9 citations · 9 across the 1 of their papers we have counts for
5 papers · 1 filter
Growth in Some Finite Three-Dimensional Matrix Groups
Brendan Murphy, James Wheeler
We study the growth of product sets in some finite three-dimensional matrix groups. In particular, we prove two results about the group of upper triangular matrices ove…
Bisector energy and pinned distances in positive characteristic
Brendan Murphy, Misha Rudnev, Sophie Stevens
We prove a new lower bound for the number of pinned distances over finite fields: if is a sufficiently small subset of , then there is an element in that de…
Group Action Combinatorics
Brendan Murphy
This paper generalizes the basic notions of additive and multiplicative combinatorics to the setting of group actions: if is a group acting on a set , and we have subsets $A…
An example related to the Erdos-Falconer question over arbitrary finite fields
Brendan Murphy, Giorgis Petridis
There exists an infinite family of examples of subsets of with elements whose distance sets are not the whole of .
On the few products, many sums problem
Brendan Murphy, Misha Rudnev, Ilya D. Shkredov +1
We prove new results on additive properties of finite sets with small multiplicative doubling in the category of real/complex sets as well as multiplicative sub…