Frontiers in combinatorics and number theory.: Volume 4 /
This book contains papers on topics in combinatorics (including graph theory) or number theory. The subject areas within correspond to the MSC (Mathematics Subject Classification) codes 05, 11, 20D60, and 52. Some topics included in this compilation are pseudorandom binary functions on rooted plane...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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New York :
Nova Publishers,
[2013]
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| Schriftenreihe: | Frontiers of combinatorics and number theory.
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| Online-Zugang: | Volltext |
| Zusammenfassung: | This book contains papers on topics in combinatorics (including graph theory) or number theory. The subject areas within correspond to the MSC (Mathematics Subject Classification) codes 05, 11, 20D60, and 52. Some topics included in this compilation are pseudorandom binary functions on rooted plane trees; class number one criteria for real quadratic fields with discriminant k2p2 4p; some product-to-sum identities; a zeta function for juggling sequences; divisibility properties of hypergeometric polynomials; the distance between perfect numbers; a new proof of a theorem of Hamidoune avoiding; c. |
| Beschreibung: | 1 online resource (x, 209 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781628089585 162808958X |
| ISSN: | 2324-9536 |
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| 505 | 0 | |a FRONTIERS OF COMBINATORICS AND NUMBER THEORY. VOLUME 4; LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA; CONTENTS; PREFACE; Chapter 1: PSEUDORANDOM BINARY FUNCTIONS ON ROOTED PLANE TREES; Abstract; 1. Introduction; 2. Notation, Terminology, Definitions; 3. The Measures of Pseudorandomness of Binary Functions on Almost Uniform Trees; 4. The Measures of Pseudorandomness of Binary Functions on General Trees; 5. Measures of Pseudorandomness for a Truly Random Binary Function Defined on a Given Tree; 6. Connection between the Measures of Pseudorandomness. | |
| 505 | 8 | |a 7. Finding a Binary Function with Strong Pseudorandom Properties on an Arbitrary TreeReferences; Chapter 2: CLASS NUMBER ONE CRITERIA FOR REAL QUADRATIC FIELDS WITH DISCRIMINANT k2p2 4p; Abstract; 1. Introduction; 2. Preliminaries; 3. Class Number One Criteria for = k2p2 4p; References; Chapter 3: SOME PRODUCT-TO-SUM IDENTITIES; Abstract; 1. Introduction; 2. A Product-to-Sum Identity; 3. Proof of Theorem 1.1; 4. Proof of Theorem 1.2; 5. Proof of Theorem 1.3; 6. Final Remarks; Chapter 4: A ZETA FUNCTION FOR JUGGLING SEQUENCES; Abstract; 1. Introduction. | |
| 505 | 8 | |a 2. Background and Notation: Juggling3. Background and Notation: Zeta Functions; 4. A Norm on Juggling Sequences; 5. Zeta Functions for Ground State Juggling Sequences; 6. A 3-Ball Juggling Zeta Function; 7. A Juggling Zeta Function on b Balls; 8. Locating the Zeroes of the Zeta Function on b Balls; 9. Conclusion; References; Chapter 5: A QUADRATIC TWIST OF THE ELLIPTIC CURVE; Abstract; 1. Introduction; 2. A Family of Twists; 3. The Rank of the Family; 4. Explicit Computation of the Rank; References; Chapter 6: DIVISIBILITY PROPERTIES OF HYPERGEOMETRIC POLYNOMIALS; Abstract. | |
| 505 | 8 | |a Abstract1. Introduction; 2. Proof of Theorem 1.1; Acknowledgments; References; Chapter 10: ON SOME CONJECTURES ON THE MONOTONICITY OF SOME ARITHMETICAL SEQUENCES; Abstract; 1. Introduction; 2. Bernoulli, Tangent and Euler Numbers; 3. Apéry, Delannoy and Franel Numbers; 4. Motzkin Numbers, Schr oder Numbers and Trinomial Coefficients; References; Chapter 11: COMPLEXITY OF TRAPEZOIDAL GRAPHS WITH DIFFERENT TRIANGULATIONS; Abstract; 1. Introduction; 2. Complexity of Trapeziodal Graphs; 3. Conclusion; Acknowledgments; References. | |
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| contents | FRONTIERS OF COMBINATORICS AND NUMBER THEORY. VOLUME 4; LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA; CONTENTS; PREFACE; Chapter 1: PSEUDORANDOM BINARY FUNCTIONS ON ROOTED PLANE TREES; Abstract; 1. Introduction; 2. Notation, Terminology, Definitions; 3. The Measures of Pseudorandomness of Binary Functions on Almost Uniform Trees; 4. The Measures of Pseudorandomness of Binary Functions on General Trees; 5. Measures of Pseudorandomness for a Truly Random Binary Function Defined on a Given Tree; 6. Connection between the Measures of Pseudorandomness. 7. Finding a Binary Function with Strong Pseudorandom Properties on an Arbitrary TreeReferences; Chapter 2: CLASS NUMBER ONE CRITERIA FOR REAL QUADRATIC FIELDS WITH DISCRIMINANT k2p2 4p; Abstract; 1. Introduction; 2. Preliminaries; 3. Class Number One Criteria for = k2p2 4p; References; Chapter 3: SOME PRODUCT-TO-SUM IDENTITIES; Abstract; 1. Introduction; 2. A Product-to-Sum Identity; 3. Proof of Theorem 1.1; 4. Proof of Theorem 1.2; 5. Proof of Theorem 1.3; 6. Final Remarks; Chapter 4: A ZETA FUNCTION FOR JUGGLING SEQUENCES; Abstract; 1. Introduction. 2. Background and Notation: Juggling3. Background and Notation: Zeta Functions; 4. A Norm on Juggling Sequences; 5. Zeta Functions for Ground State Juggling Sequences; 6. A 3-Ball Juggling Zeta Function; 7. A Juggling Zeta Function on b Balls; 8. Locating the Zeroes of the Zeta Function on b Balls; 9. Conclusion; References; Chapter 5: A QUADRATIC TWIST OF THE ELLIPTIC CURVE; Abstract; 1. Introduction; 2. A Family of Twists; 3. The Rank of the Family; 4. Explicit Computation of the Rank; References; Chapter 6: DIVISIBILITY PROPERTIES OF HYPERGEOMETRIC POLYNOMIALS; Abstract. Abstract1. Introduction; 2. Proof of Theorem 1.1; Acknowledgments; References; Chapter 10: ON SOME CONJECTURES ON THE MONOTONICITY OF SOME ARITHMETICAL SEQUENCES; Abstract; 1. Introduction; 2. Bernoulli, Tangent and Euler Numbers; 3. Apéry, Delannoy and Franel Numbers; 4. Motzkin Numbers, Schr oder Numbers and Trinomial Coefficients; References; Chapter 11: COMPLEXITY OF TRAPEZOIDAL GRAPHS WITH DIFFERENT TRIANGULATIONS; Abstract; 1. Introduction; 2. Complexity of Trapeziodal Graphs; 3. Conclusion; Acknowledgments; References. |
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| series2 | Frontiers of combinatorics and number theory, |
| spelling | Frontiers in combinatorics and number theory. Volume 4 / Zhi-Wie Sun, editor. New York : Nova Publishers, [2013] ©2013 1 online resource (x, 209 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Frontiers of combinatorics and number theory, 2324-9536 Includes bibliographical references and index. Online resource; title from PDF title page (ebrary, viewed June 16, 2014). FRONTIERS OF COMBINATORICS AND NUMBER THEORY. VOLUME 4; LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA; CONTENTS; PREFACE; Chapter 1: PSEUDORANDOM BINARY FUNCTIONS ON ROOTED PLANE TREES; Abstract; 1. Introduction; 2. Notation, Terminology, Definitions; 3. The Measures of Pseudorandomness of Binary Functions on Almost Uniform Trees; 4. The Measures of Pseudorandomness of Binary Functions on General Trees; 5. Measures of Pseudorandomness for a Truly Random Binary Function Defined on a Given Tree; 6. Connection between the Measures of Pseudorandomness. 7. Finding a Binary Function with Strong Pseudorandom Properties on an Arbitrary TreeReferences; Chapter 2: CLASS NUMBER ONE CRITERIA FOR REAL QUADRATIC FIELDS WITH DISCRIMINANT k2p2 4p; Abstract; 1. Introduction; 2. Preliminaries; 3. Class Number One Criteria for = k2p2 4p; References; Chapter 3: SOME PRODUCT-TO-SUM IDENTITIES; Abstract; 1. Introduction; 2. A Product-to-Sum Identity; 3. Proof of Theorem 1.1; 4. Proof of Theorem 1.2; 5. Proof of Theorem 1.3; 6. Final Remarks; Chapter 4: A ZETA FUNCTION FOR JUGGLING SEQUENCES; Abstract; 1. Introduction. 2. Background and Notation: Juggling3. Background and Notation: Zeta Functions; 4. A Norm on Juggling Sequences; 5. Zeta Functions for Ground State Juggling Sequences; 6. A 3-Ball Juggling Zeta Function; 7. A Juggling Zeta Function on b Balls; 8. Locating the Zeroes of the Zeta Function on b Balls; 9. Conclusion; References; Chapter 5: A QUADRATIC TWIST OF THE ELLIPTIC CURVE; Abstract; 1. Introduction; 2. A Family of Twists; 3. The Rank of the Family; 4. Explicit Computation of the Rank; References; Chapter 6: DIVISIBILITY PROPERTIES OF HYPERGEOMETRIC POLYNOMIALS; Abstract. Abstract1. Introduction; 2. Proof of Theorem 1.1; Acknowledgments; References; Chapter 10: ON SOME CONJECTURES ON THE MONOTONICITY OF SOME ARITHMETICAL SEQUENCES; Abstract; 1. Introduction; 2. Bernoulli, Tangent and Euler Numbers; 3. Apéry, Delannoy and Franel Numbers; 4. Motzkin Numbers, Schr oder Numbers and Trinomial Coefficients; References; Chapter 11: COMPLEXITY OF TRAPEZOIDAL GRAPHS WITH DIFFERENT TRIANGULATIONS; Abstract; 1. Introduction; 2. Complexity of Trapeziodal Graphs; 3. Conclusion; Acknowledgments; References. This book contains papers on topics in combinatorics (including graph theory) or number theory. The subject areas within correspond to the MSC (Mathematics Subject Classification) codes 05, 11, 20D60, and 52. Some topics included in this compilation are pseudorandom binary functions on rooted plane trees; class number one criteria for real quadratic fields with discriminant k2p2 4p; some product-to-sum identities; a zeta function for juggling sequences; divisibility properties of hypergeometric polynomials; the distance between perfect numbers; a new proof of a theorem of Hamidoune avoiding; c. Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Analyse combinatoire. Théorie des nombres. MATHEMATICS General. bisacsh Combinatorial analysis fast Number theory fast Sun, Zhi-Wei, editor. Frontiers of combinatorics and number theory. FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=662150 Volltext |
| spellingShingle | Frontiers in combinatorics and number theory. Frontiers of combinatorics and number theory. FRONTIERS OF COMBINATORICS AND NUMBER THEORY. VOLUME 4; LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA; CONTENTS; PREFACE; Chapter 1: PSEUDORANDOM BINARY FUNCTIONS ON ROOTED PLANE TREES; Abstract; 1. Introduction; 2. Notation, Terminology, Definitions; 3. The Measures of Pseudorandomness of Binary Functions on Almost Uniform Trees; 4. The Measures of Pseudorandomness of Binary Functions on General Trees; 5. Measures of Pseudorandomness for a Truly Random Binary Function Defined on a Given Tree; 6. Connection between the Measures of Pseudorandomness. 7. Finding a Binary Function with Strong Pseudorandom Properties on an Arbitrary TreeReferences; Chapter 2: CLASS NUMBER ONE CRITERIA FOR REAL QUADRATIC FIELDS WITH DISCRIMINANT k2p2 4p; Abstract; 1. Introduction; 2. Preliminaries; 3. Class Number One Criteria for = k2p2 4p; References; Chapter 3: SOME PRODUCT-TO-SUM IDENTITIES; Abstract; 1. Introduction; 2. A Product-to-Sum Identity; 3. Proof of Theorem 1.1; 4. Proof of Theorem 1.2; 5. Proof of Theorem 1.3; 6. Final Remarks; Chapter 4: A ZETA FUNCTION FOR JUGGLING SEQUENCES; Abstract; 1. Introduction. 2. Background and Notation: Juggling3. Background and Notation: Zeta Functions; 4. A Norm on Juggling Sequences; 5. Zeta Functions for Ground State Juggling Sequences; 6. A 3-Ball Juggling Zeta Function; 7. A Juggling Zeta Function on b Balls; 8. Locating the Zeroes of the Zeta Function on b Balls; 9. Conclusion; References; Chapter 5: A QUADRATIC TWIST OF THE ELLIPTIC CURVE; Abstract; 1. Introduction; 2. A Family of Twists; 3. The Rank of the Family; 4. Explicit Computation of the Rank; References; Chapter 6: DIVISIBILITY PROPERTIES OF HYPERGEOMETRIC POLYNOMIALS; Abstract. Abstract1. Introduction; 2. Proof of Theorem 1.1; Acknowledgments; References; Chapter 10: ON SOME CONJECTURES ON THE MONOTONICITY OF SOME ARITHMETICAL SEQUENCES; Abstract; 1. Introduction; 2. Bernoulli, Tangent and Euler Numbers; 3. Apéry, Delannoy and Franel Numbers; 4. Motzkin Numbers, Schr oder Numbers and Trinomial Coefficients; References; Chapter 11: COMPLEXITY OF TRAPEZOIDAL GRAPHS WITH DIFFERENT TRIANGULATIONS; Abstract; 1. Introduction; 2. Complexity of Trapeziodal Graphs; 3. Conclusion; Acknowledgments; References. Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Analyse combinatoire. Théorie des nombres. MATHEMATICS General. bisacsh Combinatorial analysis fast Number theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85028802 http://id.loc.gov/authorities/subjects/sh85093222 |
| title | Frontiers in combinatorics and number theory. |
| title_auth | Frontiers in combinatorics and number theory. |
| title_exact_search | Frontiers in combinatorics and number theory. |
| title_full | Frontiers in combinatorics and number theory. Volume 4 / Zhi-Wie Sun, editor. |
| title_fullStr | Frontiers in combinatorics and number theory. Volume 4 / Zhi-Wie Sun, editor. |
| title_full_unstemmed | Frontiers in combinatorics and number theory. Volume 4 / Zhi-Wie Sun, editor. |
| title_short | Frontiers in combinatorics and number theory. |
| title_sort | frontiers in combinatorics and number theory |
| topic | Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Analyse combinatoire. Théorie des nombres. MATHEMATICS General. bisacsh Combinatorial analysis fast Number theory fast |
| topic_facet | Combinatorial analysis. Number theory. Analyse combinatoire. Théorie des nombres. MATHEMATICS General. Combinatorial analysis Number theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=662150 |
| work_keys_str_mv | AT sunzhiwei frontiersincombinatoricsandnumbertheoryvolume4 |