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Zero-sum problem

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589: 537: 125: 169: 516: 630: 438: 429:; Stanchescu, Y. With a foreword by Javier Cilleruelo, Marc Noy and Oriol Serra (Coordinators of the DocCourse). Basel: Birkhäuser. pp.  425:. Advanced Courses in Mathematics CRM Barcelona. Elsholtz, C.; Freiman, G.; Hamidoune, Y. O.; Hegyvári, N.; Károlyi, G.; Nathanson, M.; 473: 417:
Geroldinger, Alfred (2009). "Additive group theory and non-unique factorizations". In Geroldinger, Alfred; Ruzsa, Imre Z. (eds.).
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Reiher, Christian (2007), "On Kemnitz' conjecture concerning lattice-points in the plane",
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Erdős, Paul; Ginzburg, A.; Ziv, A. (1961). "Theorem in the additive number theory".
521: 89: 526:"Covering Systems, Restricted Sumsets, Zero-sum Problems and their Unification" 388: 338: 369: 174: 525: 193:− 2. (Indeed, the lower bound is easy to see: the multiset containing 51: 458:
Additive Number Theory: Inverse Problems and the Geometry of Sumsets
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after its discoverers. It may also be deduced from the
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The classic result in this area is the 1961 theorem of
556:" N.W. Sauer (ed.) R.E. Woodrow (ed.) B. Sands (ed.), 220:
More general results than this theorem exist, such as
189:, but that the same is not true of multisets of size 2 554:
Zero-sum trees: a survey of results and open problems
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Combinatorial number theory and additive group theory
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Finite and Infinite Combinatorics in Sets and Logic
544:Zero-Sum Ramsey Theory: Graphs, Sequences and More 163: 119: 624: 8: 46:. Concretely, given a finite abelian group 185:the sum of whose elements is a multiple of 631: 617: 120:{\displaystyle \mathbb {Z} /n\mathbb {Z} } 328: 141: 113: 112: 104: 100: 99: 97: 61:such that every sequence of elements of 370:"A Weighted Erdős-Ginzburg-Ziv Theorem" 271: 564:, Kluwer Acad. Publ. (1993) pp. 19–29 57:, one asks for the smallest value of 7: 585: 583: 181:− 1 integers has a subset of size 92:. They proved that for the group 42:problems about the structure of a 25: 205:-subset summing to a multiple of 587: 209:.) This result is known as the 173:Explicitly this says that any 1: 540:(open-access journal article) 462:Graduate Texts in Mathematics 456:Nathanson, Melvyn B. (1996). 603:. You can help Knowledge by 538:Zero-sum problems - A survey 517:Erdős, Ginzburg, Ziv Theorem 499:"Erdös-Ginzburg-Ziv theorem" 201:− 1 copies of 1 contains no 569:Zero-sum problems: a survey 504:Encyclopedia of Mathematics 368:Grynkiewicz, D. J. (2006), 686: 582: 211:Erdős–Ginzburg–Ziv theorem 18:Erdős-Ginzburg-Ziv theorem 389:10.1007/s00493-006-0025-y 339:10.1007/s11139-006-0256-y 281:Bull. Res. Council Israel 215:Cauchy–Davenport theorem 164:{\displaystyle k=2n-1.} 599:-related article is a 260:Zero-sum Ramsey theory 165: 121: 670:Mathematical problems 317:The Ramanujan Journal 305:Nathanson (1996) p.48 166: 122: 38:are certain kinds of 238:David J. Grynkiewicz 234:weighted EGZ theorem 226:Kemnitz's conjecture 197:− 1 copies of 0 and 140: 96: 44:finite abelian group 27:Mathematical problem 650:Combinatorics stubs 546:(workshop homepage) 255:Subset sum problem 250:Davenport constant 232:in 2003), and the 161: 117: 73:terms that sum to 612: 611: 579:(1996) pp. 93–113 464:. Vol. 165. 