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states that for each assignment of finitely many colors to the positive integers, there exist arbitrarily large sets of integers all of whose nonempty sums have the same color; the name was chosen as a memorial to
Folkman by his friends. In
477:. After his brain surgery, Folkman was despairing that he had lost his mathematical skills. As soon as Folkman received Graham and Erdős at the hospital, Erdős challenged Folkman with mathematical problems, helping to rebuild his
1015:
J. Folkman: An upper bound on the chromatic number of a graph, in: Combinatorial theory and its application, II (Proc. Colloq., Balatonfüred, 1969), North-Holland, Amsterdam, 1970, 437–457.
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visited Jon
Folkman after Folkman awoke from surgery for brain cancer. To restore Folkman's confidence, Erdős immediately challenged him to solve
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For r > max{p, q}, let F(p, q; r) denote the minimum number of vertices in a graph G that has the following properties:
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639:
488:, blamed himself for failing to notice suicidal behaviors in Folkman. Several years later Fulkerson also killed himself.
1028:(1969), "Quasi-equilibria in markets with non-convex preferences (Appendix 2: The Shapley–Folkman theorem, pp. 35–37)",
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291:, and he discovered the semi-symmetric graph with the fewest possible vertices, now known as the
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The
Folkman-Lawrence representation theorem is called the "Lawrence representation theorem" by
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The man who loved only numbers: the story of Paul Erdős and the search for mathematical truth
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Folkman, J. (1970), "Graphs with monochromatic complete subgraphs in every edge coloring",
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173:(December 8, 1938 – January 23, 1969) was an American mathematician, a student of
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891:"On the foundations of combinatorial theory, I: Theory of Möbius functions"
848:"On the foundations of combinatorial theory, I: Theory of Möbius functions"
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Folkman later purchased a gun and killed himself. Folkman's supervisor at RAND,
209:
174:
158:
42:
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273:
257:
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1110:
Erickson, Martin (1993). "An upper bound for the
Folkman number F(3, 3; 5)".
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236:, Folkman is known for his pioneering and posthumously-published studies of
1125:
733:. Graduate texts in mathematics. Vol. 152. New York: Springer-Verlag.
610:
264:; in proving Rota's conjecture, Folkman characterized the structure of the
1147:
Dudek, Andrzej; Rödl, Vojtěch (2008). "On the
Folkman Number f(2, 3, 4)".
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in every 2-coloring of the edges, settling a problem previously posed by
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847:
588:
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in any green-red coloring of the edges of G there is either a green K
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is "one of the cornerstones of the theory of oriented matroids". In
449:
208:
852:
758:"III Enumeration in geometric lattices, 2. Homology"
626:, Mathematical Association of America, retrieved 2010-10-17.
225:
Jon
Folkman contributed important theorems in many areas of
197:, under the supervision of Milnor, with a thesis entitled
791:
Folkman, Jon (1966). "The homology groups of a lattice".
614:, both of which were dedicated to the memory of Folkman.
469:; while hospitalized, Folkman was visited repeatedly by
652:
Folkman, J.; Lawrence, J. (1978), "Oriented matroids",
950:
Folkman, J. (1967), "Regular line-symmetric graphs",
199:
Equivariant Maps of
Spheres into the Classical Groups
897:. Boston, MA: Birkhäuser Boston, Inc. pp.
816:. Boston, MA: Birkhäuser Boston, Inc. pp.
764:. Boston, MA: Birkhäuser Boston, Inc. pp.
889:Rota, Gian-Carlo; Kung, Joseph P. S., eds. (1986).
242:
Folkman–Lawrence topological representation theorem
152:
142:
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114:
79:
69:
50:
28:
21:
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332:of vertices contains an independent set of size (|
567:Transactions of the American Mathematical Society
1089:(2nd ed.), New York: John Wiley and Sons,
808:Folkman, Jon; Kung, Joseph P. S., eds. (1986).
415:G contains no complete subgraph on r vertices,
399:, the Rado–Folkman–Sanders theorem describes "
295:. He proved the existence, for every positive
8:
193:in 1960. He received his Ph.D. in 1964 from
531:. January 24, 1969. p. 20 – via
597:(1971), "Optimal ranking of tournaments",
18:
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465:In the late 1960s, Folkman suffered from
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217:with the fewest possible vertices, the
724:in remark 7.23 on page 211:
375:their results are used to explain why
328:is a finite graph such that every set
383:, despite individual nonconvexities.
7:
1256:20th-century American mathematicians
793:Journal of Mathematics and Mechanics
434:F(3, 3; 5) < 18 (Martin Erickson)
309:-free graph which has a monocolored
983:SIAM Journal on Applied Mathematics
88:Shapley–Folkman lemma & theorem
810:"The homology groups of a lattice"
795:. Vol. 15. pp. 631–636.
