Knowledge

XYZ inequality

Source đź“ť

36: 258: 419: 341: 315: 286: 165: 65: 17: 587: 353: 519: 582: 87: 58: 497: 425: 507: 502: 48: 52: 44: 344: 69: 320: 294: 577: 271: 561: 482: 8: 515: 549: 486: 541: 490: 470: 450: 133: 531: 462: 113: 557: 478: 437: 125: 253:{\displaystyle P(x\prec y)P(x\prec z)\leqslant P((x\prec y)\wedge (x\prec z))} 571: 545: 536: 474: 117: 101: 27:
Inequality for the number of extensions of partial orders to linear orders
553: 466: 453:(1984), "A correlational inequality for linear extensions of a poset", 268:(A) is the probability that a linear order extending the partial order 121: 414:{\displaystyle P(x\prec z)\leqslant P(x\prec z\mid x\prec y).} 156: 356: 323: 297: 274: 168: 530:(3), Institute of Mathematical Statistics: 824–827, 413: 335: 309: 280: 252: 569: 57:but its sources remain unclear because it lacks 520:"The XYZ conjecture and the FKG inequality" 535: 317:increases if one adds the condition that 124:and Bill Sands in 1981. It was proved by 88:Learn how and when to remove this message 449: 137: 14: 570: 155:are incomparable elements of a finite 514: 291:In other words, the probability that 129: 112:, is an inequality for the number of 120:. The inequality was conjectured by 29: 24: 25: 599: 588:Independence (probability theory) 34: 405: 381: 372: 360: 247: 244: 232: 226: 214: 211: 202: 190: 184: 172: 13: 1: 443: 132:. An extension was given by 7: 503:Encyclopedia of Mathematics 498:"Fishburn-Shepp inequality" 431: 10: 604: 426:Ahlswede–Daykin inequality 583:Theorems in combinatorics 524:The Annals of Probability 110:Fishburn–Shepp inequality 18:Fishburn–Shepp inequality 336:{\displaystyle x\prec y} 310:{\displaystyle x\prec z} 43:This article includes a 345:conditional probability 72:more precise citations. 537:10.1214/aop/1176993791 415: 343:. In the language of 337: 311: 282: 281:{\displaystyle \prec } 254: 416: 338: 312: 283: 255: 354: 321: 295: 288:has the property A. 272: 166: 424:The proof uses the 467:10.1007/BF00565648 451:Fishburn, Peter C. 411: 333: 307: 278: 250: 143:It states that if 108:, also called the 45:list of references 114:linear extensions 104:mathematics, the 98: 97: 90: 16:(Redirected from 595: 564: 539: 511: 493: 420: 418: 417: 412: 342: 340: 339: 334: 316: 314: 313: 308: 287: 285: 284: 279: 259: 257: 256: 251: 93: 86: 82: 79: 73: 68:this article by 59:inline citations 38: 37: 30: 21: 603: 602: 598: 597: 596: 594: 593: 592: 568: 567: 496: 446: 434: 355: 352: 351: 322: 319: 318: 296: 293: 292: 273: 270: 269: 167: 164: 163: 138:Fishburn (1984) 94: 83: 77: 74: 63: 49:related reading 39: 35: 28: 23: 22: 15: 12: 11: 5: 601: 591: 590: 585: 580: 566: 565: 512: 494: 461:(2): 127–137, 445: 442: 441: 440: 438:FKG inequality 433: 430: 422: 421: 410: 407: 404: 401: 398: 395: 392: 389: 386: 383: 380: 377: 374: 371: 368: 365: 362: 359: 332: 329: 326: 306: 303: 300: 277: 262: 261: 249: 246: 243: 240: 237: 234: 231: 228: 225: 222: 219: 216: 213: 210: 207: 204: 201: 198: 195: 192: 189: 186: 183: 180: 177: 174: 171: 134:Peter Fishburn 126:Lawrence Shepp 118:partial orders 106:XYZ inequality 96: 95: 53:external links 42: 40: 33: 26: 9: 6: 4: 3: 2: 600: 589: 586: 584: 581: 579: 576: 575: 573: 563: 559: 555: 551: 547: 543: 538: 533: 529: 525: 521: 517: 513: 509: 505: 504: 499: 495: 492: 488: 484: 480: 476: 472: 468: 464: 460: 456: 452: 448: 447: 439: 436: 435: 429: 427: 408: 402: 399: 396: 393: 390: 387: 384: 378: 375: 369: 366: 363: 357: 350: 349: 348: 346: 330: 327: 324: 304: 301: 298: 289: 275: 267: 241: 238: 235: 229: 223: 220: 217: 208: 205: 199: 196: 193: 187: 181: 178: 175: 169: 162: 161: 160: 158: 154: 150: 146: 141: 139: 135: 131: 127: 123: 119: 115: 111: 107: 103: 102:combinatorial 92: 89: 81: 71: 67: 61: 60: 54: 50: 46: 41: 32: 31: 19: 578:Inequalities 527: 523: 516:Shepp, L. A. 501: 458: 454: 423: 290: 265: 263: 152: 148: 144: 142: 130:Shepp (1982) 109: 105: 99: 84: 75: 64:Please help 56: 78:August 2022 70:introducing 572:Categories 444:References 122:Ivan Rival 116:of finite 546:0091-1798 508:EMS Press 491:121406218 475:0167-8094 400:≺ 394:∣ 388:≺ 376:⩽ 367:≺ 328:≺ 302:≺ 276:≺ 239:≺ 230:∧ 221:≺ 206:⩽ 197:≺ 179:≺ 518:(1982), 432:See also 562:0659563 554:2243391 510:, 2001 483:0764320 159:, then 66:improve 560:  552:  544:  489:  481:  473:  264:where 151:, and 550:JSTOR 487:S2CID 455:Order 157:poset 51:, or 542:ISSN 471:ISSN 128:in 532:doi 463:doi 136:in 100:In 574:: 558:MR 556:, 548:, 540:, 528:10 526:, 522:, 506:, 500:, 485:, 479:MR 477:, 469:, 457:, 428:. 347:, 147:, 140:. 55:, 47:, 534:: 465:: 459:1 409:. 406:) 403:y 397:x 391:z 385:x 382:( 379:P 373:) 370:z 364:x 361:( 358:P 331:y 325:x 305:z 299:x 266:P 260:, 248:) 245:) 242:z 236:x 233:( 227:) 224:y 218:x 215:( 212:( 209:P 203:) 200:z 194:x 191:( 188:P 185:) 182:y 176:x 173:( 170:P 153:z 149:y 145:x 91:) 85:( 80:) 76:( 62:. 20:)

Index

Fishburn–Shepp inequality
list of references
related reading
external links
inline citations
improve
introducing
Learn how and when to remove this message
combinatorial
linear extensions
partial orders
Ivan Rival
Lawrence Shepp
Shepp (1982)
Peter Fishburn
Fishburn (1984)
poset
conditional probability
Ahlswede–Daykin inequality
FKG inequality
Fishburn, Peter C.
doi
10.1007/BF00565648
ISSN
0167-8094
MR
0764320
S2CID
121406218
"Fishburn-Shepp inequality"

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

↑