Verfügbarkeit: Combinatorial methods with computer applications

Combinatorial methods with computer applications:

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Bibliographische Detailangaben
1. Verfasser:	Gross, Jonathan L. 1941- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Boca Raton [u.a.] Chapman & Hall / CRC Press 2008
Schriftenreihe:	Discrete mathematics and its applications
Schlagworte:	Datenverarbeitung Combinatorial analysis > Data processing Kombinatorische Analysis
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references and index
Beschreibung:	XVII, 644 S. Ill., graph. Darst.
ISBN:	9781584887430 1584887435

Internformat

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Datensatz im Suchindex

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adam_text	DISCRETE MATHEMATICS AND ITS APPLICATIONS SERIES EDITOR KENNETH H. ROSEN COMBINATORIAL METHODS WITH COMPUTER APPLICATIONS JONATHAN L. GROSS COLUMBIA UNIVERSITY NEW YORK, U.S.A ^LLCHAPMAN & HALL/CRC M * TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CHAPMAN & HALL/CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS PREFACE XIII AUTHOR XVII 0. INTRODUCTION TO COMBINATORICS 1 0.1 OBJECTIVES OF COMBINATORICS 2 0.2 ORDERING AND SELECTION 6 0.3 SOME RULES FOR COUNTING 9 0.4 COUNTING SELECTIONS 18 0.5 PERMUTATIONS 26 0.6 GRAPHS 35 0.7 NUMBER-THEORETIC OPERATIONS 43 0.8 COMBINATORIAL DESIGNS 44 GLOSSARY 46 1. SEQUENCES 49 1.1 SEQUENCES AS LISTS 50 1.2 RECURRENCES 56 1.3 PASCAL S RECURRENCE 63 1.4 DIFFERENCES AND PARTIAL SUMS 67 1.5 FALLING POWERS 74 1.6 STIRLING NUMBERS: A PREVIEW 79 1.7 ORDINARY GENERATING FUNCTIONS 85 1.8 SYNTHESIZING GENERATING FUNCTIONS 97 1.9 ASYMPTOTIC ESTIMATES 102 GLOSSARY 106 2. SOLVING RECURRENCES 111 2.1 TYPES OF RECURRENCES 112 2.2 FINDING GENERATING FUNCTIONS 116 2.3 PARTIAL FRACTIONS 121 2.4 CHARACTERISTIC ROOTS 123 2.5 SIMULTANEOUS RECURSIONS 131 2.6 FIBONACCI NUMBER IDENTITIES 138 2.7 NON-CONSTANT COEFFICIENTS 142 2.8 DIVIDE-AND-CONQUER RELATIONS 148 GLOSSARY 159 3. EVALUATING SUMS 161 3.1 NORMALIZING SUMMATIONS 162 3.2 PERTURBATION 169 3.3 SUMMING WITH GENERATING FUNCTIONS 175 3.4 FINITE CALCULUS 180 3.5 ITERATION AND PARTITIONING OF SUMS 191 3.6 INCLUSION-EXCLUSION 199 GLOSSARY 215 IX CONTENTS BINOMIAL COEFFICIENTS 217 4.1 BINOMIAL COEFFICIENT IDENTITIES 218 4.2 BINOMIAL INVERSION OPERATION 232 4.3 APPLICATIONS TO STATISTICS 239 4.4 THE CATALAN RECURRENCE 247 GLOSSARY 256 PARTITIONS AND PERMUTATIONS 259 5.1 STIRLING SUBSET NUMBERS 260 5.2 STIRLING CYCLE NUMBERS 275 5.3 INVERSIONS AND ASCENTS 288 5.4 DERANGEMENTS 293 5.5 EXPONENTIAL GENERATING FUNCTIONS 296 5.6 POSETS AND LATTICES 305 GLOSSARY 321 INTEGER OPERATORS 325 6.1 EUCLIDEAN ALGORITHM 326 6.2 CHINESE REMAINDER THEOREM 335 6.3 POLYNOMIAL DIVISIBILITY 342 6.4 PRIME AND COMPOSITE MODULI 346 6.5 EULER PHI-FUNCTION 356 6.6 THE MOEBIUS FUNCTION 362 GLOSSARY 369 GRAPH FUNDAMENTALS 371 7.1 REGULAER GRAPHS 372 7.2 WALKS AND DISTANCE 379 7.3 TREES AND ACYCLIC DIGRAPHS 384 7.4 GRAPH ISOMORPHISM 392 