Ordered sets : proceedings of the NATO Advanced Study Institute held at Banff, Canada, August 28 to September 12, 1981
Author(s)
Bibliographic Information
Ordered sets : proceedings of the NATO Advanced Study Institute held at Banff, Canada, August 28 to September 12, 1981
(NATO advanced study institutes series, ser. C . Mathematical and physical sciences ; v. 83)
D. Reidel Pub. Co. , Sold and distributed in the U.S.A. and Canada by Kluwer Boston, c1982
Available at 30 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Bibliography: p. 865-966
Description and Table of Contents
Description
This volume contains all twenty-three of the principal survey papers presented at the Symposium on Ordered Sets held at Banff, Canada from August 28 to September 12, 1981. The Symposium was supported by grants from the NATO Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada, the Canadian Mathematical Society Summer Research Institute programme, and the University of Calgary. tve are very grateful to these Organizations for their considerable interest and support. Over forty years ago on April 15, 1938 the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. in conjunction with a meeting of the American Mathematical Society. The principal addresses on that occasion were Lattices and their applications by G. Birkhoff, On the application of structure theory to groups by O. Ore, and The representation of Boolean algebras by M. H. Stone. The texts of these addresses and three others by R. Baer, H. M. MacNeille, and K. Menger appear in the Bulletin of the American Mathematical Society, Volume 44, 1938. In those days the theory of ordered sets, and especially lattice theory was described as a "vigorous and promising younger brother of group theory." Some early workers hoped that lattice theoretic methods would lead to solutions of important problems in group theory.
Table of Contents
I. Structure and Arithmetic of Ordered Sets.- Arithmetic of ordered sets.- Exponentiation and duality.- The retract construction.- II. Linear Extensions.- Linear extensions of ordered sets.- Dimension theory for ordered sets.- Linear extensions of partial orders and the FKG inequality.- III. Set Theory and Recursion.- Order types of real numbers and other uncountable orderings.- On the cofinality of partially ordered sets.- Infinite ordered sets, a recursive perspective.- IV. Lattice Theory.- The role of order in lattice theory.- Some order theoretic questions about free lattices and free modular lattices.- An introduction to the theory of continuous lattices.- Ordered sets in geometry.- (Appendix: A lattice characterization of affine n-space).- Restructuring lattice theory: an approach based on hierarchies of concepts.- V. Enumeration.- Extremal problems in partially ordered sets.- Enumeration in classes of ordered structures.- The Moebius function of a partially ordered set.- An introduction to Cohen-Macaulay partially ordered sets.- VI. Applications of Ordered Sets to Computer Sciences.- Ordered sets and linear programming.- Machine scheduling with precedence constraints.- Some ordered sets in computer science.- VII. Applications of Ordered Sets to Social Sciences.- Ordered sets and social sciences.- Some social science applications of ordered sets.- VIII. Problem Sessions.- Order types.- Combinatorics.- Linear extensions of finite ordered sets.- Scheduling and sorting.- Graphs and enumeration.- Social science and operations research.- Recursion and game theory.- Order-preserving maps.- Lattices.- Miscellaneous.- IX. A Bibliography.
by "Nielsen BookData"