General informations


The starting point of this book is Sperner's theorem, which answers the question: What is the maximum possible size of a family of pairwise un- related (with respect to inclusion) subsets of a finite set? This theorem stimulated the development of a fast growing theory dealing with extremal 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 (e.g. flow theory and polyhedral combinatorics), from linear algebra (e.g. Jordan decompositions, Lie algebra representations, and eigenvalue methods), from probability theory (e.g. limit theorems), and from enumerative combinatorics (e.g. Möbius inversion). Studying Sperner theory means learning many important techniques in discrete mathematics and combinatorial optimization on a particular theme.


Prof. Dr. Konrad Engel, 15.05.97 (

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