Verfügbarkeit: Handbook of enumerative combinatorics

Handbook of enumerative combinatorics:

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Bibliographische Detailangaben
1. Verfasser:	Bóna, Miklós (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Boca Raton CRC Press 2015
Schriftenreihe:	Discrete mathematics and its applications
Schlagworte:	Combinatorial analysis Mathematical analysis Numeration Diskrete Mathematik Kombinatorik Abzählende Kombinatorik
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Enthält Index und bibliographische Angaben
Beschreibung:	XXIII, 1061 S. Ill., graph. Darst.
ISBN:	9781482220858

Internformat

MARC


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245	1	0	\|a Handbook of enumerative combinatorics \|c ed. by Miklós Bóna
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Datensatz im Suchindex

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adam_text	CONTENTS FOREWORD XIX PREFACE XXI ACKNOWLEDGMENTS XXIII I METHODS 1 1 ALGEBRAIC ANDGEOMETRIC METHODS INENUMERATIVE COMBINATORICS 3 FEDERICOARDILA 1.1 INTRODUCTION........ .... ;, . 5 PART 1. ALGEBRAIC METHODS 6 1.2 WHATISAGOODANSWER? . ......... 6 1.3 GENERATINGFUNCTIONS ........ 9 1.3.1 THERINGOFFORMALPOWERSERIES. 10 1.3.2 ORDINARYGENERATINGFUNCTIONS. . 12 1.3.2.1 OPERATIONSON COMBINATORIALSTRUCTURES AND THEIRGENERATINGFUNCTIONS 13 1.3.2.2 EXAMPLES . ...... ... 16 1.3.3 EXPONENTIALGENERATINGFUNCTIONS .... ......... 28 1.3.3.1 OPERATIONSONLABELEDSTRUCTURESANDTHEIREX- PONENTIALGENERATINGFUNCTIONS 28 1.3.3.2 EXAMPLES........... 30 1.3.4 NICEFAMILIESOFGENERATINGFUNCTIONS ... 36 1.3.4.1 RATIONALGENERATINGFUNCTIONS. 36 1.3.4.2 ALGEBRAICANDD-FINITEGENERATINGFUNCTIONS 38 1.4 LINEARALGEBRAMETHODS ............... 43 1.4.1 DETERMINANTSINCOMBINATORICS ........ 43 1.4.1.1 PRELIMINARIES:GRAPHMATRICES.. . 43 1.4.1.2 WALKS:THETRANSFERMATRIXMETHOD 44 1.4.1.3 SPANNINGTREES:THEMATRIX-TREETHEOREM 50 1.4.1.4 EULERIANCYCLES:THEBESTTHEOREM... 53 1.4.1.5 PERFECTMATCHINGS:THEPFAFFIANMETHOD. 56 1.4.1.6 ROUTINGS:THE LINDSTROM-GESSEL-VIENNOT LEMMA. . .. 58 1.4.2 COMPUTINGDETERMINANTS 65 VII VIII 1.5 POSETS 1.5.1 1.5.2 1.5.3 1.5.4 1.5.5 1.5.6 CONTENTS 1.4.2.1 1.4.2.2 1.4.2.3 1.4.2.4 1.4.2.5 1.4.2.6 ISITKNOWN? . ROWAND COLUMN OPERATIONS . IDENTIFYING LINEARFACTORS . COMPUTING THEEIGENVALUES . LUFACTORIZATIONS . . . . . . HANKEL DETERMINANTS ANDCONTINUED FRACTIONS . 65 66 66 67 68 68 71 72 74 77 79 81 81 83 85 86 91 BASICDEFINITIONS ANDEXAMPLES . . . . . LATTICES . ZETAPOLYNOMIALS ANDORDERPOLYNOMIALS THEINCLUSION-EXCLUSION FORMULA . . . . MOBIUS FUNCTIONS ANDMOBIUS INVERSION 1.5.5.1 THEMOBIUS FUNCTION . 1.5.5.2 MOBIUS INVERSION . 1.5.5.3 THEINCIDENCE ALGEBRA . . . . 