Overview
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.
Full Product Details
Author: Joseph P. S. Kung (University of North Texas) ,
Gian-Carlo Rota ,
Catherine H. Yan (Texas A & M University)
Publisher: Cambridge University Press
Imprint: Cambridge University Press (Virtual Publishing)
ISBN: 9780511803895
ISBN 10: 0511803893
Publication Date: 05 June 2012
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Undefined
Publisher's Status: Active
Availability: Available To Order
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Reviews
'All in all ... I find Combinatorics: The Rota Way simply too good to pass up. Would that every day had 48 hours...' MAA 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
'All in all … I find Combinatorics: The Rota Way simply too good to pass up. Would that every day had 48 hours...' MAA 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
Author Information
Dr Joseph P. S. Kung is Professor of Mathematics at the University of North Texas. He is currently an editor-in-chief for the journal Advances in Applied Mathematics. Gian-Carlo Rota (1932–1999) was a Professor of Applied Mathematics and Natural Philosophy at the Massachusetts Institute of Technology. He was a member of the National Academy of Science. He was awarded the 1988 Steele Prize of the American Mathematical Society for his 1964 paper 'On the Foundations of Combinatorial Theory I. Theory of Moebius Functions.' He was the founding editor of the Journal of Combinatorial Theory. Catherine H. Yan is a Professor of Mathematics at Texas A & M University. She was a Courant Instructor at New York University (1997–1999) and a Sloan Fellow (2001–2003).
