Combinatorics The Rota Way
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Author |
: Joseph P. S. Kung |
Publisher |
: Cambridge University Press |
Total Pages |
: 409 |
Release |
: 2009-02-09 |
ISBN-10 |
: 9780521883894 |
ISBN-13 |
: 052188389X |
Rating |
: 4/5 (94 Downloads) |
Synopsis Combinatorics: The Rota Way by : Joseph P. S. Kung
Compiled and edited by two of Gian-Carlo Rota's students, this book is based on notes from his influential combinatorics courses.
Author |
: Joseph P. S. Kung |
Publisher |
: Cambridge University Press |
Total Pages |
: 397 |
Release |
: 2009-02-09 |
ISBN-10 |
: 9781139476768 |
ISBN-13 |
: 1139476769 |
Rating |
: 4/5 (68 Downloads) |
Synopsis Combinatorics: The Rota Way by : Joseph P. S. Kung
Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.
Author |
: Gian-Carlo Rota |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 299 |
Release |
: 2009-11-03 |
ISBN-10 |
: 9780817647810 |
ISBN-13 |
: 0817647813 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Indiscrete Thoughts by : Gian-Carlo Rota
Indiscrete Thoughts gives a glimpse into a world that has seldom been described - that of science and technology as seen through the eyes of a mathematician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science and of the American university. Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period. Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. This beautifully written book is destined to become an instant classic and the subject of debate for decades to come.
Author |
: Bruce E. Sagan |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 304 |
Release |
: 2020-10-16 |
ISBN-10 |
: 9781470460327 |
ISBN-13 |
: 1470460327 |
Rating |
: 4/5 (27 Downloads) |
Synopsis Combinatorics: The Art of Counting by : Bruce E. Sagan
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 |
: Jean Dhombres |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 424 |
Release |
: 2002-12-06 |
ISBN-10 |
: 0817642757 |
ISBN-13 |
: 9780817642754 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Gian-Carlo Rota on Analysis and Probability by : Jean Dhombres
Gian-Carlo Rota was born in Vigevano, Italy, in 1932. He died in Cambridge, Mas sachusetts, in 1999. He had several careers, most notably as a mathematician, but also as a philosopher and a consultant to the United States government. His mathe matical career was equally varied. His early mathematical studies were at Princeton (1950 to 1953) and Yale (1953 to 1956). In 1956, he completed his doctoral thesis under the direction of Jacob T. Schwartz. This thesis was published as the pa per "Extension theory of differential operators I", the first paper reprinted in this volume. Rota's early work was in analysis, more specifically, in operator theory, differ ential equations, ergodic theory, and probability theory. In the 1960's, Rota was motivated by problems in fluctuation theory to study some operator identities of Glen Baxter (see [7]). Together with other problems in probability theory, this led Rota to study combinatorics. His series of papers, "On the foundations of combi natorial theory", led to a fundamental re-evaluation of the subject. Later, in the 1990's, Rota returned to some of the problems in analysis and probability theory which motivated his work in combinatorics. This was his intention all along, and his early death robbed mathematics of his unique perspective on linkages between the discrete and the continuous. Glimpses of his new research programs can be found in [2,3,6,9,10].
Author |
: Philippe Flajolet |
Publisher |
: Cambridge University Press |
Total Pages |
: 825 |
Release |
: 2009-01-15 |
ISBN-10 |
: 9781139477161 |
ISBN-13 |
: 1139477161 |
Rating |
: 4/5 (61 Downloads) |
Synopsis Analytic Combinatorics by : Philippe Flajolet
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 |
: Berge |
Publisher |
: Academic Press |
Total Pages |
: 189 |
Release |
: 1971-04-20 |
ISBN-10 |
: 9780080955810 |
ISBN-13 |
: 0080955819 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Principles of Combinatorics by : Berge
Berge's Principles of Combinatorics is now an acknowledged classic work of the field. Complementary to his previous books, Berge's introduction deals largely with enumeration. The choice of topics is balanced, the presentation elegant, and the text can be followed by anyone with an interest in the subject with only a little algebra required as a background. Some topics were here described for the first time, including Robinston-Shensted theorum, the Eden-Schutzenberger theorum, and facts connecting Young diagrams, trees, and the symmetric group.
Author |
: François Bergeron |
Publisher |
: Cambridge University Press |
Total Pages |
: 484 |
Release |
: 1998 |
ISBN-10 |
: 0521573238 |
ISBN-13 |
: 9780521573238 |
Rating |
: 4/5 (38 Downloads) |
Synopsis Combinatorial Species and Tree-like Structures by : François Bergeron
The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for the specification and analysis of these structures. Of particular importance is their capacity to transform recursive definitions of tree-like structures into functional or differential equations, and vice versa. The goal of this book is to present the basic elements of the theory and to give a unified account of its developments and applications. It offers a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis and differential equations. This book will be a valuable reference to graduate students and researchers in combinatorics, analysis, and theoretical computer science.
Author |
: Alan Tucker |
Publisher |
: John Wiley & Sons |
Total Pages |
: 408 |
Release |
: 1980 |
ISBN-10 |
: STANFORD:36105031541597 |
ISBN-13 |
: |
Rating |
: 4/5 (97 Downloads) |
Synopsis Applied Combinatorics by : Alan Tucker
Author |
: Martin Aigner |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 493 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642591013 |
ISBN-13 |
: 3642591019 |
Rating |
: 4/5 (13 Downloads) |
Synopsis Combinatorial Theory by : Martin Aigner
This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. ". . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics." Publicationes Mathematicae Debrecen