Combinatorics: The Rota Way (Cambridge Mathematical Library) by Joseph P. S. Kung (PDF)

Description

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.

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Reviews from Amazon users which were colected at the time this book was published on the website:

⭐If you want to come to understand combinatorics form the higher point of view, this is your book. If you want the nitty-gritty, hands-on version, read Richard guy and Bud Brown’s Unity of Combinatorics.WAIT, why chose? read them both!

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