Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.
This book presents what seems to be the most significant work on hypergraphs.
Written by two of the leading researchers in the subject, this book is aimed at mathematically mature undergraduates, and highlights the elegance and power of this field of study.
This book begins with an elementary combinatorial approach to finite geometries based on finite sets of points and lines, and moves into the classical work on affine and projective planes.
Intended for graduate students, instructors teaching extremal combinatorics and researchers, this book serves as a sound introduction to the theory of extremal set systems.
This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.
The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be.
Table 10.2 The points and lines under the automorphism φ2 p φ2(p) L A B L1 B D L2 C F L3 D C L4 E A L5 F G L6 G E L7 φ2(L) L7 L4 L6 L3 L1 L5 L2 Table 10.3 The points and lines under the automorphism ψ1 p ψ 1 (p) L A A L1 B D C E ψ1 (L) ...
-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.
The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures.
This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory.