Combinatorial Reasoning : (Record no. 32837)
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| fixed length control field | 10126nam a22004933i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC7104119 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724115655.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2014 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781118833704 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781118652183 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC7104119 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL7104119 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1414458507 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA164 .D48 2014 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 511/.6 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | DeTemple, Duane. |
| 245 10 - TITLE STATEMENT | |
| Title | Combinatorial Reasoning : |
| Remainder of title | An Introduction to the Art of Counting. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Newark : |
| Name of producer, publisher, distributor, manufacturer | John Wiley & Sons, Incorporated, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2014. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2014. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (484 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | New York Academy of Sciences Series |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Intro -- Combinatorial Reasoning -- Contents -- Preface -- Features of This Text -- Flexibility for Courses -- Part I The Basics of Enumerative Combinatorics -- 1 Initial Encounters with Combinatorial Reasoning -- 1.1 Introduction -- 1.2 The Pigeonhole Principle -- 1.2.1 Applications to Ranges and Domains of Functions -- 1.2.2 An Application to the Chinese Remainder Theorem -- 1.2.3 Generalizations of the Pigeon Principle -- Problems -- 1.3 Tiling Chessboards with Dominoes -- Problems -- 1.4 Figurate Numbers -- 1.4.1 More General Polygonal Numbers -- Problems -- 1.5 Counting Tilings of Rectangles -- 1.5.1 Tiling a Rectangle with Squares of Two Colors -- 1.5.2 Tiling a 1 × n Rectangle with Exactly r Gray Squares -- 1.5.3 Tiling a 1 × n Rectangle with Squares and Dominoes -- Problems -- 1.6 Addition and Multiplication Principles -- 1.6.1 Addition Principles -- 1.6.2 Multiplication Principle -- 1.6.3 Combining the Addition and Multiplication Principles -- Problems -- 1.7 Summary and Additional Problems -- Problems -- References -- 2 Selections, Arrangements, and Distributions -- 2.1 Introduction -- 2.2 Permutations and Combinations -- 2.2.1 Permutations -- 2.2.2 Combinations -- 2.2.3 Applications to Probability -- Problems -- 2.3 Combinatorial Models -- 2.3.1 Tiling Models -- 2.3.2 Block Walking Models -- 2.3.3 The Committee Selection Model -- 2.3.4 The Flagpole Model -- Problems -- 2.4 Permutations and Combinations with Repetitions -- 2.4.1 Multisets -- 2.4.2 Permutations with Repetition -- 2.4.3 Combinations with Repetition -- Problems -- 2.5 Distributions to Distinct Recipients -- 2.5.1 Distributions of Distinct Objects to Distinct Recipients -- 2.5.2 Distributions of Identical Objects to Distinct Recipients -- 2.5.3 Mixed Distribution Problems -- 2.5.4 Equations for Distributions -- 2.5.5 Counting Functions -- Problems. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 2.6 Circular Permutations and Derangements -- 2.6.1 Circular Permutations -- 2.6.2 Derrangements -- Problems -- 2.7 Summary and Additional Problems -- Problems -- Reference -- 3 Binomial Series and Generating Functions -- 3.1 Introduction -- 3.2 The Binomial and Multinomial Theorems -- 3.2.1 The Binomial Theorem -- 3.2.2 The Multinomial Theorem -- Problem -- 3.3 Newtons Binomial Series -- 3.3.1 Generating Function for the Multichoose Coefficients -- 3.3.2 Generalized Binomial Coefficients and Newtons Binomial Series -- Problem -- 3.4 Ordinary Generating Functions -- 3.4.1 Deriving Ordinary Generating Functions -- 3.4.2 Products of Ordinary Generating Functions -- 3.4.3 Counting with Ordinary Generating Functions -- Problem -- 3.5 Exponential Generating Functions -- 3.5.1 Deriving Exponential Generating Functions -- 3.5.2 Products of Exponential Generating Functions -- 3.5.3 Counting with Exponential Generating Functions -- 3.5.4 Comparison between Exponential and Ordinary Generating Functions -- Problems -- 3.6 Summary and Additional Problems -- Problems -- References -- 4 Alternating Sums, Inclusion-Exclusion Principle, Rook Polynomials, and Fibonacci Nim -- 4.1 Introduction -- 4.2 Evaluating Alternating Sums with the DIE Method -- 4.2.1 Using the DIE Method -- 4.2.2 Applications of the DIE Method to Tiling Problems -- Problems -- 4.3 The Principle of Inclusion-Exclusion (PIE) -- 4.3.1 PIE for Three Subsets -- 4.3.2 PIE in General -- 4.3.3 An Application of PIE to Number Theory -- Problems -- 4.4 Rook Polynomials -- 4.4.1 PIE Applications -- 4.4.2 Using Ordinary Generating Functions -- 4.4.3 Another Computational Strategy -- Problems -- 4.5 (OPTIONAL) Zeckendorf Representations and Fibonacci NIM -- 4.5.1 Zeckendorfs Theorem -- 4.5.2 Fibonacci Nim -- Problems -- 4.6 Summary and Additional Problems -- Problems -- References -- 5 Recurrence Relations. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 5.1 Introduction -- 5.2 The Fibonacci Recurrence Relation -- 5.2.1 The E Operator and Its Application to First-Order Recurrences -- 5.2.2 The E Operator and the Fibonacci Recurrence -- 5.2.3 The Binet Formulas -- Problems -- 5.3 Second-Order Recurrence Relations -- 5.3.1 Solving Homogeneous Second-Order Linear Recurrence Relations -- 5.3.2 A Coupled First-Order System of Linear Recurrence Relations -- 5.3.3 Repeated Eigenvalues -- 5.3.4 Complex Eigenvalues -- 5.3.5 A Connection with Linear Algebra -- Problems -- 5.4 Higher-Order Linear Homogeneous Recurrence Relations -- 5.4.1 Nonrepeated Eigenvalues -- 5.4.2 Repeated Eigenvalues -- Problems -- 5.5 Nonhomogeneous Recurrence Relations -- 5.5.1 Solving for Initial Conditions -- 5.5.2 Finding a Particular Solution -- Problems -- 5.6 Recurrence Relations and Generating Functions -- 5.6.1 Ordinary Generating Functions for Linear Recurrence Relations -- 5.6.2 Generating Functions for More General Recurrence Relations -- Problems -- 5.7 Summary and Additional Problems -- Problems -- References -- 6 Special Numbers -- 6.1 Introducation -- 6.2 Stirling Numbers -- 6.2.1 Polynomials and the Difference Operator -- 6.2.2 Stirling Numbers of the Second Kind -- 6.2.3 Bell Numbers -- 6.2.4 Stirling Numbers of the First Kind -- 6.2.5 Identities for Stirling Numbers -- Problems -- 6.3 Harmonic Numbers -- 6.3.1 Growth Rate of the Harmonic Numbers -- 6.3.2 Connection to Probability -- 6.3.3 Connection to Stirling Numbers -- 6.3.4 The Domino Stacking Problem -- 6.3.5 Summation by Parts -- Problems -- 6.4 Bernoulli Numbers -- 6.4.1 Exponential Generating Functions -- 6.4.2 Sum of Integer kth Powers -- 6.4.3 Bernoulli Numbers and Trigonometric Taylor Series -- Problems -- 6.5 Eulerian Numbers -- 6.5.1 Triangle Identity for Eulerian Numbers -- 6.5.2 The Number of Ascents in a Permutation of [n]. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 6.5.3 Sums of Integer Powers and Worpitzkys Identity -- Problems -- 6.6 Partition Numbers -- 6.6.1 Unrestricted Partitions -- 6.6.2 Restricted Partition Numbers -- 6.6.3 Eulers Pentagonal Number Theorem -- Problems -- 6.7 Catalan Numbers -- 6.7.1 Triangulations of a Convex Polygonal Region by Its Diagonals -- 6.7.2 Other Occurrences of Catalan Numbers -- Problems -- 6.8 Summary and Additional Problems -- 6.8.1 Counting Functions and Distributions -- Problems -- References -- Part II Two Additional Topics in Enumeration -- 7 Linear Spaces and Recurrence Sequences -- 7.1 Introduction -- 7.2 Vector Spaces of Sequences -- 7.2.1 Three Vector Spaces Associated with a Recurrence Relation -- 7.2.2 The Order of a Recurrence Relation -- 7.2.3 The Ring of Recurrence Sequences -- 7.2.4 Upper Bounds for the Order of a Recurrence Sequence -- 7.2.5 Bases and Representations -- Problems -- 7.3 Nonhomogeneous Recurrences and Systems of Recurrences -- 7.3.1 Nonhomogeneous Recurrences -- 7.3.2 Systems of Linear Recursion Relations -- Problems -- 7.4 Identities for Recurrence Sequences -- 7.4.1 The Operator Method -- 7.4.2 Free and Bound Variables -- 7.4.3 Elementary Applications of the Operator Method -- 7.4.4 Expressing Sums in Closed Form -- 7.4.5 Sums with Binomial Coefficients -- Problems -- 7.5 Summary and Additional Problems -- Problems -- 8 Counting with Symmetries -- 8.1 Introduction -- 8.2 Algebraic Discoveries -- 8.2.1 Groups of Actions -- 8.2.2 Cycle Decomposition -- 8.2.3 A Preview of the Cycle Index and Pattern Inventory -- 8.2.4 More Groups of Symmetries -- 8.2.5 Fixed Points and Stabilizer Subgroups -- 8.2.6 Orbits -- 8.2.7 Comparing the Number of Fixed Points, Stabilizers, and Orbits -- 8.2.8 Colorings and Labelings -- Problems -- 8.3 Burnsides Lemma -- 8.3.1 Equivalence Classes of Colorings -- 8.3.2 The Proof of Burnsides Lemma -- Problems. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 8.4 The Cycle Index and Pólyas Method of Enumeration -- 8.4.1 Monomials and the Cycle Index -- 8.4.2 Total Number of Colorings Determined from the Cycle Index -- 8.4.3 Pólyas Inventory Function -- Problems -- 8.5 Summary and Additional Problems -- Problems -- References -- Part III Notations Index, Appendices, and Solutions to Selected Odd Problems -- Index of Notations -- Appendix A: Mathematical Induction -- A.1 Principle of Mathematical Induction -- A.2 Principle of Strong Induction -- A.3 Well Ordering Principle -- Appendix B: Searching the Online Encyclopedia of Integer Sequences (OEIS) -- B.1 Searching a Sequence -- B.2 Searching an Array -- B.3 Other Searches -- B.4 Beginnings of OEIS -- Appendix C: Generalized Vandermonde Determinants -- Hints, Short Answers, and Complete Solutions to Selected Odd Problems -- Problem Answers and Solutions -- Index. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Combinatorial analysis-Textbooks. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Mathematical analysis-Textbooks. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | DeTemple, Duane |
| Title | Combinatorial Reasoning |
| Place, publisher, and date of publication | Newark : John Wiley & Sons, Incorporated,c2014 |
| International Standard Book Number | 9781118652183 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | New York Academy of Sciences Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=7104119">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=7104119</a> |
| Public note | Click to View |
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