1.5.5.4 COMPUTING MOBIUS FUNCTIONS EULERIAN POSETS, FLAGI-VECTORS, ANDFLAGH-VECTORS PART2.DISCRETEGEOMETRICMETHODS 93 1.6 POLYTOPES 93 1.6.1 BASICDEFINITIONS ANDCONSTRUCTIONS 93 1.6.2 EXAMPLES............. 98 1.6.3 COUNTING FACES . . . . . . . . . . . . 100 1.6.4 COUNTING LATTICEPOINTS: EHRHART THEORY 102 1.7 HYPERPLANE ARRANGEMENTS . . . . . . . . . . 108 . 1.7.1 BASICDEFINITIONS . . . . . . . . . . . . 109 1.7.2 THECHARACTERISTIC POLYNOMIAL . . . . . 110 1.7.3 PROPERTIES OFTHECHARACTERISTIC POLYNOMIAL 112 1.7.3.1 DELETIONANDCONTRACTION ... 112 1.7.3.2 SIGNALTERNATION ANDUNIMODALITY 114 1.7.3.3 GRAPHS ANDPROPER COLORINGS .. 114 1.7.3.4 FREEARRANGEMENTS ..... 115 1.7.3.5 SUPERSOLVABILITY....... 116 1.7.4 COMPUTING THECHARACTERISTIC POLYNOMIAL 117 1.7.5 THECD-INDEX OFANARRANGEMENT. . . . . 125 1.8 MATROIDS............................... 126 1.8.1 MAINEXAMPLE: VECTORCONFIGURATIONS ANDLINEARMATROIDS 127 1.8.2 BASICDEFINITIONS . . 128 1.8.3 EXAMPLES....... 130 1.8.4 BASICCONSTRUCTIONS .. 133 1.8.5 AFEWSTRUCTURAL RESULTS 134 1.8.6 THETUTTEPOLYNOMIAL . . . . . . . . . . . . . . . . . 138 1.8.6.1 EXPLICIT DEFINITION . . . . . . . . . . . . . 138 1.8.6.2 RECURSIVE DEFINITION ANDUNIVERSALITY PROPERTY 138 1.8.6.3 ACTIVITY INTERPRETATION. . .. 140 CONTENTS IX 1.8.7 1.8.6.4 FINITE FIELDINTERPRETATION 140 TUTTEPOLYNOMIAL EVALUATIONS . 141 1.8.7.1 GENERAL EVALUATIONS . . . 142 1.8.7.2 GRAPHS.......... 143 1.8.7.3 HYPERPLANE ARRANGEMENTS 146 1.8.7.4 ALGEBRAS FROMARRANGEMENTS 146 1.8.7.5 ERROR-CORRECTING CODES. . . . 147 1.8.7.6 PROBABILITY ANDSTATISTICAL MECHANICS 148 1.8.7.7 OTHER APPLICATIONS. . . . . . 149 COMPUTING THETUTTEPOLYNOMIAL . . . . . . . . 150 GENERALIZATIONS OFTHETUTTEPOLYNOMIAL .... 153 MATROID SUBDIVISIONS, VALUATIONS, AND THE DERKSEN-FINK 1.8.8 1.8.9 1.8.10 INVARIANT .......................... 155 2 ANALYTICMETHODS 173 HELMUT PRODINGER 2.1 INTRODUCTION............................. 174 2.2 COMBINATORIAL CONSTRUCTIONS AND ASSOCIATED ORDINARY GENERATING FUNCTIONS 175 II TOPICS 2.3 COMBINATORIAL CONSTRUCTIONS ANDASSOCIATED EXPONENTIAL GENERATING FUNCTIONS . PARTITIONS ANDQ-SERIES . . . . . . . . . . . . . . . SOMEAPPLICATIONS OFTHEADDING ASLICETECHNIQUE LAGRANGE INVERSION FORMULA . . . . . . . . . . . . LATTICE PATHENUMERATION: THECONTINUED FRACTION THEOREM LATTICE PATHENUMERATION: THEKERNEL METHOD . . . . GAMMA ANDZETAFUNCTION . . . . . . . . . . . . . . HARMONIC NUMBERS ANDTHEIRGENERATING FUNCTIONS . APPROXIMATION OFBINOMIAL COEFFICIENTS . MELLIN TRANSFORM ANDASYMPTOTICS OFHARMONIC SUMS THEMELLIN-PERRON FORMULA . MELLIN-PERRON FORMULA: DIVIDE-AND-CONQUER RECURSIONS RICE S METHOD . . . . . . . . . . . . . . . . APPROXIMATE COUNTING . SINGULARITY ANALYSIS OFGENERATING FUNCTIONS LONGEST RUNSINWORDS . . . . . . . . . . . . INVERSIONS INPERMUTATIONS ANDPUMPING MOMENTS THETREEFUNCTION . THESADDLEPOINT METHOD . HWANG S QUASI-POWER THEOREM 180 187 191 194 196 201 205 208 209 211 218 222 223 227 231 236 238 241 244 247 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 253 3 ASYMPTOTICNORMALITYINENUMERATION E.RODNEY CANFIELD 255 X 3.1 INTRODUCTION........ 