32 citations · 67 across the 11 of their papers we have counts for
15 papers
Uniform distribution of saddle connection lengths in all orbits
Donald Robertson, Benjamin Dozier
For every flat surface, almost every flat surface in its orbit has the following property: the sequence of its saddle connection lengths in non-decreasi…
A proof of Erdős's conjecture
Bryna Kra, Joel Moreira, Florian K. Richter +1
We show that every set of natural numbers with positive upper density can be shifted to contain the restricted sumset …
Infinite Sumsets in Sets with Positive Density
Bryna Kra, Joel Moreira, Florian K. Richter +1
Motivated by questions asked by Erdos, we prove that any set with positive upper density contains, for any , a sumset , where…
Determinantal formulas with major indices
Thomas McConville, Donald Robertson, Clifford Smyth
We give a simple proof of a major index determinant formula in the symmetric group discovered by Krattenthaler and first proved by Thibon using noncommutative symmetric functions.…
Unique equilibrium states for some intermediate beta transformations
Leonard Carapezza, Marco López, Donald Robertson
We prove uniqueness of equilibrium states for subshifts corresponding to intermediate beta transformations with having the property that the orbit of 0 is bounded away from…
Uniform distribution of saddle connection lengths
Jon Chaika, Donald Robertson
For almost every flat surface the sequence of saddle connection lengths listed in increasing order is uniformly distributed mod one.
A proof of a sumset conjecture of Erdős
Joel Moreira, Florian Karl Richter, Donald Robertson
In this paper we show that every set with positive density contains for some pair of infinite subsets of , settling a conjecture of E…
Ergodicity of skew products over linearly recurrent IETs
Jon Chaika, Donald Robertson
We prove that the skew product over a linearly recurrent interval exchange transformation defined by almost any real-valued, mean-zero linear combination of characteristic function…
Disjointness for measurably distal group actions and applications
Joel Moreira, Florian K. Richter, Donald Robertson
We generalize Berg's notion of quasi-disjointness to actions of countable groups and prove that every measurably distal system is quasi-disjoint from every measure preserving syste…
Mild mixing of certain interval exchange transformations
Donald Robertson
We prove that irreducible, linearly recurrent, type W interval exchange transformations are always mild mixing. For every irreducible permutation the set of linearly recurrent inte…
Triangles in cartesian squares of quasirandom groups
Vitaly Bergelson, Donald Robertson, Pavel Zorin-Kranich
We prove that triangular configurations are plentiful in large subsets of cartesian squares of finite quasirandom groups from classes having the quasirandom ultraproduct property,…
Polynomial multiple recurrence over rings of integers
Vitaly Bergelson, Donald Robertson
We generalize the polynomial Szemerédi theorem to intersective polynomials over the ring of integers of an algebraic number field, by which we mean polynomials having a common root…
Polynomial recurrence with large intersection over countable fields
Vitaly Bergelson, Donald Robertson
We give a short proof of polynomial recurrence with large intersection for additive actions of finite-dimensional vector spaces over countable fields on probability spaces, improvi…
Finite Products Sets and Minimally Almost Periodic Groups
Vitaly Bergelson, Cory Christopherson, Donald Robertson +1
We construct, in locally compact, second countable, amenable groups, sets with large density that fail to have certain combinatorial properties. For the property of being a shift o…
Characteristic factors for commuting actions of amenable groups
Donald Robertson
We describe characteristic factors for certain averages arising from commuting actions of locally compact, second-countable, amenable groups. Under some ergodicity assumptions we u…