Symmetric functions and combinatorial operators on polynomials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2003
|
| Series: | Regional conference series in mathematics
99 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XI, 268 S. |
| ISBN: | 0821828711 |
Staff View
MARC
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| 245 | 1 | 0 | |a Symmetric functions and combinatorial operators on polynomials |c Alain Lascoux |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2003 | |
| 300 | |a XI, 268 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Regional conference series in mathematics |v 99 | |
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 7 | |a Fonctions symétriques |2 ram | |
| 650 | 7 | |a Fractions continues |2 ram | |
| 650 | 7 | |a Padé, Approximants de |2 ram | |
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Record in the Search Index
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| adam_text | Contents
Preface vii
Chapter 1. Symmetric functions 1
1.1. Alphabets 1
1.2. Partitions 1
1.3. Generating Functions of Symmetric Functions 5
1.4. Matrix Generating Functions 7
1.5. Cauchy Formula 13
1.6. Scalar Product 14
1.7. Differential Calculus 16
1.8. Operators on Isobaric Determinants 18
1.9. Pieri Formulas 22
Exercises 24
Chapter 2. Symmetric Functions as Operators and A Rings 31
2.1. Algebraic Operations on Alphabets 31
2.2. Lambda Operations 32
2.3. Interpreting Polynomials and ^ series 33
2.4. Lagrange Inversion 35
2.5. Some relations between multiples of alphabets 36
Exercises 38
Chapter 3. Euclidean Division 47
3.1. Euclid s Algorithm 47
3.2. Remainders as Schur functions 50
3.3. Companion Matrix 51
3.4. Bezout s Matrix 52
3.5. Sylvester s Summations 54
3.6. Sturm Sequence 55
3.7. Wroriski s Algorithm 57
3.8. Division and Continued Fractions 57
Exercises 59
Chapter 4. Reciprocal Differences and Continued Fractions 63
4.1. Euler s Recursions 63
4.2. Continued Fraction Expression of a Formal Series 64
4.3. Interpolation of a Function by a Continued Fraction 66
4.4. Relation between Stieltjes and Wronski Continued Fractions 69
4.5. Jacobi s Tridiagonal Matrix 70
4.6. Motzkin Paths 71
iv CONTENTS
4.7. Dyck Paths 72
4.8. Link between Enumeration of Motzkin and Dyck Paths 73
Exercises 75
Chapter 5. Division, encore 79
5.1. Derived Alphabets 79
5.2. Normalized Differences 81
5.3. Associated Continued Fractions 82
5.4. Hankel Forms 83
Exercises 84
Chapter 6. Pade Approximants 87
6.1. Recovering a Rational Function from a Taylor Series 87
6.2. Pade Table 88
6.3. Euclid and Pade 89
6.4. Rational Interpolation 90
Exercises 92
Chapter 7. Symmetrizing Operators 95
7.1. Divided Differences 95
7.2. Compatibility with Complete Functions 97
7.3. Braid Relations 97
7.4. Decomposing in the Basis of Permutations 99
7.5. Generating Series by Symmetrization 100
7.6. Maximal Symmetrizers 101
7.7. Schur Functions and Bott s Theorem 102
7.8. Lagrange Interpolation 105
7.9. Finite Derivation 108
7.10. Calogero s Raising and Lowering Operators 110
Exercises 112
Chapter 8. Orthogonal Polynomials 117
8.1. Orthogonal Polynomials as Symmetric Functions 117
8.2. Reproducing Kernels 118
8.3. Continued Fractions 119
8.4. Higher Order Kernels 120
8.5. Even Moments 123
8.6. Zeros 125
8.7. The Moment Generating Function 128
8.8. Jacobi s Matrix and Paths 129
8.9. Discrete Measures 131
Exercises 133
Chapter 9. Schubert Polynomials 141
9.1. Newton Interpolation Formula 141
9.2. Newton and Euclid 142
9.3. Discrete Wronskian 143
9.4. Schubert Polynomials 145
9.5. Vanishing Properties 147
9.6. Newton Interpolation in Several Variables 148
CONTENTS V
9.7. Interpolation of Symmetric Functions 150
9.8. Key Polynomials 152
Exercises 153
Chapter 10. The Ring of Polynomials as a Module over Symmetric Ones 157
10.1. Quadratic Form on ^M 157
10.2. Kernel 158
10.3. Shifts 162
10.4. Generating Function in the NilCoxeter Algebra 163
10.5. NilPlactic Kernel 165
10.6. Basis of Elementary Symmetric Functions 168
10.7. Yang Baxter Basis 170
10.8. Yang Baxter Elements as Permutations 172
Exercises 174
Chapter 11. The plactic algebra 175
11.1. Tableaux 175
11.2. Plactic Algebra 176
11.3. Littlewood Richardson Rule 178
11.4. Action of the Symmetric Group on the Free Algebra 179
11.5. Free Key Polynomials 181
11.6. Plactic Schubert Polynomials 182
Appendix A. Complements 185
A.I. Minor Identities 185
A.2. Exact sequences 190
A.3. Cauchy Residue Formula 192
A.4. Differential calculus on symmetric functions 195
Appendix B. Solutions of exercises 197
B.I 197
B.2 205
B.3 217
B.4 222
B.5 224
B.6 228
B.7 231
B.8 238
B.9 253
B.10 257
Bibliography 261
Index 267
|
| any_adam_object | 1 |
| author | Lascoux, Alain ca. 20. Jh./21. Jh |
| author_GND | (DE-588)12984554X |
| author_facet | Lascoux, Alain ca. 20. Jh./21. Jh |
| author_role | aut |
| author_sort | Lascoux, Alain ca. 20. Jh./21. Jh |
| author_variant | a l al |
| building | Verbundindex |
| bvnumber | BV017622863 |
| classification_rvk | SI 195 |
| ctrlnum | (OCoLC)470420908 (DE-599)BVBBV017622863 |
| dewey-full | 515.22 512.94 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 512 - Algebra |
| dewey-raw | 515.22 512.94 |
| dewey-search | 515.22 512.94 |
| dewey-sort | 3515.22 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)1071861417 Konferenzschrift 2001 Raleigh NC gnd-content |
| genre_facet | Konferenzschrift 2001 Raleigh NC |
| id | DE-604.BV017622863 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:20:02Z |
| institution | BVB |
| isbn | 0821828711 |
| language | English |
| lccn | 2003066740 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010601463 |
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| physical | XI, 268 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | American Mathematical Society |
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| series | Regional conference series in mathematics |
| series2 | Regional conference series in mathematics |
| spelling | Lascoux, Alain ca. 20. Jh./21. Jh. Verfasser (DE-588)12984554X aut Symmetric functions and combinatorial operators on polynomials Alain Lascoux Providence, R.I. American Mathematical Society 2003 XI, 268 S. txt rdacontent n rdamedia nc rdacarrier Regional conference series in mathematics 99 Includes bibliographical references and index Euclide, Algorithme d' ram Fonctions symétriques ram Fractions continues ram Padé, Approximants de ram Polynômes orthogonaux ram Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Symmetrische Funktion (DE-588)4342453-3 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2001 Raleigh NC gnd-content Symmetrische Funktion (DE-588)4342453-3 s Polynom (DE-588)4046711-9 s Gruppentheorie (DE-588)4072157-7 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Regional conference series in mathematics 99 (DE-604)BV000004346 99 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010601463&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lascoux, Alain ca. 20. Jh./21. Jh Symmetric functions and combinatorial operators on polynomials Regional conference series in mathematics Euclide, Algorithme d' ram Fonctions symétriques ram Fractions continues ram Padé, Approximants de ram Polynômes orthogonaux ram Gruppentheorie (DE-588)4072157-7 gnd Polynom (DE-588)4046711-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd Symmetrische Funktion (DE-588)4342453-3 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4046711-9 (DE-588)4148816-7 (DE-588)4342453-3 (DE-588)1071861417 |
| title | Symmetric functions and combinatorial operators on polynomials |
| title_auth | Symmetric functions and combinatorial operators on polynomials |
| title_exact_search | Symmetric functions and combinatorial operators on polynomials |
| title_full | Symmetric functions and combinatorial operators on polynomials Alain Lascoux |
| title_fullStr | Symmetric functions and combinatorial operators on polynomials Alain Lascoux |
| title_full_unstemmed | Symmetric functions and combinatorial operators on polynomials Alain Lascoux |
| title_short | Symmetric functions and combinatorial operators on polynomials |
| title_sort | symmetric functions and combinatorial operators on polynomials |
| topic | Euclide, Algorithme d' ram Fonctions symétriques ram Fractions continues ram Padé, Approximants de ram Polynômes orthogonaux ram Gruppentheorie (DE-588)4072157-7 gnd Polynom (DE-588)4046711-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd Symmetrische Funktion (DE-588)4342453-3 gnd |
| topic_facet | Euclide, Algorithme d' Fonctions symétriques Fractions continues Padé, Approximants de Polynômes orthogonaux Gruppentheorie Polynom Darstellungstheorie Symmetrische Funktion Konferenzschrift 2001 Raleigh NC |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010601463&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
| work_keys_str_mv | AT lascouxalain symmetricfunctionsandcombinatorialoperatorsonpolynomials |