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.
Les mer
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.
Les mer
'All in all … I find Combinatorics: The Rota Way simply too good to pass up. Would that every day had 48 hours...' MAA Reviews
Compiled and edited by two of Gian-Carlo Rota's students, this book is based on notes from his influential combinatorics courses.
Produktdetaljer
ISBN
9780521883894
Publisert
2009-02-09
Utgiver
Vendor
Cambridge University Press
Vekt
650 gr
Høyde
235 mm
Bredde
157 mm
Dybde
25 mm
Aldersnivå
UU, 05
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
408