3.2 THENORMAL DISTRIBUTION . . 3.3 METHOD 1:DIRECT APPROACH 3.4 METHOD 2:NEGATIVE ROOTS .. 3.5 METHOD 3:MOMENTS . 3.6 METHOD 4:SINGULARITY ANALYSIS 3.7 LOCALLIMITTHEOREMS ..... 3.8 MULTIVARIATE ASYMPTOTIC NORMALITY 3.9 NORMALITY INSERVICE TOAPPROXIMATE ENUMERATION 4 TREES MICHAEL DRMOTA 4.1 INTRODUCTION..... 4.2 BASICNOTIONS .... 4.3 GENERATING FUNCTIONS 4.3.1 GENERATING FUNCTIONS ANDCOMBINATORIAL CONSTRUCTIONS 4.3.2 THELAGRANGE INVERSION FORMULA 4.3.3 THEDISSYMMETRY THEOREM . 4.3.4 ASYMPTOTICS 4.4 UNLABELED TREES . 4.4.1 BINARY TREES . . . . 4.4.2 PLANTED PLANETREES . 4.4.3 UNLABELED PLANETREES 4.4.4 GENERAL UNLABELED TREES 4.4.5 SIMPLY GENERATED TREESANDGALTON-WATSON TREES 4.5 LABELED TREES . 4.5.1 CAYLEY TREESANDRELATED TREES 4.5.2 RECURSIVE TREES. . 4.5.3 WELL-LABELED TREES 4.6 SELECTED TOPICSONTREES 4.6.1 SPANNING TREES 4.6.2 K-TREES ... 4.6.3 SEARCH TREES . ... 5 PLANAR MAPS GILLESSCHAEFFER 5.1 INTRODUCTION . 5.2 WHAT ISAMAP? . 5.2.1 AFEWDEFINITIONS 5.2.2 PLANEMAPS,ROOTED MAPSANDORIENTATIONS 5.2.3 WHICH MAPS SHALLWECOUNT? . 5.3 COUNTING TREE-ROOTED MAPS . 5.3.1 MULLIN S DECOMPOSITION . 5.3.2 SPANNING TREESANDORIENTATIONS ..5.3.3 VERTEXBLOWING ANDPOLYHEDRAL NETS . CONTENTS 255 256 258 262 266 270 272 274 276 281 281 283 286 286 292 293 294 295 295 299 304 305 308 310 311 316 318 321 321 324 329 335 336 336 336 339 342 344 344 348 350 7 UNIMODALITY,LOG-CONCAVITY,REAL-ROOTEDNESS ANDBEYOND PETTERBRANDEN 7.1 INTRODUCTION . CONTENTS 6 GRAPHS XL 5.3.4 ASUMMARYANDSOMEOBSERVATIONS ... 352 5.4 COUNTINGPLANARMAPS .... ......... .. 353 5.4.1 THEEXACTNUMBEROFROOTEDPLANARMAPS 353 5.4.2 UNROOTEDPLANARMAPS ........ .. 358 5.4.3 1 VOBIJECTIONSBETWEENMAPSANDTREES .... .. . 360 5.4.4 SUBSTITUTIONRELATIONS 364 5.4.5 ASYMPTOTIC ENUMERATION AND UNIFORM RANDOM PLANAR MAPS. ................. 367 5.4.6 DISTANCESINPLANARMAPS 370 5.4.7 LOCALLIMIT,CONTINUUMLIMIT. ... . 373 5.5 BEYONDPLANARMAPS,ANEVENSHORTERACCOUNT 374 5.5.1 PATTERNSANDUNIVERSALITY. ... ... ..... 375 5.5.2 THEBIJECTIVECANVASANDMASTERBIJECTIONS ..... 376 5.5.3 MAPSONSURFACES 380 5.5.4 DECORATEDMAPS .......... ......... 382 MARCNOY 6.1 INTRODUCTION 6.2 397 ............... 398 400 401 404 405 406 409 409 411 412 412 414 417 420 420 422 423 426 426 428 428 429 430 6.3 6.4 GRAPHDECOMPOSITIONS . 6.2.1 GRAPHSWITHGIVENCONNECTIVITY 6.2.2 GRAPHSWITHGIVENMINIMUMDEGREE. 6.2.3 BIPARTITEGRAPHS .... ....... CONNECTEDGRAPHSWITHGIVENEXCESS . REGULARGRAPHS . 6.4.1 THEPAIRINGMODEL... 6.4.2 DIFFERENTIALEQUATIONS ..... MONOTONEANDHEREDITARYCLASSES .... 