50 citations · 353 across the 37 of their papers we have counts for
5 papers · 1 filter
On the dimension of additive sets
P. Candela, H. A. Helfgott
We study the relations between several notions of dimension for an additive set, some of which are well-known and some of which are more recent, appearing for instance in work of S…
On growth in an abstract plane
Nick Gill, H. A. Helfgott, Misha Rudnev
There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over or , geometric statements on growth often…
An explicit incidence theorem in F_p
Harald Andres Helfgott, Misha Rudnev
Let , a prime. Assume that has elements, . See as a set of points in the plane over $\mathbb…
Edge Effects on Local Statistics in Lattice Dimers: A Study of the Aztec Diamond (Finite Case)
Harald Helfgott
We compute the probability of any local pattern at an arbitrary position in a random dimer configuration in a square grid with an Aztec-diamond boundary.
Enumeration of tilings of diamonds and hexagons with defects
Harald Helfgott, Ira M. Gessel
We show how to count tilings of Aztec diamonds and hexagons with defects using determinants. In several cases these determinants can be evaluated in closed form. In particular, we…