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  3. Sperner Theory
  • Cited by 101
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
1997
Online ISBN:
9780511574719
DOI:
https://doi.org/10.1017/CBO9780511574719
Subjects:
Mathematics (general), Mathematics, Logic, Categories and Sets, Algebra
Series:
Encyclopedia of Mathematics and its Applications (65)
Information

Book description

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.

Reviews

‘The presentation is very good and the book should be understandable for a non-specialist.’

Source: European Mathematical Society

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