6.5.1 MONOTONECLASSES . 6.5.2 HEREDITARYCLASSES :.... PLANARGRAPHS . GRAPHSONSURFACESANDGRAPHMINORS 6.7.1 GRAPHSONSURFACES . 6.7.2 GRAPHMINORS .. . . 6.7.3 PARTICULARCLASSES . DIGRAPHS . 6.8.1 ACYCLICDIGRAPHS. 6.8.2 STRONGLYCONNECTEDDIGRAPHS UNLABELEDGRAPHS . 6.9.1 COUNTINGGRAPHSUNDERSYMMETRIES 6.9.2 ASYMPTOTICS . .,. 6.5 6.6 6.7 6.8 6.9 437 438 XLL CONTENTS 7.2 7.3 PROBABILISTIC CONSEQUENCES OFREAL-ROOTEDNESS UNIMODALITY ANDY-NONNEGATIVITY . . . . . 7.3.1 ANACTIONONPERMUTATIONS .... 7.3.2 Y-NONNEGATIVITY OFH-POLYNOMIALS 7.3.3 BARYCENTRIC SUBDIVISIONS .... 7.3.4 UNIMODALITY OFH-POLYNOMIALS LOG-CONCAVITY ANDMATROIDS INFINITELOG-CONCAVITY . . . . . . THENEGGERS-STANLEY CONJECTURE PRESERVING REAL-ROOTEDNESS ... 7.7.1 THESUBDIVISION OPERATOR COMMON INTERLEAVERS . 7.8.1 S-EULERIAN POLYNOMIALS . 7.8.2 EULERIAN POLYNOMIALS FORFINITECOXETER GROUPS MULTIVARIATE TECHNIQUES . . . . . . . . . . 7.9.1 STABLEPOLYNOMIALS ANDMATROIDS 7.9.2 STRONG RAYLEIGH MEASURES .... 7.9.3 THESYMMETRIC EXCLUSION PROCESS 7.9.4 THE GRACE-WALSH-SZEGF THEOREM, ANDTHEPROOF OFTHE- OREM7.5.1 441 442 443 446 447 449 450 452 453 456 459 460 464 465 468 469 470 472 7.4 7.5 7.6 7.7 7.8 7.9 474 476 7.10 HISTORICAL NOTES I I ** , I IT I I I I , , * I ** 8 WORDS DOMINIQUE PERRINANDANTONIORESTIVO 8.1 INTRODUCTION........ 8.2 PRELIMINARIES . 8.2.1 GENERATING SERIES 8.2.2 AUTOMATA 8.3 CONJUGACY..... 8.3.1 PERIODS . . 8.3.2 NECKLACES 8.3.3 CIRCULAR CODES 8.4 LYNDON WORDS ..... 8.4.1 THEFACTORIZATION THEOREM . 8.4.2 GENERATING LYNDON WORDS . 8.5 EULERIAN GRAPHS ANDDEBRUIJN CYCLES 8.5.1 THEBEST THEOREM . 8.5.2 THEMATRIX-TREE THEOREM . 8.5.3 LYNDON WORDS ANDDEBRUIJN CYCLES 8.6 UNAVOIDABLE SETS . 8.6.1 ALGORITHMS . . . . . . . . . . . . . . 8.6.2 UNAVOIDABLE SETSOFCONSTANT LENGTH . 8.6.3 CONCLUSION....... 8.7 .. THEBURROWS-WHEELER TRANSFORM 8.7.1 THEINVERSETRANSFORM . 485 486 487 488 491 492 492 493 497 500 501 503 504 507 508 510 512 513 516 519 521 522 CONTENTS XIII 8.7.2 DESCENTS OFAPERMUTATION. . . . . . . . . . . . . 524 8.8 THEGESSEL-REUTENAUER BIJECTION ..... . . . . . . . . . 525 8.8.1 GESSEL-REUTENAUER BIJECTION ANDDEBRUIJN CYCLES 527 8.9 SUFFIXARRAYS . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 530 8.9.1 SUFFIXARRAYS ANDBURROWS-WHEELER TRANSFORM 530 8.9.2 COUNTING SUFFIXARRAYS . ... . . . . . . . . . . . .. 532 10 LATTICE PATHENUMERATION CHRISTIAN KRATTENTHALER 10.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . 10.2 LATTICE PATHSWITHOUT RESTRICTIONS . 10.3 LINEAR BOUNDARIES OFSLOPE 1 . 10.4 SIMPLEPATHS WITHLINEARBOUNDARIES OFRATIONAL SLOPE,I . 10.5 SIMPLEPATHS WITHLINEARBOUNDARIES WITHRATIONAL SLOPE,II 10.6 SIMPLEPATHS WITHAPIECEWISE LINEARBOUNDARY . 10.7 SIMPLEPATHS WITHGENERAL BOUNDARIES . 