Combinatorics: The Rota Way

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.

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 is the founding editor of 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).

'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