Combinatorial methods with computer applications
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall / CRC Press
2008
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| Schriftenreihe: | Discrete mathematics and its applications
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall / CRC Press |c 2008 | |
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| 490 | 0 | |a Discrete mathematics and its applications | |
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Datensatz im Suchindex
| _version_ | 1819646330884063232 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Gross, Jonathan L. 1941- |
| author_GND | (DE-588)124283926 |
| author_facet | Gross, Jonathan L. 1941- |
| author_role | aut |
| author_sort | Gross, Jonathan L. 1941- |
| author_variant | j l g jl jlg |
| building | Verbundindex |
| bvnumber | BV023324314 |
| callnumber-first | Q - Science |
| callnumber-label | QA164 |
| callnumber-raw | QA164 |
| callnumber-search | QA164 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 170 SK 890 |
| ctrlnum | (OCoLC)163605025 (DE-599)BVBBV023324314 |
| dewey-full | 511/.60285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.60285 |
| dewey-search | 511/.60285 |
| dewey-sort | 3511 560285 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV023324314 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T21:01:21Z |
| institution | BVB |
| isbn | 9781584887430 1584887435 |
| language | English |
| lccn | 2007032273 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016508357 |
| oclc_num | 163605025 |
| open_access_boolean | |
| owner | DE-20 |
| owner_facet | DE-20 |
| physical | XVII, 644 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Chapman & Hall / CRC Press |
| record_format | marc |
| series2 | Discrete mathematics and its applications |
| 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_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 |
| url | 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 |
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