10.8 ELEMENTARY RESULTS ONMOTZKIN ANDSCHRODER PATHS . 10.9 ACONTINUED FRACTION FORTHEWEIGHTED COUNTING OFMOTZKIN PATHS 10.10 LATTICE PATHS ANDORTHOGONAL POLYNOMIALS 10.11 MOTZKIN PATHS INASTRIP . 10.12 FURTHER RESULTS FORLATTICEPATHS INTHEPLANE . 10.13 NON-INTERSECTING LATTICEPATHS . 10.14 LATTICE PATHS ANDTHEIRTURNS . . . . . . . . . . . . 10.15 MULTIDIMENSIONAL LATTICEPATHS . 10.16 MULTIDIMENSIONAL LATTICE PATHSBOUNDED BYAHYPERPLANE 9 THINGS JAMESPROPP 9.1 INTRODUCTION.......................... 9.2 THETRANSFER MATRIX METHOD . . . . . . . .. . 9.3 OTHERDETERMINANT METHODS . 9.3.1 THEPATHMETHOD . 9.3.2 THEPERMANENT-DETERMINANT ANDHAFNIAN-PFAFFIAN METHOD 9.3.3 THESPANNING TREEMETHOD . . . . REPRESENTATION-THEORETIC METHODS . . . . . . OTHERCOMBINATORIAL METHODS . . . . . . . . . . . . . 9.4 9.5 9.6 9.7 RELATED TOPICS, ANDANATTEMPT ATHISTORY SOMEEMERGENT THEMES .... 9.7.1 RECURRENCE RELATIONS. 9.7.2 SMOOTHNESS ..... 9.7.3 NON-PERIODIC WEIGHTS 9.7.4 OTHER NUMERICAL PATTERNS 9.7.5 SYMMETRY . SOFTWARE 9.8 9.9 FRONTIERS . 541 541 548 551 551 553 555 556 559 562 565 565 566 568 569 570 571 573 589 589 592 594 598 606 611 612 615 618 622 629 633 638 651 657 658 10.17 MULTIDIMENSIONAL PATHSWITHAGENERAL BOUNDARY. . . . . . . 658 10.18 THEREFLECTION PRINCIPLE INFULLGENERALITY . . . . . . . . . . . 659 10.19 Q-COUNTING OFLATTICEPATHS ANDROGERS-RAMANUJAN IDENTITIES 667 10.20 SELF-AVOIDING WALKS . . . . . . . . . . . . . . . . . . . . . . 670 XIV CONTENTS 11CATALANPATHSANDQ,T-ENUMERATION 679 JAMESHAGLUND 11.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . 680 11.2 INTRODUCTION TOQ-ANALOGUES ANDCATALAN NUMBERS .... 680 11.2.1 PERMUTATION STATISTICS ANDGAUSSIAN POLYNOMIALS 680 11.2.2 THECATALAN NUMBERS ANDDYCKPATHS . 686 11.2.3 THE Q- VANDERMONDE CONVOLUTION 689 11.2.4 SYMMETRIC FUNCTIONS. . . . . . . . . . 691 11.2.4.1 THEBASICS . . . . . . . . . 691 11.2.4.2 TABLEAUX ANDSCHURFUNCTIONS . 694 11.2.4.3 STATISTICS ONTABLEAUX . . . . . 697 11.2.5 REPRESENTATION THEORY . . . . . . . . . . . 698 11.2.5.1 THERINGOFCOINVARIANTS ANDTHESPACEOFDIAG- ONALHARMONICS 701 11.3 THEQ,T-CATALAN NUMBERS 702 11.3.1 THEBOUNCE STATISTIC . . . . . . . . . 704 11.3.2 THESPECIAL VALUEST = 1ANDT = 1/Q 707 11.3.3 THESYMMETRY PROBLEM ANDTHEDINVSTATISTIC 709 11.3.4 Q-LAGRANGE INVERSION . . . . . 712 11.4 PARKING FUNCTIONS ANDTHEHILBERT SERIES 716 11.4.1 EXTENSION OFTHEDINVSTATISTIC . 716 11.4.2 ANEXPLICIT FORMULA 718 11.4.3 THESTATISTIC AREA .... 721 11.4.4 THEPMAJ STATISTIC . . . . 722 11.4.5 THECYCLIC-SHIFT OPERATION 725 11.4.6 TESLERMATRICES. . . . . . 729 11.5 THEQ,R-SCHRODER POLYNOMIAL . . . 731 11.5.1 THESCHRODER BOUNCE ANDAREASTATISTICS. 731 11.5.2 RECURRENCES ANDEXPLICIT FORMULAE 734 11.5.3 THESPECIAL VALUET = 1/Q 738 11.5.4 ASCHRODER DINV-STATISTIC ... 