Classic Papers in Combinatorics

by Gessel, Ira; Rota, Gian-Carlo

• ISBN13: 9780817648411
• ISBN10: 0817648410
• Edition: Reprint
• Format: Paperback
• Copyright: 2008-12-30
• Publisher: Birkhauser

Summary

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.

Table of Contents

Introduction.- On a Problem of Formal Logic.- Non-separable and Planar Graphs.- A Combinatorial Problem in Geometry.- On Representatives of Subsets.- On the Abstract Properties of Linear Dependence.- The Dissection of Rectangles into Squares.- On Colouring the Nodes of a Network.- Solution of the 'œProblème des Ménages'.- A Ring in Graph Theory.- A Decomposition Theorem for Partially Ordered Sets.- The Marriage Problem.- Circuits and Trees in Oriented Linear Graphs.- The Factors of Graphs.- A Partition Calculus in Set Theory.- Maximal Flow through a Network.- On Picture-writing.- A Theorem on Flows in Networks.- Combinatorial Problems in Matrices of Zeros and Ones.- Graph Theory and Probability.- The Statistics of Dimers on a Lattice: I. The Number of Dimer Arrangements on a Quadratic Lattice.- Longest Increasing and Decreasing Subsequences.- On a Theorem of R. Jungen.- Regularity and Positional Games.- On Well-Quasi-Ordering Finite Trees.- On the Foundations of Combinatorial Theory: I. Theory of Möbius Functions.- Paths, Trees, and Flowers.- A Theorem of Finite Sets.- A Short Proof of Sperner's Lemma.- Möbius Inversion on Lattices.- A Generalization of a Combinatorial Theorem of Macaulay.- Short Proof of a Conjecture by Dyson.- On a Lemma of Littlewood and Oxford on the Distributions of Linear Combinations of Vectors.- Ramsey's Theory for a Class of Categories.- A Characterizations of Perfect Graphs.- A Note on the Line Reconstruction Problem.- Acyclic Orientation of Graphs.- Valuations of Distributive Lattices I.-Valuations of Distributive Lattices II.- Valuations of Distributive Lattices III.- Permissions.-Index.