Jacob E. Goodman
Jacob Eli Goodman (born November 15, 1933) is an American geometer who has spent most of his career at the City College of New York, where he is now professor emeritus. In 1986 he and Richard Pollack were the founding co-editors-in-chief of the journal Discrete and Computational Geometry.
Jacob E. Goodman
|Alma mater||New York University |
|Known for||Open affine subsets of algebraic varieties|
Allowable sequences and wiring diagrams
Geometric transversal theory
Discrete and Computational Geometry
Handbook of Discrete and Computational Geometry
New York Composers Circle
|Awards||Lester R. Ford Award (Mathematical Association of America, 1990)|
|Institutions||City College of New York|
|Doctoral advisor||Heisuke Hironaka|
Together, he and Pollack (his long-term collaborator) introduced concepts such as "allowable sequences of permutations" and "wiring diagrams", which have played an important role in discrete geometry, specifically in the study of arrangements of pseudolines and (more generally) oriented matroids. His work with Pollack includes such results as the first nontrivial bounds on the number of order types of polytopes, and a generalization of the Hadwiger transversal theorem to higher dimensions. In addition to the work above, Goodman is also known as the originator of the "pancake problem", an elementary question on permutations which he published under the pseudonym Harry Dweighter (sounds like "harried waiter"), and which gave rise to the concept of pancake sorting, which turns out to play a role in DNA rearrangements in molecular biology.
- Dweighter, Harry; Garey, Michael R.; Johnson, David S.; Lin, Shen (1977), "Solutions of Elementary Problem E2569", Amer. Math. Monthly, 84: 296, doi:10.2307/2318878, JSTOR 2318878.
- Goodman, Jacob E. (1980), "Proof of a conjecture of Burr, Grünbaum, and Sloane", Discrete Math., 32: 27–35, doi:10.1016/0012-365x(80)90096-5.
- Goodman, Jacob E.; Pollack, Richard (1983), "Multidimensional sorting", SIAM J. Comput., 12 (3): 484–507, doi:10.1137/0212032.
- Goodman, Jacob E.; Pollack, Richard (1984), "Semispaces of configurations, cell complexes of arrangements", Journal of Combinatorial Theory, Series A, 37 (3): 257–293, doi:10.1016/0097-3165(84)90050-5.
- Goodman, Jacob E.; Pollack, Richard (1995), "Foundations of a theory of convexity on affine Grassmann manifolds", Mathematika, 42 (2): 305–328, doi:10.1112/s0025579300014613.
- Goodman, Jacob E.; Pollack, Richard; Sturmfels, Bernd (1990), "The intrinsic spread of a configuration in R^d", J. Amer. Math. Soc., 3: 639–651, doi:10.1090/s0894-0347-1990-1046181-2
- Cappell, Sylvain; Goodman, Jacob E.; Pach, János; Pollack, Richard; Sharir, Micha; Wenger, Rephael (1994), "Common tangents and common transversals", Advances in Mathematics, 106 (2): 198–215, doi:10.1006/aima.1994.1056.
- Goodman, Jacob E.; Pach, János; Pollack, Richard, eds. (2008), Surveys on Discrete and Computational Geometry: Twenty Years Later, Contemporary Mathematics, 453, Amer. Math. Soc..
- Jacob Eli Goodman at the Mathematics Genealogy Project
- "Discrete & Computational Geometry".
- Bjorner, Anders; Las Vergnas, Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter M. (1999), Oriented Matroids, 2nd Ed., Encyclopedia of Mathematics and its Applications, 46, Cambridge University Press
- Goodman, Jacob E.; Pollack, Richard (1986), "There are asymptotically far fewer polytopes than we thought", Bull. Amer. Math. Soc., 46: 127–129, doi:10.1090/s0273-0979-1986-15415-7
- Goodman, Jacob E.; Pollack, Richard (1988), "Hadwiger's transversal theorem in higher dimensions", J. Amer. Math. Soc. (1): 301–309
- Dweighter, Harry (1975), "Elementary Problem E2569", Amer. Math. Monthly, 82: 1010, doi:10.2307/2318260, JSTOR 2318260
- "Pancake Sorting".
- Goodman, Jacob E.; O'Rourke, Joseph (2004), Handbook of Discrete and Computational Geometry, Encyclopedia of Mathematics and its Applications, 2nd Ed., 46, CRC Press
- "About NYCC".
- List of Fellows of the American Mathematical Society, retrieved 2013-01-19.