Jon Folkman
| Jon Hal Folkman | |
|---|---|
| Born |
December 8, 1938 Ogden, Weber County, Utah |
| Died | January 23, 1969 (aged 30) |
| Residence | United States |
| Nationality | American |
| Fields | Combinatorics |
| Institutions | RAND Corporation |
| Alma mater | Princeton University |
| Doctoral advisor | John Milnor |
| Known for |
Folkman graph Shapley–Folkman lemma & theorem Folkman–Lawrence representation Folkman's theorem (memorial) Homology of lattices and matroids |
| Notable awards | Putnam Fellow (1960) |
Jon Hal Folkman (December 8, 1938 – January 23, 1969) was an American mathematician, a student of John Milnor, and a researcher at the RAND Corporation.
Folkman was a Putnam Fellow in 1960. He received his Ph.D. in 1964 from Princeton University, under the supervision of Milnor, with a thesis entitled Equivariant Maps of Spheres into the Classical Groups.
Jon Folkman contributed important theorems in many areas of combinatorics.
In geometric combinatorics, Folkman is known for his pioneering and posthumously-published studies of oriented matroids; in particular, the Folkman–Lawrence topological representation theorem is "one of the cornerstones of the theory of oriented matroids". In lattice theory, Folkman solved an open problem on the foundations of combinatorics by proving a conjecture of Gian–Carlo Rota; in proving Rota's conjecture, Folkman characterized the structure of the homology groups of "geometric lattices" in terms of the free Abelian groups of finite rank. In graph theory, he was the first to study semi-symmetric graphs, and he discovered the semi-symmetric graph with the fewest possible vertices, now known as the Folkman graph. He proved the existence, for every positive h, of a finite Kh + 1-free graph which has a monocolored Kh in every 2-coloring of the edges, settling a problem previously posed by Paul Erdős and András Hajnal. He further proved that if G is a finite graph such that every set S of vertices contains an independent set of size (|S| − k)/2 then the chromatic number of G is at most k + 2.
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