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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.Read more
- Emphasizes unifying ideas in combinatorics
- Shows connections with other areas of mathematics
- Gives elementary accounts of topics like entropy, linear lattices, umbral calculus, and Baxter algebras, not available elsewhere in book form
Reviews & endorsements
"...simply too good to pass up."
Michael Berg, MAA ReviewsSee more reviews
"...stimulating, valuable book..."
D.V. Chopra, Choice Magazine
"Students and researchers of combinatorics, as well as logicians and computer scientists, should keep a copy on their bookshelves."
Walter Carnielli, reviews.com
"A mathematician or computer scientist wanting to learn more about the science of combinatorics will find a good read here. The content is well written, very accurate and well edited."
John Mount, SIGACT News
"This book represents a valuable contribution to combinatorics in general, and I think that it could be useful to all researchers dealing with matters of this kind, especially younger ones, who intend to spend much of their future efforts on problems of a combinatorial nature."
Luca Ferrari, Mathematical Reviews
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- Date Published: February 2009
- format: Paperback
- isbn: 9780521737944
- length: 408 pages
- dimensions: 228 x 152 x 22 mm
- weight: 0.55kg
- contains: 3 b/w illus. 209 exercises
- availability: Available
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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