Combinatorics of permutations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2004
|
| Schriftenreihe: | Discrete mathematics and its applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 383 S. graph. Darst. |
| ISBN: | 1584884347 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | DISCRETE MATHEMATICS AND ITS APPLICATIONS SERIES EDITOR KENNETH H. ROSEN
COMBINATORICS OF PERMUTATIONS MIKLOS BONA CHAPMAN & HALL/CRC A CRC PRESS
COMPANY BOCA RATON LONDON NEW YORK WASHINGTON, D.C. CONTENTS NO WAY
AROUND IT. INTRODUCTION. 1 1 IN ONE LINE AND CLOSE. PERMUTATIONS AS
LINEAR ORDERS. RUNS. 3 1.1 DESCENTS 3 1.1.1 THE DEFINITION OF DESCENTS 3
1.1.2 EULERIAN NUMBERS 4 1.1.3 STIRLING NUMBERS AND EULERIAN NUMBERS 11
1.1.4 GENERATING FUNCTIONS AND EULERIAN NUMBERS 14 1.1.5 THE SEQUENCE OF
EULERIAN NUMBERS 16 1.2 ALTERNATING RUNS 24 EXERCISES 31 PROBLEMS PLUS
36 SOLUTIONS TO PROBLEMS PLUS 38 2 IN ONE LINE AND ANYWHERE.
PERMUTATIONS AS LINEAR ORDERS. INVERSIONS. 43 2.1 INVERSIONS 43 2.1.1
THE GENERATING FUNCTION OF PERMUTATIONS BY INVERSIONS 43 2.1.2 MAJOR
INDEX 52 2.1.3 AN APPLICATION: DETERMINANTS AND GRAPHS 55 2.2 INVERSIONS
IN PERMUTATIONS OF MULTISETS 57 2.2.1 INVERSIONS AND GAUSSIAN
COEFFICIENTS 60 2.2.2 MAJOR INDEX AND PERMUTATIONS OF MULTISETS 61
EXERCISES 64 PROBLEMS PLUS 67 SOLUTIONS TO PROBLEMS PLUS 69 3 IN MANY
CIRCLES. PERMUTATIONS AS PRODUCTS OF CYCLES. 73 3.1 DECOMPOSING A
PERMUTATION INTO CYCLES 73 3.1.1 AN APPLICATION: SIGN AND DETERMINANTS
75 3.1.2 AN APPLICATION: GEOMETRIC TRANSFORMATIONS 78 3.2 TYPE AND
STIRLING NUMBERS 79 3.2.1 THE TYPE OF A PERMUTATION 79 3.2.2 AN
APPLICATION: CONJUGATE PERMUTATIONS 80 3.2.3 AN APPLICATION: TREES AND
TRANSPOSITIONS 81 COMBINATORICS OF PERMUTATIONS 3.2.4 PERMUTATIONS WITH
A GIVEN NUMBER OF CYCLES 85 3.2.5 GENERATING FUNCTIONS FOR STIRLING
NUMBERS 92 3.2.6 AN APPLICATION: REAL ZEROS AND PROBABILITY 95 3.3 CYCLE
DECOMPOSITION VERSUS LINEAR ORDER 96 3.3.1 THE TRANSITION LEMMA 96 3.3.2
APPLICATIONS OF THE TRANSITION LEMMA 98 3.4 PERMUTATIONS WITH RESTRICTED
CYCLE STRUCTURE 100 3.4.1 THE EXPONENTIAL FORMULA 100 3.4.2 THE CYCLE
INDEX AND ITS APPLICATIONS 110 EXERCISES 115 PROBLEMS PLUS 120 SOLUTIONS
TO PROBLEMS PLUS 123 IN ANY WAY BUT THIS. PATTERN AVOIDANCE. THE BASICS.
