Mathematical Sciences Seminar - Erdös-Rademacher problems in discrete structures
When:
—
Venue:
Birkbeck Main Building, Malet Street
No booking required
What is the largest size of a structure without any forbidden configurations? If we can solve this classical problem in extremal combinatorics, we ask: given a fixed size larger than this value, how many forbidden configurations must a structure of this size contain? I will discuss two such problems:
-the number of k-cliques in an n-vertex e-edge graph;
-the number of additive k-tuples x_1 + ... + x_k = y in an a-sized subset of an abelian group G.
The first problem was initiated by Rademacher in the 40s and revisited by Erdös in the 50s; since then it has had a long and rich history. The second is a counting version of a theorem of Green and Ruzsa. The new results I will mention are joint work with subsets of Ostap Chervak, Hong Liu and Oleg Pikhurko.
Contact name:
Department of Economics, Mathematics and Statistics