1997/01/28 by Konrad Engel · 1 citation
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Polynomial and algebraic computation #Markov Chains and Monte Carlo Methods #Mathematics #Number theory #Pairwise comparison #Eigenvalues and eigenvectors #Algebra over a field #Set (abstract data type) #Fixed-point theorem #Point (geometry) #Set theory #Probability theory #Finite set #Discrete mathematics #Combinatorics #Computer science #Pure mathematics
paper · doi:10.1017/cbo9780511574719
openalex publication_date 1997/01/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/05/28
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 (with respect to inclusion) subsets of a finite set? This 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. Researchers and graduate students in discrete mathematics, optimisation, algebra, probability theory, number theory, and geometry will find many powerful new methods arising from Sperner theory.