739 11.5.5 THESHUFFLECONJECTURE . . . . . 740 11.6 RATIONAL CATALAN COMBINATORICS . . . . . 742 11.6.1 THESUPERPOLYNOMIAL INVARIANT OFATORUSKNOT 742 11.6.2 TESLERMATRICES ANDTHESUPERPOLYNOMIAL 745 12PERMUTATIONCLASSES 753 VINCENTVATTER 12.R INTRODUCTION . 754 12.1.1 BASICS 755 CONTENTS XV 12.1.2 AVOIDINGAPERMUTATIONOFLENGTHTHREE 12.1.3 WILT-EQUIVALENCE . 12.1.4 AVOIDINGALONGERPERMUTATION . 12.2 GROWTHRATESOFPRINCIPALCLASSES . 12.2.1 MATRICESANDTHEINTERVALMINORORDER. 12.2.2 THENUMBEROFLIGHTMATRICES . 12.2.3 MATRICESAVOIDING H ARELIGHT . 12.2.4 DENSEMATRICESCONTAINMANYPERMUTATIONS.. 12.2.5 DENSEMATRICESAVOIDING H 12.3 NOTIONSOFSTRUCTURE . 12.3.1 MERGINGANDSPLITTING . 12.3.2 THESUBSTITUTIONDECOMPOSITION 12.3.3 ATOMICITY . 12.4 THESETOFALLGROWTHRATES . 12.4.1 MONOTONEGRIDCLASSES. 12.4.2 GEOMETRICGRIDCLASSES. 12.4.3 GENERALIZEDGRIDCLASSES.. 12.4.4 SMALLPERMUTATIONCLASSES . 759 761 766 771 773 777 778 780 782 786 788 792 797 800 803 808 815 818 13 PARKING FUNCTIONS 835 CATHERINE H.YAN 13.1 INTRODUCTION ......... ...... 836 13.2 PARKINGFUNCTIONSANDLABELEDTREES ... 837 13.2.1 LABELEDTREESWITHPRUFERCODE 837 13.2.2 INVERSIONSOFLABELEDTREES. .. 839 13.2.3 GRAPHSEARCHINGALGORITHMS .. 843 13.2.4 EXTERNALACTIVITYOFLABELEDTREES 847 13.2.5 SPARSECONNECTEDGRAPHS. . 848 13.3 MANYFACESOFPARKINGFUNCTIONS ..... 850 13.3.1 HASHINGANDLINEARPROBING ... 850 13.3.2 LATTICEOFNONCROSSINGPARTITIONS 852 13.3.3 HYPERPLANEARRANGEMENTS .. 855 13.3.4 ALLOWABLEINPUT-OUTPUTPAIRSINAPRIORITYQUEUE 857 13.3.5 TWOVARIATIONSOFPARKINGFUNCTIONS 858 13.4 GENERALIZEDPARKINGFUNCTIONS 859 13.4.1 U-PARKINGFUNCTIONS .. .. ... 859 13.4.2 APARKINGPOLYTOPE .,..... 861 13.4.3 THEORYOFGONCAROVPOLYNOMIALS 864 13.4.4 CLASSICALPARKINGFUNCTIONS ........ ........ 870 13.5 PARKINGFUNCTIONSASSOCIATEDWITHGRAPHS 874 13.5.1 G-PARKINGFUNCTIONS. ................... 874 13.5.2 ABELIANSANDPILEMODEL .................. 875 13.5.3 MULTIPARKINGFUNCTIONS,GRAPHSEARCHING,ANDTHETUTTE POLYNOMIAL. ..................... . 878 13.6 FINALREMARKS :. 884 XVI 14 STANDARD YOUNGTABLEAUX RONADIN ANDYUVALROICHMAN 14.1 INTRODUCTION .... 14.1.1 APPETIZER 14.1.2 GENERAL . 14.2 PRELIMINARIES 14.2.1 DIAGRAMSANDTABLEAUX 14.2.2 CONNECTEDNESSANDCONVEXITY 14.2.3 INVARIANCEUNDERSYMMETRY . 14.2.4 ORDINARY,SKEWANDSHIFTEDSHAPES. 14.2.5 INTERPRETATIONS . 14.2.5.1 THEYOUNGLATTICE . 14.2.5.2 BALLOTSEQUENCESANDLATTICEPATHS. 14.2.5.3 THEORDERPOLYTOPE . 14.2.5.4 OTHERINTERPRETATIONS 14.2.6 MISCELLANEA .. 14.3 FORMULASFORTHINSHAPES .. 14.3.1 HOOKSHAPES .... 14.3.2 TWO-ROWEDSHAPES. 14.3.3 ZIGZAGSHAPES ... 14.4 JEUDETAQUINANDTHERSCORRESPONDENCE. 14.4.1 JEUDETAQUIN . 14.4.2 THEROBINSON-SCHENSTEDCORRESPONDENCE. 14.4.3 ENUMERATIVEAPPLICATIONS 14.5 FORMULASFORCLASSICALSHAPES 14.5.1 ORDINARYSHAPES 14.5.2 SKEWSHAPES . 14.5.3 SHIFTEDSHAPES . 