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.
Although the recorder is often the instrument with which children will make their first musical discoveries, it is also an instrument of the highest artistic merit. This series links these two extreme
(Schott). Although the recorder is often the instrument with which children will make their first musical discoveries, it is also an instrument of the highest artistic merit. This series links these t
Although the recorder is often the instrument with which children will make their first musical discoveries, it is also an instrument of the highest artistic merit. This series links these two extreme
Although the recorder is often the instrument with which children will make their first musical discoveries, it is also an instrument of the highest artistic merit. This series links these two extreme
(Schott). Although the recorder is often the instrument with which children will make their first musical discoveries, it is also an instrument of the highest artistic merit. This series links these t
(Schott). Although the recorder is often the instrument with which children will make their first musical discoveries, it is also an instrument of the highest artistic merit. This series links these t
(Schott). Although the recorder is often the instrument with which children will make their first musical discoveries, it is also an instrument of the highest artistic merit. This series links these t