14:
1281:Suicides by firearm in California
580:10.1090/S0002-9947-1971-0284352-8
365:Shapley–Folkman lemma and theorem
340:)/2 then the chromatic number of
1155:(1). Informa UK Limited: 63–67.
756:Kung, Joseph P. S., ed. (1986).
538:
953:Journal of Combinatorial Theory
895:A Source book in matroid theory
814:A Source book in matroid theory
762:A Source book in matroid theory
655:Journal of Combinatorial Theory
92:Folkman–Lawrence representation
1161:10.1080/10586458.2008.10129023
700:. Cambridge University Press.
561:(1971), "Ramsey's theorem for
1:
967:10.1016/S0021-9800(67)80069-3
640:Mathematics Genealogy Project
407:The Folkman Number F(p, q; r)
371:are approximately convex; in
367:: Their results suggest that
669:10.1016/0095-8956(78)90039-4
324:. He further proved that if
287:, he was the first to study
1261:Princeton University alumni
552:Birth and death dates from
528:The Ogden Standard-Examiner
1297:
1241:Additive combinatorialists
624:Putnam competition results
377:economies with many agents
355:, Folkman worked with his
248:theory, Folkman solved an
177:, and a researcher at the
164:
125:
1271:Mathematicians from Utah
1149:Experimental Mathematics
446:Brain cancer and despair
1276:People from Ogden, Utah
1246:RAND Corporation people
1113:Journal of Graph Theory
727:Ziegler, Günter M.
234:geometric combinatorics
62:Los Angeles, California
1126:10.1002/jgt.3190170604
722:Günter M. Ziegler
611:10.1002/net.3230010204
462:
437:F(2, 3; 4) < 1000 (
388:additive combinatorics
373:mathematical economics
252:on the foundations of
222:
213:Jon Folkman found the
16:American mathematician
1194:, Hyperion, pp.
1120:(6). Wiley: 679–681.
731:Lectures on Polytopes
486:Delbert Ray Fulkerson
459:mathematical problems
453:
289:semi-symmetric graphs
240:; in particular, the
212:
270:"geometric lattices"
215:semi-symmetric graph
195:Princeton University
74:Princeton University
686:Las Vergnas, Michel
1077:; Rothschild, B.;
907:10.1007/BF00531932
865:10.1007/BF00531932
565:-parameter sets",
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223:
1266:Lattice theorists
1205:978-0-7868-6362-4
707:978-0-521-77750-6
698:Oriented Matroids
684:Björner, Anders;
559:Rothschild, B. L.
430:Some results are
401:partition regular
392:Folkman's theorem
379:have approximate
238:oriented matroids
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127:Scientific career
96:Folkman's theorem
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272:in terms of the
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154:Doctoral advisor
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54:January 23, 1969
39:December 8, 1938
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266:homology groups
262:Gian–Carlo Rota
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277:Abelian groups
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189:Folkman was a
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363:to prove the
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361:Lloyd Shapley
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322:András Hajnal
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293:Folkman graph
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256:by proving a
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254:combinatorics
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227:combinatorics
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219:Folkman graph
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1030:Econometrica
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523:"Obituaries"
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510:FamilySearch
508:
500:
483:
467:brain cancer
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439:Vojtěch Rödl
429:
410:
385:
369:sums of sets
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285:graph theory
250:open problem
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170:
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143:Institutions
126:
56:(1969-01-23)
1236:1969 deaths
1226:1938 births
1072:Page 81 in
592:, and from
573:: 257–292,
344:is at most
281:finite rank
175:John Milnor
159:John Milnor
98:(memorial)
43:Ogden, Utah
1220:Categories
1075:Graham, R.
743:. (paper).
492:References
479:confidence
475:Paul Erdős
455:Paul Erdős
422:or a red K
381:equilibria
359:colleague
318:Paul Erdős
258:conjecture
35:1938-12-08
1169:1058-6458
1134:0364-9024
1038:CiteSeerX
989:: 19–24,
933:121334025
882:121334025
426:subgraph.
185:Schooling
1188:(1998),
1081:(1990),
846:(1964).
729:(1995).
696:(1999).
599:Networks
403:" sets.
205:Research
109:matroids
105:lattices
101:Homology
1196:109–110
1060:1909201
1003:0268080
925:0174487
899:213–242
874:0174487
836:0188116
818:243–248
801:0188116
784:0890330
766:201–202
638:at the
589:1996010
246:lattice
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799:
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737:
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587:
283:. In
133:Fields
121:(1960)
115:Awards
1056:JSTOR
929:S2CID
878:S2CID
585:JSTOR
1200:ISBN
1165:ISSN
1130:ISSN
1091:ISBN
911:ISBN
822:ISBN
770:ISBN
735:ISBN
702:ISBN
473:and
357:RAND
320:and
274:free
107:and
64:, US
51:Died
45:, US
29:Born
1157:doi
1122:doi
1048:doi
991:doi
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860:doi
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