14.6 MOREPROOFSOFTHEHOOKLENGTHFORMULA 14.6.1 APROBABILISTICPROOF . 14.6.2 BIJECTIVEPROOFS . 14.6.3 PARTIALDIFFERENCEOPERATORS 14.7 FORMULASFORSKEWSTRIPS . 14.7.1 ZIGZAGSHAPES . 14.7.2 SKEWSTRIPSOFCONSTANTWIDTH 14.8 TRUNCATEDANDOTHERNON-CLASSICALSHAPES 14.8.1 TRUNCATEDSHIFTEDSTAIRCASESHAPE 14.8.2 TRUNCATEDRECTANGULARSHAPES .. 14.8.3 OTHERTRUNCATEDSHAPES ..... 14.8.4 PROOFAPPROACHESFORTRUNCATEDSHAPES 14.9 RIMHOOKANDDOMINOTABLEAUX .. 14.9.1 DEFINITIONS . * 14.9.2 THER-QUOTIENTANDR-CORE 14.10Q-ENUMERATION . 14.10.1 PERMUTATIONSTATISTICS .. CONTENTS 895 896 896 898 898 898 899 900 901 903 903 903 904 905 905 905 905 906 907 908 908 910 911 913 913 916 918 919 919 921 926 930 930 933 938 938 939 941 942 944 944 945 949 949 14.10.2 STATISTICSONTABLEAUX 950 14.10.3 THINSHAPES 952 14.10.3.1 HOOKSHAPES. . .. 952 14.10.3.2 ZIGZAGSHAPES ... 952 14.10.3.3 TWO-ROWEDSHAPES. 953 14.10.4 THEGENERALCASE. . ...... 955 14.10.4.1 COUNTINGBYDESCENTS 955 14.10.4.2 COUNTINGBYMAJORINDEX 956 14.10.4.3 COUNTINGBYINVERSIONS. 957 14.11COUNTINGREDUCEDWORDS 957 14.11.1 COXETERGENERATORSANDREDUCEDWORDS 957 14.11.2 ORDINARYANDSKEWSHAPES. .. ... 958 14.11.3 SHIFTEDSHAPES ............ 960 14.12APPENDIX1:REPRESENTATIONTHEORETICASPECTS 961 14.12.1 DEGREESANDENUMERATION .... .. 961 14.12.2 CHARACTERSANDQ-ENUMERATION. ... 963 14.13APPENDIX2:ASYMPTOTICSANDPROBABILISTICASPECTS 964 CONTENTS 15 COMPUTER ALGEBRA MANUEL KAUERS 15.1 INTRODUCTION . 15.2 COMPUTERALGEBRAESSENTIALS . 15.2.1 NUMBERS . 15.2.1.1 INTEGERSANDRATIONALNUMBERS. 15.2.1.2 ALGEBRAICNUMBERS ..... ,. 15.2.1.3 REALANDCOMPLEXNUMBERS .. 15.2.1.4 FINITEFIELDSANDMODULARARITHMETIC 15.2.1.5 LATTICEREDUCTION . 15.2.2 POLYNOMIALS . 15.2.2.1 ARITHMETICANDFACTORIZATION 15.2.2.2 EVALUATIONANDINTERPOLATION 15.2.2.3 GROBNERBASES . 15.2.2.4 CYLINDRICALALGEBRAICDECOMPOSITION 15.2.3 FORMALPOWERSERIES ........ 15.2.3.1 TRUNCATEDPOWERSERIES 15.2.3.2 LAZYPOWERSERIES .. 15.2.3.3 GENERALIZEDSERIES... 15.2.3.4 THEMULTIVARIATECASE . 15.2.4 OPERATORS . 15.2.4.1 OREALGEBRAS . 15.2.4.2 ACTIONSANDSOLUTIONS .. COUNTINGALGORITHMS . 15.3.1 SPECIALPURPOSEALGORITHMS . 1532 C BI .1 . .. OMMATONA SPECIES.......... ..... 15.3.2.1 FORMALDEFINITIONANDASSOCIATEDSERIES 15.3 XVII 975 976 977 978 978 978 979 980 981 983 984 985 985 987 988 988 989 990 990 991 992 993 996 996 999 1000 XVLLL INDEX 15.3.2.2 STANDARDCONSTRUCTIONS 15.3.2.3 RECURSIVESPECIFICATIONS. 15.3.3 PARTITIONANALYSIS . 15.3.3.1 Q-CA1CULUS . 15.3.3.2 EHRHARTTHEORY .. 15.3.4 COMPUTATIONALGROUPTHEORY. 15.3.4.1 PERMUTATIONGROUPS 15.3.4.2 FINITELYPRESENTEDGROUPS 15.3.5 SOFTWARE 15.4 SYMBOLICSUMMATION . 15.4.1 CLASSICALALGORITHMS . 15.4.1.1 HYPERGEOMETRICTERMS. 15.4.1.2 GOSPER SALGORITHM .. 15.4.1.3 ZEILBERGER SALGORITHM. 15.4.1.4 PETKOVSEK SALGORITHM. 15.4.2 ILL-THEORY . 