Bar-Ilan Combinatorics Seminar The next meeting of the seminar will take place, IYH, (when) Sunday, 24 Adar (March 18), 14:00-15:30 (where) Room 201 (Math & CS Seminar Room), Building 216, Bar-Ilan University (who) Gili Golan (Bar-Ilan University) (what) Hindman's coloring theorem in arbitrary semigroups Abstract: Hindman's Theorem asserts that, for each finite coloring of $\N$, there are distinct $a_1, a_2, \dots \in \N$ such that all sums $a_{i_1} + a_{i_2} + \dots + a_{i_m}$ ($m \ge 1$, $i_1 < i_2 < \dots < i_m$) have the same color. Shevrin's classification of semigroups and a proof of Hindman's Theorem, due to Galvin and Glazer, imply together that, for each infinite semigroup $S$, there are distinct $a_1, a_2, \dots \in S$ such that all but finitely many of the products $a_{i_1}a_{i_2}\cdots a_{i_m}$ ($m \ge 1$, $i_1 < i_2 < \dots < i_m$) have the same color. Using these methods, we characterize the semigroups $S$ such that, for each finite coloring of $S$, there is an infinite subsemigroup $T$ of $S$, such that all but finitely many members of $T$ have the same color. Simple proofs. No background is needed. Joint work with Boaz Tsaban. ************************************************************************* You are all invited! Graduate students are especially welcome. Seminar organizer: Ron Adin <radin@math.biu.ac.il> Seminar's homepage: <http://www.math.biu.ac.il/~radin/comsem/comsem.html> ************************************************************************* --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Adin <radin@math.biu.ac.il>