# Combinatorics Seminar

When: Sunday, March 20, 10am

Where: Schreiber 309

Speaker: David Conlon, Oxford

Title:
Finite reflection groups and graph norms

## Abstract:

Given a graph H and a symmetric function
f:[0,1]^{2}→ℝ,
define the absolute H-norm of f by

‖f‖_{H} := (∫
∏_{ij∈E(H)} |f(x_{i},x_{j})|
dμ^{|V(H)|})^{1/|E(H)|},

where μ is the Lebesgue measure on [0,1]. We say that H is
weakly
norming if the absolute H-norm is a norm on the vector space of
symmetric functions. Classical results show that weakly norming
graphs are necessarily bipartite. In the other direction, it is
known that even cycles, complete bipartite graphs and hypercubes
are all weakly norming. Using results from the theory of finite
reflection groups, we demonstrate that any graph which is
edge-transitive under the action of a certain natural family of
automorphisms is weakly norming. This result includes all
previous examples of weakly norming graphs and adds many more.
Joint work with Joonkyung Lee.

redesigned by barak soreq