440:978-3-7643-8961-1 36:zero-sum problems 16:(Redirected from 677: 633: 626: 619: 591: 584: 550:Arie Bialostocki 512: 487: 452: 424: 409: 407: 374: 365: 359: 357: 332: 323:(1–3): 333–337, 312: 306: 303: 297: 296: 276: 230:Christian Reiher 170: 168: 167: 162: 126: 124: 123: 118: 116: 108: 103: 86:Abraham Ginzburg 21: 685: 684: 680: 679: 678: 676: 675: 674: 640: 639: 638: 637: 534: 532:Further reading 497: 494: 476: 466:Springer-Verlag 455: 441: 416: 413: 412: 372: 367: 366: 362: 314: 313: 309: 304: 300: 278: 277: 273: 268: 246: 222:Olson's theorem 138: 137: 94: 93: 50:and a positive 28: 23: 22: 15: 12: 11: 5: 683: 681: 673: 672: 667: 662: 657: 652: 642: 641: 636: 635: 628: 621: 613: 610: 609: 592: 581: 580: 573:Discrete Math. 565: 547: 541: 533: 530: 529: 528: 519: 513: 493: 492:External links 490: 489: 488: 474: 453: 439: 411: 410: 383:(4): 445–453, 360: 307: 298: 270: 269: 267: 264: 263: 262: 257: 252: 245: 242: 160: 157: 154: 151: 148: 145: 115: 111: 107: 102: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 682: 671: 668: 666: 663: 661: 660:Combinatorics 658: 656: 655:Ramsey theory 653: 651: 648: 647: 645: 634: 629: 627: 622: 620: 615: 614: 608: 606: 602: 598: 597:combinatorics 593: 590: 586: 578: 574: 570: 566: 563: 562:Nato ASI Ser. 559: 555: 551: 548: 545: 542: 539: 536: 535: 531: 527: 523: 520: 518: 514: 510: 506: 505: 500: 496: 495: 491: 485: 481: 477: 475:0-387-94655-1 471: 467: 463: 459: 454: 450: 446: 442: 436: 432: 428: 423: 422: 415: 414: 406: 402: 398: 394: 390: 386: 382: 378: 377:Combinatorica 371: 364: 361: 356: 352: 348: 344: 340: 336: 331: 326: 322: 318: 311: 308: 302: 299: 294: 290: 286: 282: 275: 272: 265: 261: 258: 256: 253: 251: 248: 247: 243: 241: 239: 235: 231: 227: 223: 218: 216: 212: 208: 204: 200: 196: 192: 188: 184: 180: 176: 171: 158: 155: 152: 149: 146: 143: 135: 133: 130: 109: 105: 91: 87: 83: 78: 76: 72: 68: 64: 60: 56: 53: 49: 45: 41: 40:combinatorial 37: 33: 32:number theory 19: 605:expanding it 594: 576: 572: 561: 557: 522:Sun, Zhi-Wei 502: 457: 427:Solymosi, J. 420: 380: 376: 363: 320: 316: 310: 301: 284: 280: 274: 219: 210: 206: 202: 198: 194: 190: 186: 182: 178: 172: 136: 131: 127:of integers 79: 70: 66: 62: 58: 54: 47: 35: 29: 515:PlanetMath 236:(proved by 228:(proved by 90:Abraham Ziv 665:Paul Erdős 644:Categories 567:Y. Caro, " 484:0859.11003 449:1221.20045 405:1121.11018 355:1126.11011 330:1603.06161 293:0063.00009 266:References 240:in 2005). 82:Paul Erdős 509:EMS Press 347:119600313 287:: 41–43. 156:− 69:contains 397:33448594 244:See also 175:multiset 65:of size 511:, 2001 52:integer 482:  472:  447:  437:  403:  395:  353:  345:  291:  129:modulo 88:, and 595:This 433:–86. 393:S2CID 373:(PDF) 343:S2CID 325:arXiv 601:stub 470:ISBN 435:ISBN 177:of 2 577:152 552:, " 480:Zbl 445:Zbl 401:Zbl 385:doi 351:Zbl 335:doi 289:Zbl 285:10F 224:, 30:In 646:: 575:, 571:" 560:, 524:, 507:, 501:, 478:. 468:. 460:. 443:. 399:, 391:, 381:26 379:, 375:, 349:, 341:, 333:, 321:13 319:, 283:. 217:. 159:1. 134:, 84:, 77:. 34:, 632:e 625:t 618:v 607:. 486:. 451:. 431:1 408:. 387:: 358:. 337:: 327:: 295:. 207:n 203:n 199:n 195:n 191:n 187:n 183:n 179:n 153:n 150:2 147:= 144:k 132:n 114:Z 110:n 106:/ 101:Z 75:0 71:n 67:k 63:G 59:k 55:n 48:G 20:)

Index

Erdős-Ginzburg-Ziv theorem
number theory
combinatorial
finite abelian group
integer
0
Paul Erdős
Abraham Ginzburg
Abraham Ziv
modulo
multiset
Cauchy–Davenport theorem
Olson's theorem
Kemnitz's conjecture
Christian Reiher
weighted EGZ theorem
David J. Grynkiewicz
Davenport constant
Subset sum problem
Zero-sum Ramsey theory
Zbl
0063.00009
arXiv
1603.06161
doi
10.1007/s11139-006-0256-y
S2CID
119600313
Zbl
1126.11011

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