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＜電子ブック＞
Ramsey Theory : Yesterday, Today, and Tomorrow / edited by Alexander Soifer
(Progress in Mathematics. ISSN:2296505X ; 285)

版	1st ed. 2011.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2011
本文言語	英語
大きさ	XIV, 190 p. 28 illus : online resource
著者標目	Soifer, Alexander editor SpringerLink (Online service)
件　名	LCSH:Discrete mathematics LCSH:Dynamical systems LCSH:Convex geometry  LCSH:Discrete geometry FREE:Discrete Mathematics FREE:Dynamical Systems FREE:Convex and Discrete Geometry
一般注記	How This Book Came into Being -- Table of Contents -- Ramsey Theory before Ramsey, Prehistory and Early History: An Essay in 13 Parts -- Eighty Years of Ramsey R(3, k). . . and Counting! -- Ramsey Numbers Involving Cycles -- On the function of Erdὅs and Rogers -- Large Monochromatic Components in Edge Colorings of Graphs -- Szlam’s Lemma: Mutant Offspring of a Euclidean Ramsey Problem: From 1973, with Numerous Applications -- Open Problems in Euclidean Ramsey Theory -- Chromatic Number of the Plane and Its Relatives, History, Problems and Results: An Essay in 11 Parts -- Euclidean Distance Graphs on the Rational Points -- Open Problems Session Ramsey theory is a relatively “new,” approximately 100 year-old direction of fascinating mathematical thought that touches on many classic fields of mathematics such as combinatorics, number theory, geometry, ergodic theory, topology, combinatorial geometry, set theory, and measure theory. Ramsey theory possesses its own unifying ideas, and some of its results are among the most beautiful theorems of mathematics. The underlying theme of Ramsey theory can be formulated as: any finite coloring of a large enough system contains a monochromatic subsystem of higher degree of organization than the system itself, or as T.S. Motzkin famously put it, absolute disorder is impossible. Ramsey Theory: Yesterday, Today, and Tomorrow explores the theory’s history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike. Contributors: J. Burkert, A. Dudek, R.L. Graham, A. Gyárfás, P.D. Johnson, Jr., S.P. Radziszowski, V. Rödl, J.H. Spencer, A. Soifer, E. Tressler HTTP:URL=https://doi.org/10.1007/978-0-8176-8092-3

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