Mathematical Sciences Seminar - Product-free sets in Groups
When:
—
Venue:
Birkbeck Main Building, Malet Street
No booking required
A set S of positive integers is sum-free if for all a,b in S a+b is not in S. It's easy to see that any finite sum-free set of positive integers is contained in a strictly larger sum-free set, so we tend to frame questions in terms of sum-free sets of {1,...,n}. For example, what is the maximum cardinality of a sum-free set of {1,...,n}? How many sum-free sets of {1,...,n} are there; can we categorize sum-free sets that are maximal not by cardinality but by inclusion, how small can such sets be, and so on. Such questions were generalised rst to cyclic groups, then abelian groups, and then to general groups, where we speak of `product-free sets'. In this talk I'll give an overview of what's known in the general groups case, before describing some recent work with Chimere Anabanti.
Contact name:
Department of Economics, Mathematics and Statistics