7.5 GRAPH AUTOMORPHISM 399 7.6 SUBGRAPHS 404 7.7 SPANNING TREES 408 7.8 EDGE WEIGHTS 413 7.9 GRAPH OPERATIONS 418 GLOSSARY 426 GRAPH THEORY TOPICS 431 8.1 TRAVERSABILITY 432 8.2 PLANARITY 440 8.3 COLORING 448 8.4 ANALYTIC GRAPH THEORY 456 8.5 DIGRAPH MODELS 463 8.6 NETWORK FLOWS 469 8.7 TOPOLOGICAL GRAPH THEORY 476 GLOSSARY 485 CONTENTS XI 9. GRAPH ENUMERATION 489 9.1 BURNSIDE-POLYA COUNTING 490 9.2 BURNSIDE S LEMMA 503 9.3 COUNTING SMALL SIMPLE GRAPHS 514 9.4 PARTITIONS OF INTEGERS 522 9.5 CALCULATING A CYCLE INDEX 527 9.6 GENERAL GRAPHS AND DIGRAPHS 534 GLOSSARY 538 10. COMBINATORIAL DESIGNS 541 10.1 LATIN SQUARES 542 10.2 BLOCK DESIGNS 551 10.3 CLASSICAL FINITE GEOMETRIES 560 10.4 PROJECTIVE PLANES 565 10.5 AFFINE PLANES 571 GLOSSARY 577 APPENDIX 581 AI RELATIONS AND FUNCTIONS 581 A2 ALGEBRAIC SYSTEMS 584 A3 FINITE FIELDS AND VECTOR SPACES 590 BIBLIOGRAPHY 595 BL GENERAL READING 595 B2 REFERENCES 599 SOLUTIONS AND HINTS 603 INDEXES 629 11 INDEX OF NOTATIONS 629 12 GENERAL INDEX 635 S
adam_txt	DISCRETE MATHEMATICS AND ITS APPLICATIONS SERIES EDITOR KENNETH H. ROSEN COMBINATORIAL METHODS WITH COMPUTER APPLICATIONS JONATHAN L. GROSS COLUMBIA UNIVERSITY NEW YORK, U.S.A ^LLCHAPMAN & HALL/CRC M * TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CHAPMAN & HALL/CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS PREFACE XIII AUTHOR XVII 0. INTRODUCTION TO COMBINATORICS 1 0.1 OBJECTIVES OF COMBINATORICS 2 0.2 ORDERING AND SELECTION 6 0.3 SOME RULES FOR COUNTING 9 0.4 COUNTING SELECTIONS 18 0.5 PERMUTATIONS 26 0.6 GRAPHS 35 0.7 NUMBER-THEORETIC OPERATIONS 43 0.8 COMBINATORIAL DESIGNS 44 GLOSSARY 46 1. SEQUENCES 49 1.1 SEQUENCES AS LISTS 50 1.2 RECURRENCES 56 1.3 PASCAL'S RECURRENCE 63 1.4 DIFFERENCES AND PARTIAL SUMS 67 1.5 FALLING POWERS 74 1.6 STIRLING NUMBERS: A PREVIEW 79 1.7 ORDINARY GENERATING FUNCTIONS 85 1.8 SYNTHESIZING GENERATING FUNCTIONS 97 1.9 ASYMPTOTIC ESTIMATES 102 GLOSSARY 106 2. SOLVING RECURRENCES 111 2.1 TYPES OF RECURRENCES 112 2.2 FINDING GENERATING FUNCTIONS 116 2.3 PARTIAL FRACTIONS 121 2.4 CHARACTERISTIC ROOTS 123 2.5 SIMULTANEOUS RECURSIONS 131 2.6 FIBONACCI NUMBER IDENTITIES 138 2.7 NON-CONSTANT COEFFICIENTS 142 2.8 DIVIDE-AND-CONQUER RELATIONS 148 GLOSSARY 159 3. EVALUATING SUMS 161 3.1 NORMALIZING SUMMATIONS 162 3.2 PERTURBATION 169 3.3 SUMMING WITH GENERATING FUNCTIONS 175 3.4 FINITE CALCULUS 180 3.5 ITERATION AND PARTITIONING OF SUMS 191 3.6 INCLUSION-EXCLUSION 199 GLOSSARY 215 IX CONTENTS BINOMIAL COEFFICIENTS 217 4.1 BINOMIAL COEFFICIENT IDENTITIES 218 4.2 BINOMIAL INVERSION OPERATION 232 4.3 APPLICATIONS TO STATISTICS 239 4.4 THE CATALAN RECURRENCE 247 GLOSSARY 256 PARTITIONS AND PERMUTATIONS 259 5.1 STIRLING SUBSET NUMBERS 260 5.2 STIRLING CYCLE NUMBERS 275 5.3 INVERSIONS AND ASCENTS 288 5.4 DERANGEMENTS 293 5.5 EXPONENTIAL GENERATING FUNCTIONS 296 5.6 POSETS AND LATTICES 305 GLOSSARY 321 INTEGER OPERATORS 325 6.1 EUCLIDEAN ALGORITHM 326 6.2 CHINESE REMAINDER THEOREM 335 6.3 POLYNOMIAL DIVISIBILITY 342 6.4 PRIME AND COMPOSITE MODULI 