Polynomial Methods In Combinatorics PDF Download
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| Author | : Larry Guth |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 287 |
| Release | : 2016-06-10 |
| Genre | : Mathematics |
| ISBN | : 1470428903 |
Download Polynomial Methods in Combinatorics Book in PDF, ePub and Kindle
This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.
| Author | : Antonio Giambruno |
| Publisher | : CRC Press |
| Total Pages | : 442 |
| Release | : 2003-05-20 |
| Genre | : Mathematics |
| ISBN | : 9780203911549 |
Download Polynomial Identities And Combinatorial Methods Book in PDF, ePub and Kindle
Polynomial Identities and Combinatorial Methods presents a wide range of perspectives on topics ranging from ring theory and combinatorics to invariant theory and associative algebras. It covers recent breakthroughs and strategies impacting research on polynomial identities and identifies new concepts in algebraic combinatorics, invariant and representation theory, and Lie algebras and superalgebras for novel studies in the field. It presents intensive discussions on various methods and techniques relating the theory of polynomial identities to other branches of algebraic study and includes discussions on Hopf algebras and quantum polynomials, free algebras and Scheier varieties.
| Author | : Adam Sheffer |
| Publisher | : Cambridge University Press |
| Total Pages | : 263 |
| Release | : 2022-03-24 |
| Genre | : Mathematics |
| ISBN | : 1108832490 |
Download Polynomial Methods and Incidence Theory Book in PDF, ePub and Kindle
A thorough yet accessible introduction to the mathematical breakthroughs achieved by using new polynomial methods in the past decade.
| Author | : Adam Sheffer |
| Publisher | : Cambridge University Press |
| Total Pages | : 264 |
| Release | : 2022-03-24 |
| Genre | : Mathematics |
| ISBN | : 1108963013 |
Download Polynomial Methods and Incidence Theory Book in PDF, ePub and Kindle
The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdős's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. There has also been significant progress on a variety of problems from additive combinatorics, discrete geometry, and more. This book gives a detailed yet accessible introduction to these new polynomial methods and their applications, with a focus on incidence theory. Based on the author's own teaching experience, the text requires a minimal background, allowing graduate and advanced undergraduate students to get to grips with an active and exciting research front. The techniques are presented gradually and in detail, with many examples, warm-up proofs, and exercises included. An appendix provides a quick reminder of basic results and ideas.
| Author | : Stasys Jukna |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 389 |
| Release | : 2013-03-09 |
| Genre | : Computers |
| ISBN | : 3662046504 |
Download Extremal Combinatorics Book in PDF, ePub and Kindle
This is a concise, up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called the gems of the theory. A wide spectrum of the most powerful combinatorial tools is presented, including methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A thorough discussion of recent applications to computer science illustrates the inherent usefulness of these methods.
| Author | : Philippe Flajolet |
| Publisher | : Cambridge University Press |
| Total Pages | : 825 |
| Release | : 2009-01-15 |
| Genre | : Mathematics |
| ISBN | : 1139477161 |
Download Analytic Combinatorics Book in PDF, ePub and Kindle
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
| Author | : James Haglund |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 178 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821844113 |
Download The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics Book in PDF, ePub and Kindle
This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.
| 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 | : A. Giambruno |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 370 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821838296 |
Download Polynomial Identities and Asymptotic Methods Book in PDF, ePub and Kindle
This book gives a state of the art approach to the study of polynomial identities satisfied by a given algebra by combining methods of ring theory, combinatorics, and representation theory of groups with analysis. The idea of applying analytical methods to the theory of polynomial identities appeared in the early 1970s and this approach has become one of the most powerful tools of the theory. A PI-algebra is any algebra satisfying at least one nontrivial polynomial identity. This includes the polynomial rings in one or several variables, the Grassmann algebra, finite-dimensional algebras, and many other algebras occurring naturally in mathematics. The core of the book is the proof that the sequence of co-dimensions of any PI-algebra has integral exponential growth - the PI-exponent of the algebra. Later chapters further apply these results to subjects such as a characterization of varieties of algebras having polynomial growth and a classification of varieties that are minimal for a given exponent.
| Author | : Richard P. Stanley |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 226 |
| Release | : 2013-06-17 |
| Genre | : Mathematics |
| ISBN | : 1461469988 |
Download Algebraic Combinatorics Book in PDF, ePub and Kindle
Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
