Holdings: Combinatorics of permutations

Combinatorics of permutations:

Saved in:

Bibliographic Details
Main Author:	Bóna, Miklós (Author)
Format:	Book
Language:	English
Published:	Boca Raton [u.a.] Chapman & Hall/CRC 2004
Series:	Discrete mathematics and its applications
Subjects:	Analyse combinatoire Combinatieleer Permutaties Permutation (Mathematiques) Permutations (Mathématiques) aPermutations Permutation Kombinatorik
Online Access:	Inhaltsverzeichnis
Physical Description:	383 S. graph. Darst.
ISBN:	1584884347

Staff View

MARC


LEADER	00000nam a2200000zc 4500
001	BV019543749
003	DE-604
005	20100621
007	t
008	041105s2004 xxud\|\|\| \|\|\|\| 00\|\|\| eng d
010			\|a 2004045868
020			\|a 1584884347 \|c alk. paper \|9 1-58488-434-7
035			\|a (OCoLC)54931629
035			\|a (DE-599)BVBBV019543749
040			\|a DE-604 \|b ger \|e aacr
041	0		\|a eng
044			\|a xxu \|c US
049			\|a DE-703 \|a DE-523 \|a DE-634 \|a DE-29T \|a DE-91G
050		0	\|a QA165
082	0		\|a 511/.64 \|2 22
084			\|a SK 170 \|0 (DE-625)143221: \|2 rvk
084			\|a MAT 050f \|2 stub
084			\|a MAT 201f \|2 stub
100	1		\|a Bóna, Miklós \|e Verfasser \|0 (DE-588)1013929861 \|4 aut
245	1	0	\|a Combinatorics of permutations \|c Miklós Bóna
264		1	\|a Boca Raton [u.a.] \|b Chapman & Hall/CRC \|c 2004
300			\|a 383 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)
650		4	\|a aPermutations
650	0	7	\|a Permutation \|0 (DE-588)4173832-9 \|2 gnd \|9 rswk-swf
650	0	7	\|a Kombinatorik \|0 (DE-588)4031824-2 \|2 gnd \|9 rswk-swf
689	0	0	\|a Permutation \|0 (DE-588)4173832-9 \|D s
689	0	1	\|a Kombinatorik \|0 (DE-588)4031824-2 \|D s
689	0		\|5 DE-604
856	4	2	\|m HEBIS Datenaustausch Darmstadt \|q application/pdf \|u 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 \|3 Inhaltsverzeichnis
999			\|a oai:aleph.bib-bvb.de:BVB01-012912032

Record in the Search Index

_version_	1804132929394180096
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
any_adam_object	1
author	Bóna, Miklós
author_GND	(DE-588)1013929861
author_facet	Bóna, Miklós
author_role	aut
author_sort	Bóna, Miklós
author_variant	m b mb
building	Verbundindex
bvnumber	BV019543749
callnumber-first	Q - Science
callnumber-label	QA165
callnumber-raw	QA165
callnumber-search	QA165
callnumber-sort	QA 3165
callnumber-subject	QA - Mathematics
classification_rvk	SK 170
classification_tum	MAT 050f MAT 201f
ctrlnum	(OCoLC)54931629 (DE-599)BVBBV019543749
dewey-full	511/.64
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	511 - General principles of mathematics
dewey-raw	511/.64
dewey-search	511/.64
dewey-sort	3511 264
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01785nam a2200493zc 4500</leader><controlfield tag="001">BV019543749</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20100621 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">041105s2004 xxud\|\|\| \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2004045868</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1584884347</subfield><subfield code="c">alk. paper</subfield><subfield code="9">1-58488-434-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)54931629</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV019543749</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-523</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-91G</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA165</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511/.64</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 170</subfield><subfield code="0">(DE-625)143221:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 050f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 201f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bóna, Miklós</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1013929861</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Combinatorics of permutations</subfield><subfield code="c">Miklós Bóna</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton [u.a.]</subfield><subfield code="b">Chapman & Hall/CRC</subfield><subfield code="c">2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">383 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Discrete mathematics and its applications</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analyse combinatoire</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Combinatieleer</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Permutaties</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Permutation (Mathematiques)</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Permutations (Mathématiques)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">aPermutations</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Permutation</subfield><subfield code="0">(DE-588)4173832-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kombinatorik</subfield><subfield code="0">(DE-588)4031824-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Permutation</subfield><subfield code="0">(DE-588)4173832-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Kombinatorik</subfield><subfield code="0">(DE-588)4031824-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch Darmstadt</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-012912032</subfield></datafield></record></collection>
id	DE-604.BV019543749
illustrated	Illustrated
indexdate	2024-07-09T20:00:38Z
institution	BVB
isbn	1584884347
language	English
lccn	2004045868
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-012912032
oclc_num	54931629
open_access_boolean
owner	DE-703 DE-523 DE-634 DE-29T DE-91G DE-BY-TUM
owner_facet	DE-703 DE-523 DE-634 DE-29T DE-91G DE-BY-TUM
physical	383 S. graph. Darst.
publishDate	2004
publishDateSearch	2004
publishDateSort	2004
publisher	Chapman & Hall/CRC
record_format	marc
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
work_keys_str_mv	AT bonamiklos combinatoricsofpermutations

Holdings

There is no print copy available.

Interlibrary loan Place Request Caution: Not in THWS collection! Indexes

MARC

Record in the Search Index

There is no print copy available.

Similar Items