Open Problems Session
During the workshop Ramsey Theory Yesterday, Today and Tomorrow at Rutgers University on May 27-29, 2009, I offered a Problem Posing Session. All 30 participants of the workshop attended the session, and almost everyone came to the board and posed favorite open problems. The session was scheduled for an hour and lasted twice as long. I asked for problem submissions in writing for this volume. Below you will find all submitted problems (which is far from all the problems orally presented at the workshop). In addition, see many more open problems in the surveys of this volume. The survey by Ronald L. Graham and Eric Tressler, for one, consists entirely of open problems.
- V.Bergelson and A.Leibman. Polynomial extensions of van der Waerden’s and Szemerédi’s theorems. J. Am. Math. Soc.:725–753, 1996. http://www.math.ohio-state.edu/~vitaly/ or http://www.cs.umd.edu/~gasarch/vdw/vdw.html.Google Scholar
- V.Bergelson and A.Leibman. Set-polynomials and polynomial extension of the Hales–Jewett theorem. Ann. Math., 150:33–75, 1999. http://www.math.ohio-state.edu/~vitaly/ or http://www.cs.umd.edu/~gasarch/vdw/vdw.html.Google Scholar
- M.Walters. Combinatorial proofs of the polynomial van der Waerden theorem and the polynomial Hales–Jewett theorem. J. London Math. Soc., 61:1–12, 2000. http://jlms.oxfordjournals.org/cgi/reprint/61/1/1 or http://jlms.oxfordjournals.org/ or http://www.cs.umd.edu/~gasarch/vdw/vdw.html.Google Scholar