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Combinatorial enumeration problems --- 519.1 --- Combinatorics. Graph theory --- Combinatorial enumeration problems. --- 519.1 Combinatorics. Graph theory --- Enumeration problems, Combinatorial --- Combinatorial analysis

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I have been very gratified by the response to the first edition, which has resulted in it being sold out. This put some pressure on me to come out with a second edition and now, finally, here it is. The original text has stayed much the same, the major change being in the treatment of the hook formula which is now based on the beautiful Novelli-Pak-Stoyanovskii bijection (NPS 97]. I have also added a chapter on applications of the material from the first edition. This includes Stanley's theory of differential posets (Stn 88, Stn 90] and Fomin's related concept of growths (Fom 86, Fom 94, Fom 95], which extends some of the combinatorics of Sn-representations. Next come a couple of sections showing how groups acting on posets give rise to interesting representations that can be used to prove unimodality results (Stn 82]. Finally, we discuss Stanley's symmetric function analogue of the chromatic polynomial of a graph (Stn 95, Stn ta]. I would like to thank all the people, too numerous to mention, who pointed out typos in the first edition. My computer has been severely reprimanded for making them. Thanks also go to Christian Krattenthaler, Tom Roby, and Richard Stanley, all of whom read portions of the new material and gave me their comments. Finally, I would like to give my heartfelt thanks to my editor at Springer, Ina Lindemann, who has been very supportive and helpful through various difficult times.

Group theory --- Representations of groups --- Symmetric functions --- Représentations de groupes --- Fonctions symétriques --- Representations of groups. --- Symmetric functions. --- Représentations de groupes --- Fonctions symétriques --- Group theory. --- Combinatorics. --- Group Theory and Generalizations. --- Combinatorics --- Algebra --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics)

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Foliations is one of the major concepts of modern geometry and topology meaning a partition of topological space into a disjoint sum of leaves. This book is devoted to geometry and topology of surface foliations and their links to ergodic theory, dynamical systems, complex analysis, differential and noncommutative geometry. This comprehensive book addresses graduate students and researchers and will serve as a reference book for experts in the field.

Differential geometry. Global analysis --- Menigvuldigheden (Wiskunde) --- Varietes (Mathematiques) --- Foliations (Mathematics) --- Manifolds (Mathematics). --- Complex manifolds. --- Global analysis (Mathematics). --- Combinatorics. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Global Analysis and Analysis on Manifolds. --- Combinatorics --- Algebra --- Mathematical analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology

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Discrete mathematics --- Graph theory --- Théorie des graphes --- 519.1 --- 681.3*G22 --- Combinatorics. Graph theory --- Graph theory: graph algorithms; network problems; path and tree problems; trees--See also {681.3*F22} --- Graph theory. --- 681.3*G22 Graph theory: graph algorithms; network problems; path and tree problems; trees--See also {681.3*F22} --- 519.1 Combinatorics. Graph theory --- Théorie des graphes --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Extremal problems

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The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erdös, who himself suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background. For this revised and expanded second edition several chapters have been revised and expanded, and three new chapters have been added.

Mathematics --- Mathematics. --- Hypothesen --- Plannen --- Wiskundige bewijzen --- Wiskundige formules --- Formuleverzamelingen - Tafels en tabellen --- Math --- Science --- 510.6 --- Geometrie --- Getaltheorie --- Wiskunde --- Mathématiques --- Mathématiques. --- Erdős, Pál --- Erdős, Paul, --- Number theory. --- Geometry. --- Mathematical analysis. --- Analysis (Mathematics). --- Combinatorics. --- Computer science. --- Number Theory. --- Analysis. --- Computer Science, general. --- Informatics --- Combinatorics --- Algebra --- Mathematical analysis --- 517.1 Mathematical analysis --- Euclid's Elements --- Number study --- Numbers, Theory of --- Mathématiques. --- Erdős, Pál