Introduction to combinatorics / / Martin J. Erickson

• Autore: Erickson Martin J. <1963->
• Pubblicazione: New York, New York : , : John Wiley & Sons, Inc., , 1996; ©1996
• Descrizione fisica: 1 online resource (210 p.)
• Disciplina: 511.6
• Soggetto topico: Combinatorial analysis
• Note generali: "A Wiley-Interscience Publication."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Introduction to Combinatorics; Contents; Notation; 1 Preliminaries: Set Theory, Algebra, and Number Theory; 1.1 Sets; 1.2 Relations and Functions; 1.3 Binomial Coefficients; 1.4 Group Theory; 1.5 Number Theory; 1.6 Fields; 1.7 Linear Algebra; Notes; Exercises; I Existence; 2 The Pigeonhole Principle; 2.1 Versions of the Pigeonhole Principle; 2.2 Graph Theory; 2.3 Extremal Graphs; 2.4 Colorings of the Plane; Notes; Exercises; 3 Sequences and Partial Orders; 3.1 The Erdös-Szekeres Theorem; 3.2 Dilworth's Lemma; 3.3 Sperner's Theorem; Notes; Exercises; 4 Ramsey Theory; 4.1 Ramsey's Theorem ; 4.2 Generalizations of Ramsey's Theorem4.3 Ramsey Numbers, Bounds, and Asymptotics; 4.4 The Probabilistic Method; 4.5 Schur's Lemma; 4.6 Van der Waerden's Theorem; Notes; Exercises; II Enumeration; 5 The Fundamental Counting Problem; 5.1 Labeled and Unlabeled Sets; 5.2 The Sixteen Cases; Notes; Exercises; 6 Recurrence Relations and Explicit Formulas; 6.1 The Inclusion-Exclusion Principle; 6.2 Stirling Numbers; 6.3 Linear Recurrence Relations; 6.4 Generating Functions; 6.5 Special Generating Functions; 6.6 Partition Numbers; Notes; Exercises; 7 Permutations and Tableaux ; 7.1 Algorithm: Listing Permutations7.2 Young Tableaux; 7.3 The Robinson-Schensted Correspondence; Notes; Exercises; 8 The Pólya Theory of Counting; 8.1 Burnside's Lemma; 8.2 Labelings; 8.3 Cycle Indexes; 8.4 Pólya's Theorem; 8.5 De Bruijn's Formula; Notes; Exercises; III Construction; 9 Codes; 9.1 The Geometry of GF(2)n; 9.2 Binary Codes; 9.3 Perfect Codes; 9.4 Hamming Codes; 9.5 The Fano Configuration; Notes; Exercises; 10 Designs; 10.1 t-Designs; 10.2 Block Designs; 10.3 Projective Planes; 10.4 Latin Squares; 10.5 MOLS and OODs; 10.6 Hadamard Matrices; Notes; Exercises; 11 Big Designs ; 11.1 The Golay Codes and S(5, 8, 24)11.2 Lattices and Sphere Packings; 11.3 Leech's Lattice; Notes; Exercises; Bibliography; Index
• Sommario/riassunto: This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice.Along the way, Professor Martin J. Erickson introduces fundamental resul
• Titolo autorizzato: Introduction to combinatorics
• ISBN: 1-283-33199-3; 9786613331991; 1-118-03264-0; 1-118-03089-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910141195303321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley series in discrete mathematics and optimization.