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Introduction to Combinatorics
Introduction to Combinatorics
Autore Erickson Martin J
Edizione [2nd ed.]
Pubbl/distr/stampa Somerset : , : John Wiley & Sons, Incorporated, , 2013
Descrizione fisica 1 online resource (246 pages)
Disciplina 511.6
Collana Wiley Series in Discrete Mathematics and Optimization Ser.
Soggetto topico Combinatorial analysis
Soggetto genere / forma Electronic books.
ISBN 9781118637586
9781118637531
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Cover -- Title Page -- Copyright Page -- CONTENTS -- Preface -- 1 Basic Counting Methods -- 1.1 The multiplication principle -- 1.2 Permutations -- 1.3 Combinations -- 1.4 Binomial coefficient identities -- 1.5 Distributions -- 1.6 The principle of inclusion and exclusion -- 1.7 Fibonacci numbers -- 1.8 Linear recurrence relations -- 1.9 Special recurrence relations -- 1.10 Counting and number theory -- Notes -- 2 Generating Functions -- 2.1 Rational generating functions -- 2.2 Special generating functions -- 2.3 Partition numbers -- 2.4 Labeled and unlabeled sets -- 2.5 Counting with symmetry -- 2.6 Cycle indexes -- 2.7 Pólya's theorem -- 2.8 The number of graphs -- 2.9 Symmetries in domain and range -- 2.10 Asymmetric graphs -- Notes -- 3 The Pigeonhole Principle -- 3.1 The principle -- 3.2 The lattice point problem and SET® -- 3.3 Graphs -- 3.4 Colorings of the plane -- 3.5 Sequences and partial orders -- 3.6 Subsets -- Notes -- 4 Ramsey Theory -- 4.1 Ramsey's theorem -- 4.2 Generalizations of Ramsey's theorem -- 4.3 Ramsey numbers, bounds, and asymptotics -- 4.4 The probabilistic method -- 4.5 Schur's theorem -- 4.6 Van der Waerden's theorem -- Notes -- 5 Error-Correcting Codes -- 5.1 Binary codes -- 5.2 Perfect codes -- 5.3 Hamming codes -- 5.4 The Fano Configuration -- Notes -- 6 Combinatorial Designs -- 6.1 t-designs -- 6.2 Block designs -- 6.3 Projective planes -- 6.4 Latin squares -- 6.5 MOLS and OODs -- 6.6 Hadamard matrices -- 6.7 The Golay code and S(5,8,24) -- 6.8 Lattices and sphere packings -- 6.9 Leech's lattice -- Notes -- A Web Resources -- B Notation -- Exercise Solutions -- References -- Index.
Record Nr. UNINA-9910795811503321
Erickson Martin J  
Somerset : , : John Wiley & Sons, Incorporated, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Introduction to Combinatorics
Introduction to Combinatorics
Autore Erickson Martin J
Edizione [2nd ed.]
Pubbl/distr/stampa Somerset : , : John Wiley & Sons, Incorporated, , 2013
Descrizione fisica 1 online resource (246 pages)
Disciplina 511.6
Collana Wiley Series in Discrete Mathematics and Optimization Ser.
Soggetto topico Combinatorial analysis
Soggetto genere / forma Electronic books.
ISBN 9781118637586
9781118637531
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Cover -- Title Page -- Copyright Page -- CONTENTS -- Preface -- 1 Basic Counting Methods -- 1.1 The multiplication principle -- 1.2 Permutations -- 1.3 Combinations -- 1.4 Binomial coefficient identities -- 1.5 Distributions -- 1.6 The principle of inclusion and exclusion -- 1.7 Fibonacci numbers -- 1.8 Linear recurrence relations -- 1.9 Special recurrence relations -- 1.10 Counting and number theory -- Notes -- 2 Generating Functions -- 2.1 Rational generating functions -- 2.2 Special generating functions -- 2.3 Partition numbers -- 2.4 Labeled and unlabeled sets -- 2.5 Counting with symmetry -- 2.6 Cycle indexes -- 2.7 Pólya's theorem -- 2.8 The number of graphs -- 2.9 Symmetries in domain and range -- 2.10 Asymmetric graphs -- Notes -- 3 The Pigeonhole Principle -- 3.1 The principle -- 3.2 The lattice point problem and SET® -- 3.3 Graphs -- 3.4 Colorings of the plane -- 3.5 Sequences and partial orders -- 3.6 Subsets -- Notes -- 4 Ramsey Theory -- 4.1 Ramsey's theorem -- 4.2 Generalizations of Ramsey's theorem -- 4.3 Ramsey numbers, bounds, and asymptotics -- 4.4 The probabilistic method -- 4.5 Schur's theorem -- 4.6 Van der Waerden's theorem -- Notes -- 5 Error-Correcting Codes -- 5.1 Binary codes -- 5.2 Perfect codes -- 5.3 Hamming codes -- 5.4 The Fano Configuration -- Notes -- 6 Combinatorial Designs -- 6.1 t-designs -- 6.2 Block designs -- 6.3 Projective planes -- 6.4 Latin squares -- 6.5 MOLS and OODs -- 6.6 Hadamard matrices -- 6.7 The Golay code and S(5,8,24) -- 6.8 Lattices and sphere packings -- 6.9 Leech's lattice -- Notes -- A Web Resources -- B Notation -- Exercise Solutions -- References -- Index.
Record Nr. UNINA-9910822070303321
Erickson Martin J  
Somerset : , : John Wiley & Sons, Incorporated, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui