Additive combinatorics: a menue of research problems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
CRC Press, Taylor & Francis Group
[2018]
|
| Schriftenreihe: | Discrete mathematics and its applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and author index |
| Beschreibung: | xix, 390 Seiten |
| ISBN: | 9780815353010 |
Internformat
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| 245 | 1 | 0 | |a Additive combinatorics |b a menue of research problems |c Béla Bajnok |
| 264 | 1 | |a Boca Raton |b CRC Press, Taylor & Francis Group |c [2018] | |
| 264 | 4 | |c © 2018 | |
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| 490 | 0 | |a Discrete mathematics and its applications | |
| 500 | |a Includes bibliographical references and author index | ||
| 650 | 4 | |a Additive combinatorics | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 4 | |a Number theory | |
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Datensatz im Suchindex
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| adam_text | Contents Preface xi Notations xv I Ingredients 1 1 Number theory 5 1.1 1.2 1.3 1.4 1.5 2 Divisibility of integers...................................................................................... Congruences....................................................................................................... The Fundamental Theorem of NumberTheory............................................. Multiplicative number theory.......................................................................... Additive number theory................................................................................... 5 7 8 9 11 Combinatorics 2.1 Basic enumeration principles .......................................................................... 2.2 Counting lists, sequences, sets,and multisets ................................................. 2.3 Binomial coefficients andPascal’s Triangle...................................................... 2.4 Some recurrence relations................................................................................ 2.5 The integer lattice and its layers.................................................................... 15 3 Group theory 3.1 3.2 3.3 3.4 3.5 3.6 II 15 17 21 23 26 31 Finite abelian groups......................................................................................... Group isomorphisms........................................................................................ The Fundamental Theorem of Finite Abelian Groups................................... Subgroups and
cosets........................................................................................ Subgroups generated by subsets....................................................................... Sumsets............................................................................................................. Appetizers 32 33 34 36 39 40 47 Spherical designs....................................................................................................... Caps, centroids, and the gameSET........................................................................... How many elements does it take to span a group? ................................................. In pursuit of perfection ............................................................................................ The declaration of independence............................................................................. v 50 56 62 65 69
vi CONTENTS III Sides The The The The IV function function function function 73 Vg{n,h).................................................................................................. v± (n, h) ............................................................................................... u(n, m,h) ............................................................................................ u (n, m,h)............................................................................................ Entrees A Maximum sumset size A.l Unrestricted sumsets......................................................................................... A. 1.1 Fixed number of terms........................................................................... A. 1.2 Limited number of terms ..................................................................... A.1.3 Arbitrary number of terms .................................................................. A.2 Unrestricted signed sumsets.............................................................................. A.2.1 Fixed number of terms.......................................................................... A.2.2 Limited number of terms ..................................................................... A.2.3 Arbitrary number of terms ................................................................. A.3 Restricted sumsets............................................................................................ A.3.1 Fixed number of terms . ........................................................................ A.3.2 Limited number of
terms ..................................................................... A.3.3 Arbitrary number of terms .................................................................. A.4 Restricted signed sumsets................................................................................ A.4.1 Fixed number of terms.......................................................................... A.4.2 Limited number of terms .................................................................... A.4.3 Arbitrary number of terms ................................................................. В 76 81 83 86 93 97 97 98 99 100 101 101 103 104 104 104 105 106 107 107 108 109 Spanning sets 111 Unrestricted sumsets........................................................................................ 112 B.1.1 Fixed number of terms........................................................................... 112 B.l.2 Limited number of terms .................................................................... 112 B.1.3 Arbitrary number of terms .................................................................. 119 B.2 Unrestricted signed sumsets............................................................................. 119 B.2.1 Fixed number of terms.......................................................................... 119 B.2.2 Limited number of terms ..................................................................... 122 B.2.3 Arbitrary number of terms .................................................................. 127 B.3 Restricted
sumsets........................................................................................... 127 B.3.1 Fixed number of terms.......................................................................... 127 B.3.2 Limited number of terms .................................................................... 127 B.3.3 Arbitrary number of terms .................................................................. 129 B.4 Restricted signed sumsets............................................................................... 129 B.4.1 Fixed number of terms.......................................................................... 129 B.4.2 Limited number of terms .................................................................... 129 B.4.3 Arbitrary number of terms ................................................................. 129 B.l C Sidon sets 131 Unrestricted sumsets........................................................................................ 132 C.1.1 Fixed number of terms.......................................................................... 132 C.l.2 Limited number of terms ..................................................................... 139 C.1.3 Arbitrary number of terms .................................................................. 139 C.2 Unrestricted signed sumsets............................................................................ 139 C.l
CONTENTS C.2.1 Fixed number of terms.......................................................................... C.2.2 Limited number of terms .................................................................... C.2.3 Arbitrary number of terms ................................................................. C.3 Restricted sumsets............................................................................................ C.3.1 Fixed number of terms.......................................................................... C.3.2 Limited number of terms .................................................................... C.3.3 Arbitrary number of terms ................................................................. C.4 Restricted signed sumsets................................................................................ C.4.1 Fixed number of terms.......................................................................... C.4.2 Limited number of terms .................................................................... C.4.3 Arbitrary number of terms ................................................................. D Minimum sumset size D.l Unrestricted sumsets......................................................................................... D.1.1 Fixed number of terms.......................................................................... D.l.2 Limited number of terms .................................................................... D.1.3 Arbitrary number of terms ................................................................. D.2 Unrestricted signed
sumsets............................................................................ D.2.1 Fixed number of terms.......................................................................... D.2.2 Limited number of terms .................................................................... D.2.3 Arbitrary number of terms ................................................................. D.3 Restricted sumsets........................................................................................... D.3.1 Fixed number of terms.......................................................................... D.3.2 Limited number of terms .................................................................... D.3.3 Arbitrary number of terms ................................................................. D.4 Restricted signed sumsets............................................................................... D.4.1 Fixed number of terms.......................................................................... D.4.2 Limited number of terms .................................................................... D.4.3 Arbitrary number of terms ................................................................. E The critical number E.l Unrestricted sumsets........................................................................................ E.1.1 Fixed number of terms.......................................................................... E.l.2 Limited number of terms .................................................................... E.1.3 Arbitrary number of terms
................................................................. E.2 Unrestricted signed sumsets............................................................................ E.2.1 Fixed number of terms.......................................................................... E.2.2 Limited number of terms .................................................................... E.2.3 Arbitrary number of terms ................................................................. E.3 Restricted sumsets........................................................................................... E.3.1 Fixed number of terms.......................................................................... E.3.2 Limited number of terms .................................................................... E.3.3 Arbitrary number of terms ................................................................. E.4 Restricted signed sumsets............................................................................... E.4.1 Fixed number of terms.......................................................................... E.4.2 Limited number of terms .................................................................... E.4.3 Arbitrary number of terms ................................................................. vii 140 142 143 143 143 145 147 147 147 147 147 149 149 149 155 156 156 156 161 163 163 163 183 184 191 191 191 191 193 193 193 196 201 202 202 203 207 207 207 212 214 223 223 223 223
CONTENTS viii F Zero-sum-free sets 225 F.l Unrestricted sumsets........................................................................................ 225 F.1.1 Fixed number of terms.......................................................................... 226 F.l.2 Limited number of terms .................................................................... 230 F.1.3 Arbitrary number of terms ................................................................. 231 F.2 Unrestricted signed sumsets............................................................................ 231 F.2.1 Fixed number of terms.......................................................................... 231 F.2.2 Limited number of terms.................................................................... 235 F.2.3 Arbitrary number of terms ................................................................. 245 F.3 Restricted sumsets........................................................................................... 246 F.3.1 Fixed number of terms.......................................................................... 246 F.3.2 Limited number of terms .................................................................... 258 F.3.3 Arbitrary number of terms ................................................................. 261 F.4 Restricted signed sumsets............................................................................... 266 F.4.1 Fixed number of terms.......................................................................... 266 F.4.2 Limited number of terms
.................................................................... 269 F.4.3 Arbitrary number of terms ................................................................. 271 G Sum-free sets 275 G.l Unrestricted sumsets......................................................................................... 276 G.1.1 Fixed number of terms.......................................................................... 276 G.l.2 Limited number of terms .................................................................... 290 G.1.3 Arbitrary number of terms ................................................................. 293 G.2 Unrestricted signed sumsets....................................................................... .. . 293 G.2.1 Fixed number of terms.......................................................................... 293 G.2.2 Limited number of terms .................................................................... 293 G.2.3 Arbitrary number of terms ................................................................. 293 G.3 Restricted sumsets............................................................................................ 294 G.3.1 Fixed number of terms.......................................................................... 294 G.3.2 Limited number of terms .................................................................... 303 G.3.3 Arbitrary number of terms ................................................................. 303 G.4 Restricted signed sumsets................................................................................ 303 G.4.1
Fixed number of terms.......................................................................... 303 G.4.2 Limited number of terms .................................................................... 303 G.4.3 Arbitrary number of terms ................................................................. 303 V Pudding Proof of Proposition 2.2............................................................................................ Proof of Proposition 3.1............................................................................................ Proof of Proposition 3.4............................................................................................ Proof of Proposition 3.5............................................................................................ Proof of Proposition 4.2............................................................................................ Proof of Proposition 4.3............................................................................................ Proof of Theorem 4.4.................................................................................................. Proof of Proposition 4.9............................................................................................ Proof of Proposition 4.10 ......................................................................................... Proof of Theorem 4.17............................................................................................... Proof of Proposition 4.22
......................................................................................... Proof of Proposition 4.23 ......................................................................................... Proof of Proposition 4.26 ......................................................................................... 305 308 309 309 311 311 313 314 315 317 318 318 319 320
CONTENTS Proof of Proposition 4.29 ......................................................................................... Proof of Proposition A.42 ......................................................................................... Proof of Theorem B.8............................................................................................... Proof of Proposition B.28 ......................................................................................... Proof of Proposition B.46 ......................................................................................... Proof of Proposition B.54 ......................................................................................... Proof of Proposition B.57 ......................................................................................... Proof of Proposition C.36 ......................................................................................... Proof of Proposition C.50 ......................................................................................... Proof of Proposition C.51......................................................................................... Proof of Proposition D.6............................................................................................ Proof of Theorem D.8............................................................................................... Proof of Theorem D.9............................................................................................... Proof of Theorem
D.10............................................................................................... Proof of Theorem D.40............................................................................................... Proof of Proposition D.42 ......................................................................................... Proof of Theorem D.47 ............................................................................................... Proof of Proposition D.59 ......................................................................................... Proof of Theorem D.72 .............................................................................................. Proof of Proposition D.128 ...................................................................................... Proof of Theorem E. 15 . . . ...................................................................................... Proof of Proposition E.76 ......................................................................................... Proof of Lemma E.87 ............................................................................................... Proof of Theorem E.100 ............................................................................................ Proof of Theorem E.108 ............................................................................................ Proof of Theorem E.109 ............................................................................................ Proof of Theorem
F.6............................................................................................... Proof of Proposition F.27 ......................................................................................... Proof of Proposition F.28 ......................................................................................... Proof of Proposition F.32 ......................................................................................... Proof of Proposition F.35 ......................................................................................... Proof of Proposition F.46 ......................................................................................... Proof of Proposition F.80 ......................................................................................... Proof of Proposition F.83 ......................................................................................... Proof of Theorem F.88 ............................................................................................... Proof of Proposition F.116......................................................................................... Proof of Proposition F.156 ......................................................................................... Proof of Proposition F.179 ......................................................................................... Proof of Proposition G.22 ......................................................................................... Proof of Theorem
G.27............................................................................................... Proof of Proposition G.64 ......................................................................................... Proof of Corollary G.65 ............................................................................................ Proof of Theorem G.67.............................................................................................. Proof of Proposition G.73 ......................................................................................... Proof of Proposition G.74 ......................................................................................... Proof of Proposition G.82 ......................................................................................... ix 321 322 323 325 325 327 327 329 330 331 332 333 334 335 335 336 337 344 346 348 349 350 350 351 351 353 354 355 356 356 357 358 360 361 362 363 363 365 365 368 369 370 372 373 373 374 Bibliography 377 Author Index 388
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| isbn | 9780815353010 |
| language | English |
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| spelling | Bajnok, Béla 1961- Verfasser (DE-588)1035619946 aut Additive combinatorics a menue of research problems Béla Bajnok Boca Raton CRC Press, Taylor & Francis Group [2018] © 2018 xix, 390 Seiten txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications Includes bibliographical references and author index Additive combinatorics Combinatorial analysis Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s Kombinatorische Analysis (DE-588)4164746-4 s Zahlentheorie (DE-588)4067277-3 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030801403&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bajnok, Béla 1961- Additive combinatorics a menue of research problems Additive combinatorics Combinatorial analysis Number theory Zahlentheorie (DE-588)4067277-3 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd Kombinatorik (DE-588)4031824-2 gnd |
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| title | Additive combinatorics a menue of research problems |
| title_auth | Additive combinatorics a menue of research problems |
| title_exact_search | Additive combinatorics a menue of research problems |
| title_full | Additive combinatorics a menue of research problems Béla Bajnok |
| title_fullStr | Additive combinatorics a menue of research problems Béla Bajnok |
| title_full_unstemmed | Additive combinatorics a menue of research problems Béla Bajnok |
| title_short | Additive combinatorics |
| title_sort | additive combinatorics a menue of research problems |
| title_sub | a menue of research problems |
| topic | Additive combinatorics Combinatorial analysis Number theory Zahlentheorie (DE-588)4067277-3 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Additive combinatorics Combinatorial analysis Number theory Zahlentheorie Kombinatorische Analysis Kombinatorik |
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