Combinatorics: The Rota Way
Part of Cambridge Mathematical Library
- Authors:
- Joseph P. S. Kung, University of North Texas
- Gian-Carlo Rota
- Catherine H. Yan, Texas A & M University
- Date Published: February 2009
- availability: Available
- format: Paperback
- isbn: 9780521737944
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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.
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
'All in all … I find Combinatorics: The Rota Way simply too good to pass up. Would that every day had 48 hours...' MAA Reviews
See more reviews'… each of its chapters can be considered as a single expository work, conceived by Rota and masterfully moulded and improved by Kung and Yan.' Mathematical Reviews
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×Product details
- 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.Instructors have used or reviewed this title for the following courses
- Combinatorics
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