This volume surveys the development of combinatorics since 1930 by presenting in chronological order the fundamental results of the subject proved in over five decades of original papers by: T. van Aardenne-Ehrenfest.- R.L. Brooks.- N.G. de Bruijn.- G.F. Clements.- H.H. Crapo.- R.P. Dilworth.- J. Edmonds.- P. Erdös.- L.R. Ford, Jr.- D.R. Fulkerson.- D. Gale.- L. Geissinger.- I.J. Good.- R.L. Graham.- A.W. Hales.- P. Hall.- P.R. Halmos.- R.I. Jewett.- I. Kaplansky.- P.W. Kasteleyn.- G. Katona.- D.J. Kleitman.- K. Leeb.- B. Lindström.- L. Lovász.- D. Lubell.- C. St. J.A. Nash-Williams.- G. Pólya.-R. Rado.- F.P. Ramsey.- G.-C. Rota.- B.L. Rothschild.- H.J. Ryser.- C. Schensted.- M.P. Schützenberger.- R.P. Stanley.- G. Szekeres.- W.T. Tutte.- H.E. Vaughan.- H. Whitney.

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.

It is not often that one gets to write a preface to a collection of one's own papers. The most urgent task is to thank the people who made this book possible. That means first of all Hy Bass who, on behalf of Springer-Verlag, approached me about the idea. The late Walter Kaufmann-Biihler was very encouraging; Paulo Ribenboim helped in an important way; and Ina Lindemann saw the project through with tact and skill that I deeply appreciate. My wishes have been indulged in two ways. First, I was allowed to follow up each selected paper with an afterthought. Back in my student days I became aware of the Gesammelte Mathematische Werke of Dedekind, edited by Fricke, Noether, and Ore. I was impressed by the editors' notes that followed most of the papers and found them very usefuL A more direct model was furnished by the collected papers of Lars Ahlfors, in which the author himself supplied afterthoughts for each paper or group of papers. These were tough acts to follow, but I hope that some readers will find at least some of my afterthoughts interesting. Second, I was permitted to add eight previously unpublished items. My model here, to a certain extent, was the charming little book, A Mathematician's Miscel lany by J. E. Littlewood. In picking these eight I had quite a selection to make -from fourteen loose-leaf notebooks of such writings. Here again I hope that at least some will be found to be of interest.

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.

This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.

This book, based in part on lectures delivered at the 2006 CRM-Clay School on Additive Combinatorics, brings together some of the top researchers in one of the hottest topics in analysis today. This new subject brings together ideas from many different areas to prove some extraordinary results. The book encompasses proceedings from the school, articles on open questions in additive combinatorics, and new research.

This book highlights new and original contributions on Graph Theory and Combinatorial Optimization both from the theoretical point of view and from applications in all fields. The book chapters describe models and methods based on graphs, structural properties, discrete optimization, network optimization, mixed-integer programming, heuristics, meta-heuristics, math-heuristics, and exact methods as well as applications. The book collects selected contributions from the CTW2020 international conference (18th Cologne-Twente Workshop on Graphs and Combinatorial Optimization), held online on September 14-16, 2020. The conference was organized by IASI-CNR with the contribution of University of Roma Tre, University Roma Tor Vergata, and CNRS-LIX and with the support of AIRO. It is addressed to researchers, PhD students, and practitioners in the fields of Graph Theory, Discrete Mathematics, Combinatorial Optimization, and Operations Research.

From experimental design to cryptography, this comprehensive, easy-to-access reference contains literally all the facts you need on combinatorial designs. It includes constructions of designs, existence results, and properties of designs. Organized into six main parts, the CRC Handbook of Combinatorial Designs covers: