10 papers · 1 filter
Iterated sumset expansion in
Manik Dhar, Sammy Luo
Given a set , what conditions does one need to guarantee that iterated sumsets of the form expand quickly (say, within terms) to the…
At most 10 cylinders mutually touch: a Ramsey-theoretic approach
Travis Dillon, Junnosuke Koizumi, Sammy Luo
Littlewood asked for the maximum number of congruent infinite cylinders that can be arranged in so that every pair touches. We improve upon the proof of the seco…
Monochromatic components with many edges in random graphs
Hannah Fox, Sammy Luo
In an -coloring of edges of the complete graph on vertices, how many edges are there in the largest monochromatic connected component? A construction of Gyárfás shows that f…
On off-diagonal -Ramsey numbers
Sammy Luo, Zixuan Xu
A graph is -Ramsey if any red-blue coloring of its edges contains either a red copy of or a blue copy of . The size Ramsey number is the minimum numb…
Structure of tight (k,0)-stable graphs
Dingding Dong, Sammy Luo
We say that a graph G is -stable if removing vertices from it reduces its independence number by at most . We say that G is tight -stable if it is $(k…
A new shift operator-based polynomial method in additive combinatorics
Sammy Luo
We introduce a new form of the polynomial method based on what we call "shift operators," which we use to give efficient and intuitive new proofs of results previously shown using…