Combinatorics of permutations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2012
|
| Edition: | 2. ed. |
| Series: | Discrete mathematics and its applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 458 S. graph. Darst. |
| ISBN: | 9781439850510 |
Staff View
MARC
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| 100 | 1 | |a Bóna, Miklós |e Verfasser |0 (DE-588)1013929861 |4 aut | |
| 245 | 1 | 0 | |a Combinatorics of permutations |c Miklós Bóna |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2012 | |
| 300 | |a 458 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Discrete mathematics and its applications | |
| 650 | 7 | |a Analyse combinatoire |2 rasuqam | |
| 650 | 7 | |a Combinatieleer |2 gtt | |
| 650 | 7 | |a Permutaties |2 gtt | |
| 650 | 7 | |a Permutation (Mathematiques) |2 rasuqam | |
| 650 | 4 | |a Permutations (Mathématiques) | |
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Record in the Search Index
| _version_ | 1804149503269273600 |
|---|---|
| adam_text | Contents
Foreword
Preface to the First Edition
Preface to the Second Edition
Acknowledgments
No Way around It. Introduction.
1
1
In One Line and Close. Permutations as Linear Orders.
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
......................... 25
1.3
Alternating Subsequences
.................... 32
1.3.1
Definitions and a Recurrence Relation
......... 32
1.3.2
Alternating Runs and Alternating Subsequences
... 35
1.3.3
Alternating Permutations
................ 35
Exercises
................................. 37
Problems Plus
.............................. 43
Solutions to Problems Plus
....................... 46
2
In One Line and Anywhere. Permutations as Linear Orders.
Inversions-
53
2.1
Inversions
............................. 53
2.1.1
The Generating Function of Permutations by Inver¬
sions
............................ 53
2.1.2
Major Index
........................ 62
2.1.3
An Application: Determinants and Graphs
...... 65
2.2
Inversions in Permutations of Multisets
............. 68
2.2.1
An Application: Gaussian Polynomials and Subset
Sums
............................ 69
2.2.2
Inversions and Gaussian Coefficients
.......... 71
2.2.3
Major Index and Permutations
of Multisets......
72
Exercises
................................. 74
Problems Plus
.............................. 79
Solutions
to Problems Plus
....................... 81
In Many Circles.
Permutations as Products
of
Cycles.
85
3.1
Decomposing
a Permutation
into
Cycles
............ 85
3.1.1
An Application:
Sign and Determinants
........ 87
3.1.2
An Application:
Geometric
Transformations
...... 90
3.2
Type
and Stirling Numbers ...................
91
3.2.1
The Cycle Type
of
a Permutation
............ 91
3.2.2
An Application:
Conjugate
Permutations
....... 92
3.2.3
An Application:
Trees and
Transpositions
.......93
3.2.4
Permutations
with a Given Number of
Cycles
.....97
3.2.5
Generating Functions for Stirling Numbers
......104
3.2.6
An Application: Real Zeros and Probability
......107
3.3
Cycle Decomposition versus Linear Order
...........109
3.3.1
The Transition Lemma
..................109
3.3.2
Applications of the Transition Lemma
.........110
3.4
Permutations with Restricted Cycle Structure
.........113
3.4.1
The Exponential Formula
................113
3.4.2
The Cycle Index and Its Applications
.........122
Exercises
.................................129
Problems Plus
..............................136
Solutions to Problems Plus
.......................140
In Any Way but This. Pattern Avoidance. The Basics.
147
4.1
The Notion of Pattern Avoidance
................ 147
4.2
Patterns of Length Three
.................... 148
4.3
Monotone Patterns
........................ 151
4.4
Patterns of Length Four
..................... 154
4.4.1
The Pattern
1324..................... 155
4.4.2
The Pattern
1342..................... 161
4.4.3
The Pattern
1234..................... 176
4.5
The Proof of the Stanley-Wilf Conjecture
........... 177
4.5.1
The
Füredi-Hajnal
Conjecture
............. 177
4.5.2
Avoiding Matrices versus Avoiding Permutations
. . . 178
4.5.3
The Proof of the
Füredi-Hajnal
Conjecture
...... 178
Exercises
................................. 183
Problems Plus
.............................. 188
Solutions to Problems Plus
....................... 192
5
In This Way, but Nicely. Pattern Avoidance. Follow-Up.