129 4.1 THE NOTION OF PATTERN AVOIDANCE 129 4.2 PATTERNS OF LENGTH THREE
130 4.3 MONOTONE PATTERNS 133 4.4 PATTERNS OF LENGTH FOUR 135 4.4.1 THE
PATTERN 1324 137 4.4.2 THE PATTERN 1342 144 4.4.3 THE PATTERN 1234 158
4.5 THE PROOF OF THE STANLEY-WILF CONJECTURE 159 4.5.1 THE
FIIREDI-HAJNAL CONJECTURE 159 4.5.2 AVOIDING MATRICES VS. AVOIDING
PERMUTATIONS 160 4.5.3 THE PROOF OF THE FIIREDI-HAJNAL CONJECTURE 161
EXERCISES 164 PROBLEMS PLUS 168 SOLUTIONS TO PROBLEMS PLUS 170 IN THIS
WAY, BUT NICELY. PATTERN AVOIDANCE. FOLLOWUP. 175 5.1 POLYNOMIAL
RECURSIONS 175 5.1.1 POLYNOMIALLY RECURSIVE FUNCTIONS 175 5.1.2 CLOSED
CLASSES OF PERMUTATIONS 176 5.1.3 ALGEBRAIC AND RATIONAL POWER SERIES
178 5.1.4 THE F-RECURSIVENESS OF 5 N , R (132) 182 5.2 CONTAINING A
PATTERN MANY TIMES 191 5.2.1 PACKING DENSITIES 191 5.2.2 LAYERED
PATTERNS 193 5.3 CONTAINING A PATTERN A GIVEN NUMBER OF TIMES 198 5.3.1
A CONSTRUCTION WITH A GIVEN NUMBER OF COPIES . . . 199 5.3.2 THE
SEQUENCE {K N } N 0 201 EXERCISES 205 PROBLEMS PLUS 207 SOLUTIONS TO
PROBLEMS PLUS 208 TABLE OF CONTENTS 6 MEAN AND INSENSITIVE. RANDOM
PERMUTATIONS. 213 6.1 THE PROBABILISTIC VIEWPOINT 213 6.1.1 STANDARD
YOUNG TABLEAUX 214 6.2 EXPECTATION 229 6.2.1 LINEARITY OF EXPECTATION
231 6.3 VARIANCE AND STANDARD DEVIATION 233 6.4 AN APPLICATION: LONGEST
INCREASING SUBSEQUENCES 237 EXERCISES 238 PROBLEMS PLUS 242 SOLUTIONS TO
PROBLEMS PLUS 243 7 PERMUTATIONS VS. EVERYTHING ELSE. ALGEBRAIC
COMBINATORICS OF PERMUTATIONS. 247 7.1 THE ROBINSON-SCHENSTED-KNUTH
CORRESPONDENCE 247 7.2 POSETS OF PERMUTATIONS 257 7.2.1 POSETS ON S N
257 7.2.2 POSETS ON PATTERN AVOIDING PERMUTATIONS 265 7.2.3 AN INFINITE
POSET OF PERMUTATIONS 267 7.3 SIMPLICIAL COMPLEXES OF PERMUTATIONS 269
7.3.1 A SIMPLICIAL COMPLEX OF RESTRICTED PERMUTATIONS . . . 269 7.3.2 A
SIMPLICIAL COMPLEX OF ALL N-PERMUTATIONS 271 EXERCISES 272 PROBLEMS PLUS
276 SOLUTIONS TO PROBLEMS PLUS 278 8 GET THEM ALL. ALGORITHMS AND
PERMUTATIONS. 283 8.1 GENERATING PERMUTATIONS 283 8.1.1 GENERATING ALL
N-PERMUTATIONS 283 8.1.2 GENERATING RESTRICTED PERMUTATIONS 284 8.2
STACK SORTING PERMUTATIONS 287 8.2.1 2-STACK SORTABLE PERMUTATIONS 289
8.2.2 I-STACK SORTABLE PERMUTATIONS 291 8.2.3 UNIMODALITY 297 8.3
VARIATIONS OF STACK SORTING 300 EXERCISES 307 PROBLEMS PLUS 311
SOLUTIONS TO PROBLEMS PLUS 313 DO NOT LOOK JUST YET. SOLUTIONS TO
ODD-NUMBERED EXERCISES. 319 SOLUTIONS FOR CHAPTER 1 319 SOLUTIONS FOR
CHAPTER 2 326 SOLUTIONS FOR CHAPTER 3 330 SOLUTIONS FOR CHAPTER 4 339
SOLUTIONS FOR CHAPTER 5 347 SOLUTIONS FOR CHAPTER 6 351 COMBINATORICS OF
PERMUTATIONS SOLUTIONS FOR CHAPTER 7 355 SOLUTIONS FOR CHAPTER 8 358
REFERENCES LIST OF FREQUENTLY USED NOTATIONS INDEX 363 377 379
|
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| indexdate | 2024-07-09T20:00:38Z |
| institution | BVB |
| isbn | 1584884347 |
| language | English |
| lccn | 2004045868 |
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| physical | 383 S. graph. Darst. |
| publishDate | 2004 |
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| publisher | Chapman & Hall/CRC |
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| series2 | Discrete mathematics and its applications |
| spelling | Bóna, Miklós Verfasser (DE-588)1013929861 aut Combinatorics of permutations Miklós Bóna Boca Raton [u.a.] Chapman & Hall/CRC 2004 383 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications Analyse combinatoire rasuqam Combinatieleer gtt Permutaties gtt Permutation (Mathematiques) rasuqam Permutations (Mathématiques) aPermutations Permutation (DE-588)4173832-9 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Permutation (DE-588)4173832-9 s Kombinatorik (DE-588)4031824-2 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012912032&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bóna, Miklós Combinatorics of permutations Analyse combinatoire rasuqam Combinatieleer gtt Permutaties gtt Permutation (Mathematiques) rasuqam Permutations (Mathématiques) aPermutations Permutation (DE-588)4173832-9 gnd Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4173832-9 (DE-588)4031824-2 |
| title | Combinatorics of permutations |
| title_auth | Combinatorics of permutations |
| title_exact_search | Combinatorics of permutations |
| title_full | Combinatorics of permutations Miklós Bóna |
| title_fullStr | Combinatorics of permutations Miklós Bóna |
| title_full_unstemmed | Combinatorics of permutations Miklós Bóna |
| title_short | Combinatorics of permutations |
| title_sort | combinatorics of permutations |
| topic | Analyse combinatoire rasuqam Combinatieleer gtt Permutaties gtt Permutation (Mathematiques) rasuqam Permutations (Mathématiques) aPermutations Permutation (DE-588)4173832-9 gnd Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Analyse combinatoire Combinatieleer Permutaties Permutation (Mathematiques) Permutations (Mathématiques) aPermutations Permutation Kombinatorik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012912032&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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