : en
Publisher: Springer Nature
Release Date : 2022-09-21
Convex Cones written by Rolf Schneider and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-21 with Mathematics categories.
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.
Computer Algebra And Polynomials
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Author : Jaime Gutierrez
language : en
Publisher: Springer
Release Date : 2015-01-20
Computer Algebra And Polynomials written by Jaime Gutierrez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-20 with Computers categories.
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.
Geometric Combinatorics
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Author :
language : en
Publisher:
Release Date : 2007
Geometric Combinatorics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Combinatorial analysis categories.
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. Perhaps the most familiar examples are polytopes and simplicial complexes, but the subject is much broader. This volume is a compilation of expository articles at the interface between combinatorics and geometry, based on a three-week program of lectures at the Institute for Advanced Study/Park City Math Institute (IAS/PCMI) summer program on Geometric Combinatorics. The topics covered include posets, graphs, hyperplane arrangements, discrete Morse th.
Relations Between Combinatorics And Other Parts Of Mathematics
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Author : Dijen Ray-Chaudhuri
language : en
Publisher: American Mathematical Soc.
Release Date : 1979-12-31
Relations Between Combinatorics And Other Parts Of Mathematics written by Dijen Ray-Chaudhuri and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-12-31 with Mathematics categories.
Brings into focus interconnections between combinatorics on the one hand and geometry, group theory, number theory, special functions, lattice packings, logic, topological embeddings, games, experimental dsigns, and sociological and biological applications on the other hand.