Sperner Theory [Hardcover]

Emphasises the powerful methods arising from the fusion of combinatorial techniques with programming, linear algebra, and probability theory.This book presents results on extremal problems in finite sets and finite partially ordered sets and several of their applications from a unified point of view. The emphasis is on the powerful methods arising from the fusion of combinatorial techniques with programming, linear algebra, eigenvalue methods, and probability theory. Complete proofs of the main theorems are included.The book will serve as a graduate text introducing important techniques in discrete mathematics and optimization and as a guide for researchers working in this area.This book presents results on extremal problems in finite sets and finite partially ordered sets and several of their applications from a unified point of view. The emphasis is on the powerful methods arising from the fusion of combinatorial techniques with programming, linear algebra, eigenvalue methods, and probability theory. Complete proofs of the main theorems are included.The book will serve as a graduate text introducing important techniques in discrete mathematics and optimization and as a guide for researchers working in this area.Sperner's theorem stimulated the development of a fast-growing theory dealing with external problems on finite sets and, more generally, on finite partially ordered sets. This book presents Sperner theory from a unified point of view, bringing combinatorial techniques together with methods from programming, linear algebra, Lie-algebra representations and eigenvalue methods, probability theory, and enumerative combinatorics.1. Introduction; 2. Extremal problems for finite sets; 3. Profile-polytopes; 4. The flow-theoretic approach; 5. Symmetric chain orders; 6. Algebraic methods in Sperner theory; 7. Limit theorems; 8. Macaulay posets.'The presentation is very good and the book should be understandable for a non-specialist.' European Mathematical Society