15.4.2.1 ILL-EXPRESSIONSANDDIFFERENCEFIELDS. 15.4.2.2 INDEFINITESUMMATION .. 15.4.2.3 CREATIVETELESCOPING... 15.4.2.4 D ALEMBERTIANSOLUTIONS 15.4.2.5 NESTEDDEFINITESUMS .. 15.4.3 THEHOLONOMICSYSTEMSAPPROACH.. 15.4.3.1 D-FINITEANDHOLONOMICFUNCTIONS 15.4.3.2 CLOSUREPROPERTIES..... 15.4.3.3 SUMMATIONANDINTEGRATION . 15.4.3.4 NESTEDSUMSANDINTEGRALS . 15.4.4 IMPLEMENTATIONSANDCURRENTRESEARCHTOPICS THEGUESS-AND-PROVEPARADIGM ...... ...... 15.5 CONTENTS 1000 1002 1003 1003 1005 1007 1007 1008 1010 1011 1011 1011 1012 1013 1014 1015 1015 1017 1019 1020 1021 1021 1022 1023 1025 1026 1027 1028 1047
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language	English
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spelling	Bóna, Miklós Verfasser (DE-588)1013929861 aut Handbook of enumerative combinatorics ed. by Miklós Bóna Enumerative combinatorics Boca Raton CRC Press 2015 XXIII, 1061 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications Enthält Index und bibliographische Angaben Combinatorial analysis Mathematical analysis Numeration Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Abzählende Kombinatorik (DE-588)4132720-2 gnd rswk-swf Abzählende Kombinatorik (DE-588)4132720-2 s DE-604 Kombinatorik (DE-588)4031824-2 s Diskrete Mathematik (DE-588)4129143-8 s 1\p DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027992287&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Bóna, Miklós Handbook of enumerative combinatorics Combinatorial analysis Mathematical analysis Numeration Diskrete Mathematik (DE-588)4129143-8 gnd Kombinatorik (DE-588)4031824-2 gnd Abzählende Kombinatorik (DE-588)4132720-2 gnd
subject_GND	(DE-588)4129143-8 (DE-588)4031824-2 (DE-588)4132720-2
title	Handbook of enumerative combinatorics
title_alt	Enumerative combinatorics
title_auth	Handbook of enumerative combinatorics
title_exact_search	Handbook of enumerative combinatorics
title_full	Handbook of enumerative combinatorics ed. by Miklós Bóna
title_fullStr	Handbook of enumerative combinatorics ed. by Miklós Bóna
title_full_unstemmed	Handbook of enumerative combinatorics ed. by Miklós Bóna
title_short	Handbook of enumerative combinatorics
title_sort	handbook of enumerative combinatorics
topic	Combinatorial analysis Mathematical analysis Numeration Diskrete Mathematik (DE-588)4129143-8 gnd Kombinatorik (DE-588)4031824-2 gnd Abzählende Kombinatorik (DE-588)4132720-2 gnd
topic_facet	Combinatorial analysis Mathematical analysis Numeration Diskrete Mathematik Kombinatorik Abzählende Kombinatorik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027992287&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT bonamiklos handbookofenumerativecombinatorics AT bonamiklos enumerativecombinatorics

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