CONTENTS

PREFACE

PARTICIPANTS.

SCIENTIFIC PROGRAMME

PART I. STRUCTURE AND ARITHMETIC OF ORDERED SETS

Arithmetic of ordered sets
By B. Jonsson

Exponentiation and duality
By B.A. Davey and D. Duffus

The retract construction
By l. Rival
PART II.	LINEAR EXTENSIONS

Linear extensions of ordered sets
By R. Bonnet and M. Pouzet

Dimension theory for ordered sets
By D. Kelly and W.T. Trotter, Jr.

Linear extensions of partial orders and the FKG inequality
	By R.L. Graham	2
PART III.	SET THEORY AND RECURSION

Order types of real numbers and other uncountable orderings
	By J.E. Baumgartner	2

On the cofinality of partially ordered sets
	By E.C. Milner and M. Pouzet	2

Infinite ordered sets, a recursive perspective
	By G.F. McNulty	2
PART IV.	LATTICE THEORY

The role of order in lattice theory
	By R.P. Dilworth	3

Some order theoretic questions about free lattices and free modular lattices
By R. Freese
An	introduction to the theory of continuous lattices By M.W. Mislove

Ordered sets in geometry
		By G. Birkhoff	407
	(Appendix: A lattice characterization of affine
n—space, by M.K. Bennett.)

Restructuring lattice theory:	an approach based on
hierarchies of concepts
By R. Wille

PART V. ENUMERATION

Extremal problems in partially ordered sets
		By D.B. West	473
	Enumeration in classes of ordered structures
		By R.W. Quackenbush	523
	The Möbius function of a partially ordered set
		By C. Greene	555

An introduction to Cohen—Macaulay partially
ordered sets
		By A. Björner, A.M. Garsia, and R.P. Stanley	583

PART VI. APPLICATIONS OF ORDERED SETS TO COMPUTER SCIENCES

Ordered sets and linear programming
		By A.J. Hoffman	619
	Machine scheduling with precedence constraints
		By E.L. Lawler and J.K. Lenstra	655
	Some ordered sets in computer science
		By D.S. Scott	677

PART VII. APPLICATIONS OF ORDERED SETS TO SOCIAL SCIENCES

Ordered sets and social sciences
		By J.P. Barthélemy, Cl. Flament, and B. Monjardet	72]
	Some social science applications of ordered sets
		By. K.P. Bogart	759

PART VIII. PROBLEM SESSIONS

Introduction
		By B. Sands and R.E. Woodrow	791
	Order types		793
	Combinatorics		799

CONTENTS

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

PART IX. A BIBLIOGRAPHY

Introduction
By l. Rival