Combinatorics: The Rota Way
Combinatorics: The Rota Way
Gian-Carlo Rota
Catherine H. Yan , Texas A & M University
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Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. 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. A must-have for all students and researchers in combinatorics and related areas.
- 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 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
Product details
February 2009Paperback
9780521737944
408 pages
228 × 152 × 22 mm
0.55kg
3 b/w illus. 209 exercises
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.
