23 citations · 63 across the 15 of their papers we have counts for
6 papers · 1 filter
The local dynamical structure of sets via a new Furstenberg family algebra
Angelina Blahodatna, Lauren Detmold, Daniel Glasscock +1
In this paper, we strengthen the connection between the combinatorics of difference sets and the dynamics of group rotations. Our main result shows that sets which have non-empty i…
A combinatorial proof of a sumset conjecture of Furstenberg
Daniel Glasscock, Joel Moreira, Florian K. Richter
We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if is irrational and and are -…
Shift equivalence in the generalized factor order
Jennifer Fidler, Daniel Glasscock, Brian Miceli +2
We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equiva…
What is a graphon?
Daniel Glasscock
Graphons, short for graph functions, are limiting objects for sequences of large, finite graphs with respect to the so-called cut metric. In this expository piece, we define grapho…
Multiplicative richness of additively large sets in
Vitaly Bergelson, Daniel Glasscock
In their proof of the IP Szemerédi theorem, a far reaching extension of the classic theorem of Szemerédi on arithmetic progressions, Furstenberg and Katznelson introduced an import…
On the interplay between notions of additive and multiplicative largeness and its combinatorial applications
Vitaly Bergelson, Daniel Glasscock
Many natural notions of additive and multiplicative largeness arise from results in Ramsey theory. In this paper, we explain the relationships between these notions for subsets of…