346 6.5 EULER PHI-FUNCTION 356 6.6 THE MOEBIUS FUNCTION 362 GLOSSARY 369 GRAPH FUNDAMENTALS 371 7.1 REGULAER GRAPHS 372 7.2 WALKS AND DISTANCE 379 7.3 TREES AND ACYCLIC DIGRAPHS 384 7.4 GRAPH ISOMORPHISM 392 7.5 GRAPH AUTOMORPHISM 399 7.6 SUBGRAPHS 404 7.7 SPANNING TREES 408 7.8 EDGE WEIGHTS 413 7.9 GRAPH OPERATIONS 418 GLOSSARY 426 GRAPH THEORY TOPICS 431 8.1 TRAVERSABILITY 432 8.2 PLANARITY 440 8.3 COLORING 448 8.4 ANALYTIC GRAPH THEORY 456 8.5 DIGRAPH MODELS 463 8.6 NETWORK FLOWS 469 8.7 TOPOLOGICAL GRAPH THEORY 476 GLOSSARY 485 CONTENTS XI 9. GRAPH ENUMERATION 489 9.1 BURNSIDE-POLYA COUNTING 490 9.2 BURNSIDE'S LEMMA 503 9.3 COUNTING SMALL SIMPLE GRAPHS 514 9.4 PARTITIONS OF INTEGERS 522 9.5 CALCULATING A CYCLE INDEX 527 9.6 GENERAL GRAPHS AND DIGRAPHS 534 GLOSSARY 538 10. COMBINATORIAL DESIGNS 541 10.1 LATIN SQUARES 542 10.2 BLOCK DESIGNS 551 10.3 CLASSICAL FINITE GEOMETRIES 560 10.4 PROJECTIVE PLANES 565 10.5 AFFINE PLANES 571 GLOSSARY 577 APPENDIX 581 AI RELATIONS AND FUNCTIONS 581 A2 ALGEBRAIC SYSTEMS 584 A3 FINITE FIELDS AND VECTOR SPACES 590 BIBLIOGRAPHY 595 BL GENERAL READING 595 B2 REFERENCES 599 SOLUTIONS AND HINTS 603 INDEXES 629 11 INDEX OF NOTATIONS 629 12 GENERAL INDEX 635 S
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spelling	Gross, Jonathan L. 1941- Verfasser (DE-588)124283926 aut Combinatorial methods with computer applications Jonathan L. Gross Boca Raton [u.a.] Chapman & Hall / CRC Press 2008 XVII, 644 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications Includes bibliographical references and index Datenverarbeitung Combinatorial analysis Data processing Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 s Datenverarbeitung (DE-588)4011152-0 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016508357&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Gross, Jonathan L. 1941- Combinatorial methods with computer applications Datenverarbeitung Combinatorial analysis Data processing Datenverarbeitung (DE-588)4011152-0 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd
subject_GND	(DE-588)4011152-0 (DE-588)4164746-4
title	Combinatorial methods with computer applications
title_auth	Combinatorial methods with computer applications
title_exact_search	Combinatorial methods with computer applications
title_exact_search_txtP	Combinatorial methods with computer applications
title_full	Combinatorial methods with computer applications Jonathan L. Gross
title_fullStr	Combinatorial methods with computer applications Jonathan L. Gross
title_full_unstemmed	Combinatorial methods with computer applications Jonathan L. Gross
title_short	Combinatorial methods with computer applications
title_sort	combinatorial methods with computer applications
topic	Datenverarbeitung Combinatorial analysis Data processing Datenverarbeitung (DE-588)4011152-0 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd
topic_facet	Datenverarbeitung Combinatorial analysis Data processing Kombinatorische Analysis
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