Combinatorics: The Rota Way

Combinatorics: The Rota Way

by Joseph P. S. Kung, Gian-Carlo Rota, Catherine H. Yan
     
 

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ISBN-10: 052173794X

ISBN-13: 9780521737944

Pub. Date: 02/28/2009

Publisher: Cambridge University Press

Written by two of Gian-Carlo Rota's former students, this book is based on notes from his courses and on personal discussions with him. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory,

Overview

Written by two of Gian-Carlo Rota's former students, this book is based on notes from his courses and on personal discussions with him. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. This book should be on the shelf of all students and researchers in combinatorics and related areas.

Product Details

ISBN-13:
9780521737944
Publisher:
Cambridge University Press
Publication date:
02/28/2009
Series:
Cambridge Mathematical Library Series
Edition description:
New Edition
Pages:
408
Product dimensions:
6.00(w) x 8.90(h) x 1.00(d)

Table of Contents

1. Sets, functions, and relations; 2. Matching theory; 3. Partially ordered sets and lattices; 4. Generating functions and the umbral calculus; 5. Symmetric functions and Baxter algebras; 6. Determinants, matrices, and polynomials; 7. Selected solutions.

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