197
5.1
Polynomial Recurrences
.....................197
5.1.1
Polynomially Recursive Functions
............197
5.1.2
Closed Classes of Permutations
.............198
5.1.3
Algebraic and Rational Power Series
..........200
5.1.4
The P-Recursiveness of
5„>r(132)
............204
5.2
Containing a Pattern Many Times
...............214
5.2.1
Packing Densities
.....................214
5.2.2
Layered Patterns
.....................215
5.3
Containing a Pattern a Given Number of Times
........220
5.3.1
A Construction with a Given Number of Copies
.... 221
5.3.2
The Sequence
{fc„}„>o
..................222
Exercises
.................................226
Problems Plus
..............................228
Solutions to Problems Plus
.......................230
6
Mean and Insensitive. Random Permutations.
235
6.1
The Probabilistic Viewpoint
...................235
6.1.1
Standard Young Tableaux
................237
6.2
Expectation
............................251
6.2.1
An Application: Finding the Maximum Element of a
Sequence
.........................252
6.2.2
Linearity of Expectation
.................253
6.3
Variance and Standard Deviation
................256
6.3.1
An Application: Asmyptotically Normal Distributions
259
6.4
An Application: Longest Increasing Subsequences
.......261
Exercises
.................................263
Problems Plus
..............................267
Solutions to Problems Plus
.......................269
7
Permutations and the Rest. Algebraic Combinatorics of Per¬
mutations.
275
7.1
The Robinson-Schensted-Knuth Correspondence
.......275
7.2
Posets of Permutations
......................285
7.2.1
Posets on Sn
.......................285
7.2.2
Posets on Pattern-Avoiding Permutations
.......294
7.2.3
An Infinite
Poset
of Permutations
............296
7.3
Simplicia!
Complexes of Permutations
.............297
7.3.1
A Simplicial Complex of Restricted Permutations
. . . 298
7.3.2
A SimpHcial Complex of AH n-Peraiutations
......299
Exercises
.................................301
Problems Plus
..............................305
Solutions to Problems Plus
.......................307
8
Get Them
AU.
Algorithms and Permutations.
313
8.1
Generating Permutations
....................313
8.1.1
Generating All
η
-Permutations.............
313
8.1.2
Generating Restricted Permutations
..........314
8.2
Stack Sorting Permutations
...................317
8.2.1
2-Stack Sortable Permutations
.............319
8.2.2
t-Stack Sortable Permutations
..............321
8.2.3
Unhnodality
........................327
8.3
Variations of Stack Sorting
...................330
Exercises
.................................338
Problems Plus
..............................342
Solutions to Problems Plus
.......................344
9
How Did We Get Here? Permutations as Genome Rearrange¬
ments.
351
9.1
Introduction
............................351
9.2
Block Transpositions
.......................352
9.3
Block Interchanges
........................356
9.3.1
The Average Number of Block Interchanges Needed
to Sort
ρ
..........................363
9.4
Block Transpositions Revisited
.................372
Exercises
.................................380
Problems Plus
..............................381
Solutions to Problems Plus
.......................382
Do Not Look Just Yet. Solutions to Odd-Numbered Exercises.
385
Solutions for Chapter
1 .........................385
Solutions for Chapter
2 .........................392
Solutions for Chapter
3.........................396
Solutions for Chapter
4 .........................406
Solutions for Chapter
5.........................415
Solutions for Chapter
6.........................419
Solutions for Chapter
7.........................424
Solutions for Chapter
8 .........................427
Solutions for Chapter
9.........................431
References
435
List of Frequently Used Notation
453
Index 455
|
| any_adam_object | 1 |
| author | Bóna, Miklós |
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| discipline | Mathematik |
| edition | 2. ed. |
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| id | DE-604.BV040445059 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:24:04Z |
| institution | BVB |
| isbn | 9781439850510 |
| language | English |
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| physical | 458 S. graph. Darst. |
| publishDate | 2012 |
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| publisher | CRC Press |
| record_format | marc |
| series2 | Discrete mathematics and its applications |
| spelling | Bóna, Miklós Verfasser (DE-588)1013929861 aut Combinatorics of permutations Miklós Bóna 2. ed. Boca Raton [u.a.] CRC Press 2012 458 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 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025292817&sequence=000002&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=025292817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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