Bar-Ilan Combinatorics Seminar The first meeting of the seminar in Semester B will take place, IYH, (when) Sunday, 10 Adar (March 4), 14:00-15:30 (where) Room 201 (Math & CS Seminar Room), Building 216, Bar-Ilan University (who) Zur Luria (Hebrew University) (what) Upper bounds on the number of Steiner triple systems and 1-factorizations Abstract: A 1-factorization of the complete graph Kn is a partition of its edges into n-1 perfect matchings. A Steiner triple system on [n] = {1,...,n} is a collection T of triples such that each pair in [n] is contained in a unique triple. We will discuss the connections between these (and other) objects, and present previously known bounds on their number. We'll prove that the number of 1-factorizations of Kn is at most ((1+o(1)) n/e^2)^(n^2/2) and that the number of Steiner triple systems on [n] is at most ((1+o(1)) n/e^2)^(n^2/6). The proofs make use of information entropy. Joint work with Nati Linial. ************************************************************************* 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>